One study found 13.5% of baseball players threw left-handed while 30.3% batted with a left-sided preference.3 The overall percentage of left-handedness for men in the general population is just 11.6%.4 Left-handed throwing fielders who batted with a left-sided preference were found to hit more home runs, had higher slugging percentages, but also had more strikeouts than did right-handed throwing fielders who batted with a left-sided preference.5 The study’s authors theorized that performance differences were due to hand dominance or hand specialization in the batters’ swings.

In contrast, John Walsh proposed in The Hardball Times that performance differences in baseball based on throwing hand are largely due to positional bias.6 Right-handed fielders dominate four positions in baseball: catcher, second base, shortstop, and third base. This positional bias exists because these positions favor a right-handed thrower. The other positions in baseball, which include first base and the outfield positions, do not favor a player by throwing hand. Therefore, according to Walsh, weak-hitting players who throw right-handed but are exceptional defenders have opportunities to play positions that weak-hitting left-handed throwers are not afforded. As a result of positional bias, the overabundance of weak-hitting right-handed throwers may skew performance data and, as a result, make it appear that left-sided batters perform better overall than right-sided batters.

We can see this positional bias demonstrated in the records of the National Baseball Hall of Fame. Only eight players admitted to Cooperstown threw left, batted left, and played catcher, second base, shortstop, or third base. For all eight of these players, first base or outfield were their primary positions. The most recent player in that list, Lou Gehrig, was only listed at shortstop for one game in 1934 to keep his consecutive-games-played record intact and was removed before ever taking the field.7 Prior to Gehrig, left-hander Jim Bottomley, a career first baseman, appeared in one game at second base in 1924.8 That appearance lasted only one inning.9

Examining the handedness of position players in the Hall of Fame supports Walsh’s finding that positional bias, rather than intrinsic abilities associated with handedness, is largely responsible for the observed differences between right-handed and left-handed players.

JON C. NACHTIGAL, PhD, is an assistant softball coach at Purdue University Fort Wayne. He received a doctorate in sport administration from the University of New Mexico and has taught sport management at Simpson College and New Mexico. He publishes softball research at FastpitchAnalytics.com.

JOHN C. BARNES, PhD, is an associate professor in the sports administration program at the University of New Mexico. His book, Same Players, Different Game: An Examination of the Commercial College Athletics Industry, will be available in 2020. He holds a Bachelor of Science degree in physical education from California State Polytechnic University, Pomona; a Master of Science degree in kinesiology from University of Nevada, Las Vegas; and a PhD in sports administration from the University of New Mexico.

Notes

1. Bradbury, John Charles, and Douglas J. Drinen. “Pigou at the Plate.” Journal of Sports Economics 9, no. 2 (September 2007): 211–24.

2. Nawrocki, Tom. “Captain Anson’s Platoon.” The National Pastime, no. 15 (1995): 34–37.

3. Grondin, Simon, Yves Guiard, Richard B. Ivry, and Stan Koren. “Manual Laterality and Hitting Performance in Major League Baseball.” Journal of Experimental Psychology: Human Perception and Performance 25, no. 3 (1999): 747–54.

4. McManus, Chris. Right Hand, Left Hand: The Origins of Asymmetry in Brains, Bodies, Atoms and Cultures. London: Phoenix, 2004.

5. Grondin, et.al. “Manual Laterality.”

6. Walsh, John. “The Advantage of Batting Left-Handed.” The Hardball Times, November 7, 2007. https://www.fangraphs.com/tht/the-advantage-of-batting-left-handed.

7. “Biography—The Official Licensing Website of Lou Gehrig.” Lou Gehrig. Accessed August 25, 2019. https://www.lougehrig.com/biography.

8. “Jim Bottomley Stats” Baseball-Reference. Accessed November 23, 2018. https://www.baseballreference.com/players/b/bottoji01.shtml.

9. The 1924 STL N Regular Season Fielding Log for Jim Bottomley. Retrosheet. Accessed September 9, 2019. https://www.retrosheet.org/boxesetc/1924/Mbottj1010031924.htm.

10. All player stats from Baseball-Reference.com.

Table 1: Appearances for left-sided batters and throwers in the Hall of Fame who played Catcher/Second Base/Shortstop/Third Base

Note: All statistics are from Baseball-Reference.com.

Much of the focus given to the shift falls into two categories. The first is a debate between whether the shift is good or bad for baseball. Sportswriters, players, and broadcasters have voiced their displeasure over how the shift has taken away from “the way the game should be played.”3, 4, 5 Commissioner Rob Manfred even considered banning the shift in 2015.6 The second category consists of various analyses, both defensively and offensively, attempting to pinpoint the effectiveness of the shift, to assess whether or not it “works” based on various statistics and metrics.7, 8

This paper falls into the second category but will focus more on hitters’ and pitchers’ approaches to dealing with the shift, rather than merely the outcomes of the shift. It is easy to say that hitters could just bunt or hit to the opposite field when shifted on, but an in-depth overview of shift outcomes based on hard data would be a welcome addition to the discussion. To help fill this void, this paper will present an overview of shift batted-ball events from the beginning of the 2017 season through the first half of the 2018 season. Further, it will identify patterns in the data regarding both hitters’ and pitchers’ approaches to the shift. Finally, conclusions will be drawn in an attempt to explain why shift outcomes occurred as they did and to identify further topics of analysis. Understanding how players approach the shift in addition to understanding the tactic itself will offer insight into its effectiveness.

Data Overview/Methods

The data for this article were scraped from MLB’s BaseballSavant.com using RStudio codes and packages based on Bill Petti’s BaseballR.9

Specifically, the raw data comprised complete game events from every game of the 2017 season through the first half of the 2018 season where an infield shift was on. Events are play outcomes, either batted balls, strikeouts, walks, or baserunning plays such as steals.

The raw data were then loaded into Microsoft Power BI to filter the data and create interactive charts and graphs for further analysis. The data were first filtered on Baseball Savant’s IF Alignment measure. This measure is broken down into three options:10

• standard — no shift
• shift — three infielders on one side of the infield (“traditional shift”)
• strategic — a catch-all for plays in which the infield was neither standard nor traditionally shifted

This article uses only events featuring the traditional shift. The filtered dataset contained approximately 37,000 batted-ball events.

The data were then broken down by batter handedness as well as pitch locations of left-hand side of the plate, middle of the plate, and right-hand side of the plate. Pitch locations were labeled by aggregating Baseball Savant’s Gameday zones. Various tables and graphs were then created for left-handed and right-handed batters to compare how shift performance differed in batter handedness and to compare if pitchers approached hitter handedness differently in shift situations.

Results

General

Of the approximately 37,000 events in the data, 27,117 occurred against left-handed batters (referred to as lefties from here on) and 9,928 occurred against right-handed batters (referred to as righties from here on). Teams shifted about three times as often against lefties than righties. Righties hit significantly better than lefties against the shift, both in terms of batting average (.259 vs .232) and slugging average (.477 vs .429).

The differences in shift events and righties’ relative success hitting against the shift compared to lefties could be explained a few ways. First, righties may just be better hitters than lefties. Second and seemingly more likely is that the physical differences in the shift benefit righties over lefties. A shift against lefties brings the shortstop closer to first base and doesn’t significantly alter the second baseman’s distance. A shift against righties draws both the second baseman and shortstop further away from first base, so even if a righty does put the ball in play into the shift, they have a better chance of getting a hit due to the increased difficulty of the throw to get an out.

In terms of pitch location, both lefties (.246 vs .197) and righties (.264 vs .242) had higher batting averages on pitches thrown down the middle or on the inside part of the plate compared to pitches thrown to the outside of the plate. However, pitchers pitched into the shift more often than not, regardless of batter stance (see Chart 1).

(Click image to enlarge)

Given that most of the opposite side of the infield is open when the shift is on, it may make sense intuitively for pitchers to pitch into the shift, but these data show that hitters were more successful on balls in play on middle/in pitch locations.

Approach to Hitting Against the Shift

Tables 1 and 2 show the outcomes of batted-ball events for lefties on middle/in and outside pitches, respectively.

(Click images to enlarge)

Given the imprecise reporting of batted-ball location in shifted infield positions (it is unclear where exactly the shortstop was positioned in the shift for a lefty or where the second baseman was positioned for a righty), I will only consider batted-balls to positions where the fielder’s location is more clearly known. An important caveat to this is that third basemen will sometimes move into shallow right field when shifting against lefties, while the shortstop will move to the left side of the infield.11

As noted above, a limitation of this article is the imprecise reporting of infielder positioning on batted-balls. As such, I will treat the third baseman’s position as “known” (where the shortstop would typically play in a non-shift situation) for lefty batted-balls. Of 19,434 batted balls on middle/in pitches, lefties hit to both sides of the field fairly evenly (35.60% of balls hit to first base, second base, right field; 27.35% hit to third base, left field). On the other hand, of 7,682 batted balls on outside pitches, lefties pulled the ball much more frequently than hitting to the opposite field (50.14% of balls hit to first base, second base, right field; 17.67% hit to third base, left field). Lefties’ batted-balls resulted in outs or errors 67.75% of the time on middle/in pitches and 69.32% of the time on outside pitches.

Breaking down lefties’ batted balls further, Table 5 shows the batted-ball locations of extra-base hits on middle/in and outside pitches.

(Click image to enlarge)

Of the 2,713 extra-base hits that occurred with the shift on for lefties, 2,056 came on middle/in pitches and 657 came on outside pitches. Of the extra-base hits on middle/in pitches, 28.65% of them were hit to right field and 23.88% to left field. Of the extra-base hits on outside pitches, 63.01% of them were hit to right field while only 6.39% were hit to left field. In sum, lefties pulled the ball significantly more often than hitting to the opposite field on outside pitches and hit to both fields on middle/in pitches. Lefties hit for power by pulling the ball on outside pitches and were able to go to both fields for power on middle/in pitches.

Righties’ batted-ball tendencies mirrored lefties’ in many ways. Tables 3 and 4 show the outcomes of batted-ball events for righties on middle/in and outside pitches, respectively.

(Click images to enlarge)

Of 7,174 batted balls on middle/in pitches, righties pulled the ball about twice as often as going to the opposite field (41.80% of balls hit to third base, shortstop, left field; 23.40%% hit to first base, right field). Of 2,754 batted balls on outside pitches, righties pulled the ball much more frequently than hitting to the opposite field (56.31% of balls hit to third base, shortstop, left field; 16.93% hit to first base, right field). Righties’ batted-balls resulted in outs or errors 66.59% of the time on middle/in pitches and 67.90% of the time on outside pitches.

Table 6 shows the batted-ball locations of extra-base hits on middle/in and outside pitches.

(Click image to enlarge)

Of the 1,084 extra-base hits that occurred with the shift on for righties, 784 came on middle/in pitches and 300 came on outside pitches. Of the extra-base hits on middle/in pitches, 44.77% of them were hit to left field while just 18.11% were hit to left field. Even more lopsided, of the extra-base hits on outside pitches, 79.33% of them were hit to left field while a mere 4% were hit to right field. Like lefties, righties hit to both fields on middle/in pitches and pulled the ball significantly more than hitting to the opposite field on outside pitches. Unlike lefties, righties hit for power mostly by pulling the ball, regardless of pitch location.

Takeaways and Explanations

After reviewing a season-and-a-half’s worth of batted-ball shift events at a deep descriptive level, several patterns emerged. First, all hitters performed better on middle/in pitches with the shift on in terms of batting average, slugging average, and avoiding getting out. More often than not, however, pitchers threw to that side of the plate. Further, hitters pulled the ball significantly more than hitting to the opposite field on outside pitches and hit to both fields somewhat evenly on middle/in pitches. Finally, lefties found success in hitting for power on outside pitches by pulling the ball and generated power to both fields on middle/in pitches. Righties, conversely, mostly generated power in the shift by pulling the ball, regardless of pitch location.

These tendencies present evidence that is counterintuitive to how one would think to approach the shift, but there may be some explanation behind how hitters and pitchers have approached it. There are several plausible explanations regarding hit location versus pitch location. First, hitters may be taking middle/in pitches to the opposite field because they are getting jammed or are slightly late on those pitches. Pitchers’ average velocity has increased over the years.12

Consequently, hitters have less time to react and are more likely to swing late. Another explanation could be that hitters are just more comfortable controlling pitches on the inner half of the plate off of their bats. The data from this project indicate that all hitters had higher batting averages, greater number of extra-base hits, and a relatively equal amount of hits to both fields on middle/in pitches. Perhaps hitters can handle middle/in pitches better, and can therefore actually better-strategically execute hitting the ball away from the shift on those pitches.

Two explanations arise to address batted-ball outcomes of outside pitches. First, hitters may have more trouble handling outside pitches compared to middle/in pitches; perhaps hitters are just not as successful at executing on outside pitches, especially in situations in which they are attempting to bunt for a hit.13

What seems more likely, however, is that hitters are set on hitting over the shift to beat it. Hitters have become increasingly more strategic and calculated in terms of valuing how and where they hit the ball. The mass quantities of data that are now available have enabled coaching staffs and players to better analyze game outcomes based on attributes of their swings. A clear example of this is the prevalence of players who have increased their launch angles to hit over the shift, a phenomenon known as the Flyball Revolution.14 A cost-benefit analysis occurs for the hitter: what is more valuable to the team, a “free” single to the opposite field or a double or home run hit into or over the shift?15 The overwhelming number of pulled balls on outside pitches suggest that hitters may be making a conscious effort to not hit with the pitch.

Understanding pitchers’ approaches to the shift is more straightforward than understanding hitters’ approaches. Pitchers were pitching into the shift because it logically makes sense; if three of your infielders are gathered on one side, why not attempt to get the hitter to hit the ball to that side by pitching the ball to that side of the plate? However, based on the data presented and the above discussions on hitters’ approaches to hitting against the shift, it actually seems detrimental for pitchers to pitch into the shift. Hitters perform better on middle/in pitches overall and are rarely hitting the ball to the open opposite field on outside pitches. Until hitters can make the mental or physical adjustments to make the pitcher pay for pitching to the open side of the field, pitchers should attack the outside part of the plate when the shift is on. While it may be a mental hurdle in itself for pitchers to throw to the exposed side of the field, the data show that they would be more successful doing so.

Next Steps

This article provides an in-depth dive into batted-ball shift outcomes and offers insight into both hitters’ and pitchers’ approaches to handling the shift, but it is just the beginning in terms of understanding the shift and how players perform in it. There are several avenues of study that could follow this article.

The first could be a comparison of how hitters and pitchers perform in non-shift situations versus shift situations. While it is not necessary to identify patterns in shift situations, comparing non-shift outcomes could shed light onto how hitters and pitchers think about the shift and how they may attempt to adjust their approach (or not) to be successful. Such a comparison would also be useful at a single-player level to identify players who are relatively more successful in shift situations. This would allow for a more granular study analyzing the effectiveness of the shift.

The second could be the addition of non-batted-ball outcomes to analysis similar to that in this article. Identifying tendencies in batted-ball outcomes only provides a partial understanding of hitters’ and pitchers’ approach to the shift as a whole. Russell Carleton presented analyses on shift expected outcomes at Baseball Prospectus and found that, while the shift decreased the number of singles pitchers allowed, it increased walks to a greater extent. Pitchers felt uncomfortable pitching with the shift on and, therefore, ended up pitching less effectively.16 Analyses such as these provide key insights into players’ approaches to the shift that batted-ball outcomes alone cannot.

CONNELLY DOAN, MA, is a Data Analyst in the San Francisco Bay Area who has applied his professional skills to the game of baseball, both personally and for RotoBaller.com. He has been a SABR member since 2018. He can be reached on Twitter (@ConnellyDoan) and through email (doanco01@gmail.com).

Notes

1 Neil Paine, “Why Baseball Revived a 60-Year-Old Strategy Designed to Stop Ted Williams,” FiveThirtyEight, October 13, 2016, https://fivethirtyeight.com/features/ahead-of-their-time-why-baseball-revived-a-60-year-old-strategy-designed-to-stop-ted-williams/.

2 Travis Sawchik, “We’ve Reached Peak Shift,” FanGraphs, November 9, 2017, https://www.fangraphs.com/blogs/weve-reached-peak-shift/.

3 Matt Snyder, “MLB Shifts Are Starting to Get More and More Excessive, so Are We Headed to a Bad Place Where Positions Don’t Matter?,” CBS Sports, May 17, 2018, https://www.cbssports.com/mlb/news/mlb-shifts-are-starting-to-get-more-and-more-excessive-so-are-we-headed-to-a-bad-place-where-positions-dont-matter/.

4 Alden Gonzalez, “How the Shift has Ruined Albert Pujols,” ESPN, August 7, 2018, http://www.espn.com/mlb/story/_/id/24270231/mlb-how-shift-ruined-albert-pujols.

5 Tom Hoffarth, “Sports Media: Hall of Famer John Smoltz Not Exactly What the Viewers This Time of Year are Looking for,” Los Angeles Times, October 15, 2018, https://www.latimes.com/sports/la-sp-sports-media-20181015-story.html.

6 Emma Baccellieri, “Proposing a Shift Ban is Easy, but How Would MLB Implement One?,” Sports Illustrated, July 25, 2018, https://www.si.com/mlb/2018/07/25/defensive-shifts-official-baseball-rules.

7 Russell A. Carleton, “Baseball Therapy: Why the Shift Persists,” Baseball Prospectus, January 3, 2018, https://www.baseballprospectus.com/news/article/36897/baseball-therapy-shift-persists/.

8 Russell A. Carleton, “Baseball Therapy: The Pretty Good Case That the Shift Doesn’t Work,” Baseball Prospectus, May 3, 2016, https://www.baseballprospectus.com/news/article/29085/baseball-therapy-the-pretty-good-case-that-the-shift-doesnt-work/.

9 “Baseballr: A Package for the R Programming Language,” baseballr, last modified May 29, 2018, http://billpetti.github.io/baseballr/.

10 “MLB Statcast Shifts,” MLB, accessed March 3, 2019, http://m.mlb.com/glossary/statcast/shifts.

11 Ben Lindbergh, “Overthinking It: Defining Positions in the Age of the Shift,” Baseball Prospectus, May 28, 2014, https://www.baseballprospectus.com/news/article/23705/overthinking-it-defining-positions-in-the-age-of-the-shift/; David Waldstein, “Who’s on Third? In Baseball’s Shifting Defenses, Maybe Nobody,” The New York Times, May 12, 2014, https://www.nytimes.com/2014/05/13/sports/baseball/whos-on-third-in-baseballs-shifting-defenses-maybe-nobody.html.

12 Anthony Castrovince, “Speed Trap: How Velocity has Changed Baseball,” MLB.com, April 2, 2016, https://www.mlb.com/news/increase-in-hard-throwers-is-changing-mlb/c-170046614.

13 Jon Weisman, “Why MLB players Don’t Bunt Against the Shift,” Dodger Thoughts, October 9, 2018. https://www.dodgerthoughts.com/2018/10/09/why-mlb-players-dont-bunt-against-the-shift/.

14 Dave Sheinin, “Why MLB Hitters Are Suddenly Obsessed With Launch Angles,” Washington Post, June 1, 2017, https://www.washingtonpost.com/graphics/sports/mlb-launch-angles-story/?utm_term=.79f08e1ac9a0.

15 Jerry Crasnick, “MLB Hitters Explain Why They Can’t Just Beat the Shift,” ESPN, July 10, 2018, http://www.espn.com/mlb/story/_/id/24049347/mlb-hitters-explain-why-just-beat-shift.

16 Russell A. Carleton, “Baseball Therapy: How to Beat the Shift”, Baseball Prospectus, May 22, 2018, https://www.baseballprospectus.com/news/article/40088/baseball-therapy-how-beat-shift/.

I started trying to relate batting to team wins back in the 1960s. I had determined that 10 extra runs over the course of a season resulted in one more win for the team. A slightly more accurate method would be to use 10 times the square root of runs per inning by both teams—a figure usually between 9 and 11. The standard deviation of the difference between expected and actual wins from 1960 through 2018 was 4.03 for the simple method and 3.97 for the advanced one. Compare that to the “Pythagorean” method (runs squared over the sum of runs squared and runs allowed squared) where it was 4.07. This could be slightly improved to 3.99 by using 1.83 for the exponent instead of 2. Both simple and advanced methods had the same number of wins for 1016 out of 1552 teams and were off by 2 or 3 for only 47 teams. Only one team since 1971 differed by more than 2 wins: the 1996 Tigers, who allowed 1103 runs. Ten runs per win gave them 53 wins while Pythagoras had 56. They actually won 53. The runs over ten method was easier to calculate than other methods and also easier to relate individual performance to team performance.

My next step was to derive team runs from player stats. We had no play-by-play data available in those days except for World Series games as published in the annual baseball guides, so I started there. I analyzed 34 games 1956–60. I calculated the probability of scoring from each base depending on the number of outs. Later, I ran a paper-and-pencil simulation, using the various advanced data I compiled from the Series data, such as first to third on a single, first to home on a double, taking a base on an out, etc. The simulation also gave me the number of times each base-out situation occurred, so I determined how the scoring probabilities increased for each batting event. For example, a walk to lead off the inning would increase the scoring probability for that batter from .16 to .39—an increase of .23. If there was a runner on first, that runner would go from .39 to .62 for a total of .46. A single would be the same except a runner on first would go to third 45 percent of the time and the increase would be .57. I then summed up each situation weight by its frequency to get an overall value. A single came out .37 runs.

However, when I tried to project the number of team runs from its batting statistics, I did not find as close relationship as I expected. Teams with high on base percentages would predict too low and vice-versa. I realized I was doing something wrong. A player can produce runs for his team three ways:

1) He can advance himself around the bases.

2) He can advance teammates around the bases.

3) He can cause other batters to get up by not making an out.

This third factor could never be measured by just using base advances. What I needed to calculate was the number of runs expected from each starting point through the end of the inning. These vary from year to year and league to league depending on the average batting. The expected number of runs to be scored from leadoff position is usually around .50, which is simply the league total of runs per inning. With play-by-play data for hundreds of thousands of regular season games now available through Retrosheet, we can do this easily for any season. Since I didn’t have those data then, I expanded my paper-and-pencil simulation to calculate the values. Under the revised values, when a walk led off the inning, the run potential went from .48 to .82—an increase of .34.

Each positive batting event has an average increase of about .50 runs, while a negative event is around minus .25. An average player with an OBA of .333 will therefore have a net value of zero. This can be higher or lower based on the distribution of walks and hits. A portion of that comes from allowing extra batters to come up. Each batter is worth about .16 runs with none out, .12 with one out, and .08 with two outs, for an average of .12. But there is also the possibility of more than one additional batter appearing. This is a converging infinite series of 1 + 1/3 + 1/9 + 1/27 etc… which sums to one and a half. So each time the batter gets on base, he adds 1.5 batters and when he goes out, he adds none, for an average of one half batter per appearance. Getting on base adds one batter and going out subtracts a half from the average. So of the .50 runs for a positive event, .12 is due to the extra batters and .38 is due to advances of the batters and other runners if any. That is the power of on base average (OBA).

It would still be a few more years before I would settle on the power of OPS, though. I made two mistakes in my original research. In the World Series data, there were only 5 cases of a runner on first when the batter doubled, and only one scored. So I used 20 percent for that. When more data became available, I found the real number was 40 percent, unless there were two outs when it was 60 percent. I did not consider intentional walks, since they had been first compiled in 1955. Worse, I made the bad assumption that walks occurred equally in all base-out situations. Actually walks—intentional or not—are more likely to occur in low value situations and less likely to occur in high value situations, thus the value of a walk was too high by about 10 percent. You can find a detailed study of intentional walks in the July 2017 edition of By the Numbers, the Statistical Analysis Committee bulletin. On average, intentional walks are worth about .15 runs.

However, you really have to look at the context of all walks, since good hitters are more apt to be walked in less favorable situations and also get more unintentional walks in intentional walk situations. Over the years the values were refined a bit, and by 1984 when John Thorn and I were writing The Hidden Game of Baseball, I had settled on .47 for a single, .83 for a double, 1.02 for a triple, 1.40 for a homer and .33 for a walk. The out factor was calculated to make the league total zero with pitcher batting subtracted and was usually around –.25. Thus an average player had a rating of zero. Subtracting pitcher batting puts the two leagues on an equal basis in the designated hitter era and also allows batters to be compared only with other non-pitchers for all years. Outs were defined as at bats minus hits. I called these linear weights. Although baseball is not linear, the values remain relatively constant over the range of environments found in normal play. High scoring years would result in the positive event values slightly higher and the out value slightly more negative. You can also calculate values for various other events. Most don’t have much influence on team stats. Stolen bases are more important for individuals. In the Deadball Era, everybody stole, but today they are more specialized. A few players may gain a fair number of runs from stealing. I used .22 for stolen bases and –.38 for caught stealing, although the impact on wins could be higher, since steals are more apt to occur in close games. The standard deviation in deriving team runs using the simple linear weight method is about 22 runs on the season. Adding steals and outs on base from caught stealing, double plays, and other items reduces the value to 20, which is about as low as you can get.

When correlating various measures to team runs, you can use runs per game, but a better method is to use runs per innings batted. Innings batted can vary based on extra innings games and games won, since a home team does not bat in the last of the ninth if ahead. In fact, you can deduce wins for the season with a standard deviation of about two if you use innings batted and innings pitched. This is half the value found by using runs scored and allowed. Wins equals games over two plus innings pitched minus innings batted.

W = Games/2 + IP – IB

It does not work for teams with an imbalance of home and away games like in the strike year of 1994, since the real difference uses home wins and road losses. Innings batted can be calculated easily if team left on base is known. LOB has been kept since 1920, although in the early years the official figures had a lot of errors. Retrosheet’s box score project, headed by Tom Ruane, now has accurate LOB calculated from team data back to 1906. Innings batted is equal to plate appearances minus runs minus left on base, all divided by three.

IB = (PA – R – LOB)/3

Thus you can estimate innings batted when LOB is not available by taking innings pitched minus one half of wins minus losses. The only unknown variable is the number of outs in games won or lost in the bottom of the last inning. Innings batted per game has a standard deviation of about one percent, which would be 14 innings per year, equivalent to about 7 runs.

But getting back to OPS. Soon after SABR was founded in 1971, Dick Cramer suggested a statistical analysis committee and I became the chairman. Dick recently published his autobiography titled When Big Data Was Small, which covered his work in baseball and science as well as his personal life. In it he mentions a paper written by his friend Paul Bamberg in 1959 for a science project. Unfortunately, Paul was ahead of his time and did not have help from people like Bob Davids, Bill James, John Thorn, or Gary Gillette to spread the word, so his work languished in obscurity until being included in Dick’s book in 2019. Others may have had the same problem of finding an outlet for their work. I was doing range factors in the 1960s and almost got an article on batting and pitching in The Sporting News in 1969, but they chickened out because they thought it was too complicated. George Lindsay published in Operations Research, but not many people noticed. Earnshaw Cook had to put out his own book and was then helped by Frank Deford, who noticed it and did a nice article in Sports Illustrated. Bill James also was aided when Dan Okrent did a piece there about his work.

At the time SABR’s publications concentrated on historical rather than analytical work, and the Statistical Analysis Committee did not yet publish its own bulletin.1 In 1973 Cramer contacted me about research he had done which showed that team runs were proportional to the product of on base percentage and slugging percentage. Dick created a simulation to measure this, entering individual batting data for Babe Ruth and others and calculating how many runs would score. I had reached a similar conclusion with my work with linear weights. I was looking at team runs as a function of their stats. We did a joint article in SABR’s Baseball Research Journal in 1974, coining the term Batter’s Run Average.

On base times slugging (OxS) exaggerates the individual player’s contribution when a team of nine identical players is used in the simulation. When I ran Ruth on the 1920 season, adding him to an average team added .79 runs per game while a team of nine Babes scored 14.11 runs per game—10.12 runs more than average or 1.12 runs per player per game, 44 percent higher, since he had the benefit of other Ruths on the team. Ruth’s on-base was 50% higher than the league and his slugging was double. The normalized formula for OxS is OBA/lg times SLG/lg, where lg is the league average. This would mean 3 times the number of runs. For NOPS (normalized OPS) the formula is OBA/lg plus SLG/lg minus 1, or 2.5, which is about what he had. So by 1978 I had converted to OPS, which has the advantage of being easy to calculate and relates individual performance directly to team wins.

In 1920, Ruth was 110 linear weight runs above average, but he was helped considerably by playing in the Polo Grounds. His OPS at home was an incredible 1.535. Anyone who thinks Ruth and Gehrig were helped by the short right field porch in Yankee Stadium is mistaken. Most players have an OPS at home about 5 percent better than on the road. Ruth’s career figure in Yankee Stadium was only 2 percent higher, while Gehrig was actually 2 percent worse at home.

It turns out that the normalized version of OPS is directly proportional to a batter’s the contribution to team wins. A player with a normalized OPS of 110 percent wil on average contribute 10 percent more runs than the average player. A player with an OBP and slugging each 10 percent higher than league average will have a normalized OPS that is 20 percent higher than average and will produce 20 percent more runs. Using raw OPS, 10 percent higher in each would mean the normalized version would also be 10 percent higher, which would also produce 20 percent more runs.

In OPS, a walk counts one for on-base and zero for slugging, while any hit counts one for on base and the number of bases for slugging. So counting both OBA and SLG, a single counts 2 and a homer 5. These are in about the same proportion as in linear weights. That is why OPS works almost as well.

Using an equation where OBP is multiplied by a factor (OBP times F plus SLG) gives a slightly more accurate correlation to actual team runs. However, the difference is very small. The standard deviation for the team runs projection per year for 1960–2018 is between 24.9 and 25.2 for any value of the multiplier between 1.4 and 2.4, but doing this complicates the calculation. Counting both equally is off by 26.4, only a little higher. Using OxS, you get a value of 25.4, a bit lower. If I had used 1.8 x OBP plus SLG, I don’t think OPS would have caught on so well. It is possible to adjust the OBP by adding stolen bases over two minus caught stealing minus grounded into double plays. This reduces the standard deviation by about half a run.

Using the normalized method helps reduce this error, since by dividing by the league average makes 33 points of OBA equivalent to about 42 points of slugging, a factor of 1.3. OBA and slugging are highly correlated, since each is very dependent on hits over at-bats, so the multiplying factor has little effect.

Taking an average player and adding ten at-bats reduces his OPS by about 12 points. Adding 10 walks raises it by 11 points, while 10 singles adds 22 points. Doubles, triples, and homers increase the value by 40, 59, and 77 points respectively. This shows a ratio of 1-2-3-5-7, a bit higher than the 1-2-3-4-5 factors for linear weights. Thus slugging is little heavier than it should be. Tom Tango addressed this problem in his wOBA calculation. He took the linear weight values for each event and created a pseudo OBA. The result looks very much like linear weight runs per appearance plus league average OBA. Tom also made an allowance for the fact that walks are more apt to occur in low value situations by reducing their value.

You can adjust for parks effects for either of these. The simple way of calculating park factor (PF) is to take runs scored per game by both teams in home games compared to road games. The park adjustment factor (PA) is that ratio plus one divided by two, since half the games are played at home and the road park factor is pretty close to one. Adjusted NOPS is just NOPS/PA. But park factor itself has a rather large error due to chance. Dallas Adams had a 1983 article in the Baseball Analyst which showed the run distribution per game for various levels of team scoring.2 From that I deduced that the standard deviation of runs in a game was equal to the square root of twice the number of runs. This is very handy when figuring if a difference in runs under various conditions is significant, either in a simulation or real life. So for a particular park, if 700 runs were scored by both teams in home games, the standard deviation of the total would be around 37. But when comparing it to road games it would be higher by the square root of two, since you are comparing two samples. This comes out to be around 52. The standard deviation of the yearly park factor itself due to chance would be around 52/700, about 7 percent. The total difference in parks is only about 10 percent. So that means the real difference between parks is also 7 percent, as the total difference squared is equal to the actual difference squared plus the random difference squared. So you have to use a park factor over several years to get a better estimate of the true value. To adjust straight OPS, you divided by the square root of the park adjustment.

If you look at park factor for all decades by club since 1901, the standard deviation is 7, which means two thirds of the teams fall between 107 and 93. The random factor is reduced to about 2 by using a ten year period.3

Dick Cramer and I were far from the only ones to make attempts over the years at coming up with a formula for relating batting stats to team runs. The legendary F.C. Lane of Baseball Magazine had some articles in the 1910s, which included run values for various events. George Lindsey did work on scoring probabilities, winning percentage, and hit values in the 1960s. Both sets of event values were very close to mine, although neither had a negative value for an out. Earnshaw Cook in the 1960s came up with a formula for what he called DX, which was number of times on base multiplied by total bases. Bill James’s runs created is on-base average times slugging average times at-bats.

Branch Rickey had a famous piece in Life magazine in 1954 which referred to research by scientists at Princeton, although Allan Roth, longtime staff statistician for the Dodgers, told us at a SABR meeting years ago that he was actually the uncredited inventor of the formula. It was close to OPS, as it used hits plus walks plus three-quarters times extra bases over at-bats. Extra bases count one for a double, two for a triple and three for a home run, otherwise known as isolated power. I suspect he did that because he didn’t want to count hits twice—however he should have. Using OBA plus three-fourths ISO gave a standard deviation of 37 runs per season, while OBA plus three-fourths SLG came out 28.

Another feature of the Rickey article was a listing of career leaders in on base average, perhaps the first time that had ever been presented. I did an article on it in the Baseball Research Journal in 1973 and, as a consultant to the American League, helped introduce OBA as an official statistic in 1979. The National League didn’t publish it until 1984 and The Sporting News didn’t show it in the Baseball Guide until 1987, covering 1986. I had not counted sacrifice flies as outs in the AL version, but the NL did. When it finally made the guide, the NL version was used. This had one big problem. The sacrifice fly rule was in effect from 1908 through 1930, 1939, and 1954 to date. But in the first two instances, sacrifice flies were not recorded separately from bunts. Although Retrosheet has filled in much of the older play-by-play, we can never determine the exact OBA for Babe Ruth, Ty Cobb, Lou Gehrig, or other players from that era. The only way to do it is assume no sacrifice flies. Ten sacrifice flies would reduce OBA by about five points.

Bob Creamer in Sports Illustrated in 1956 invented a very simple measure for players called runs produced, which was simply runs plus runs batted in minus home runs. Home runs were subtracted because that would give credit to the same run twice. However, these values turn out to be very close to the linear weight values. A walk is about .25 runs, a single .25 runs and .25 RBI, a double .4 runs and .4 RBIs, and a triple .6 run and .6 RBIs. However a homer is 1 run and 1.6 RBIs, which is 2.6, well above the linear weight value 1.4, so subtracting homers brings runs produced pretty much in line. A homer gets too much credit for RBI, since many of those runs would have scored anyway without the homer and a single too little because advancing a runner from first to second or third results in neither a run nor an RBI.

Steve Mann was one of the first analysts employed by a club—the Astros in the 1970s. (Steve and I created the BACBALL program for charting batted balls and pitches which the Phillies and Braves used for a number of years in the ’80s.) He developed Run Productivity Average which was linear weights that were equal to the average number of runs and RBIs for each event. But it was fairer because it did not favor players who have more opportunities for runs or RBIs because of their team or their lineup position. However I believe it over-values home runs.

Chuck Mullen invented a system in the 1960s with linear weights for each event multiplied by a clutch factor depending on the inning, score, and base-out situation. Bob Sudyk wrote a story in The Sporting News about it, although General Electric, who had the computer, got the credit and Chuck wasn’t even mentioned. The Cardinals used it for while then, and Chuck and I revived it in the 1990s for the Astros.

And the list goes on. Barry Codell invented Base-Out Percentage in the late 1970s, basically bases over outs. Tom Boswell’s Total Average came out about the same time and was similar. None of them really caught on, because I suspect people weren’t ready for them. OPS combines simplicity with reasonable accuracy and I think that is why it is popular.

PETE PALMER is the co-author with John Thorn of “The Hidden Game of Baseball” and co-editor with Gary Gillette of “The Barnes and Noble ESPN Baseball Encyclopedia” (five editions). Pete worked as a consultant to Sports Information Center, the official statisticians for the American League 1976–87. Pete introduced on-base average as an official statistic for the American League in 1979 and invented on-base plus slugging (OPS), now universally used as a good measure of batting strength. Among his many accolades, he won the SABR Bob Davids Award in 1989 and was selected as an inaugural recipient of the Henry Chadwick Award.

Sources

Adams, Dallas (1987). The distribution of runs scored. Baseball Analyst, Vol. 1, Num. 1 pages 8-10.

Bamberg, Paul (1959). “Mathematical Analysis of Batting Performance.”

Codell, Barry (1979). “The Base-Out Percentage.” SABR Baseball Research Journal, No. 8, pages 35-39.

Cook, Earnshaw with Wendell R. Garner (1966). Percentage Baseball. Cambridge, MA: MIT Press.

Cramer, Richard D. and Pete Palmer (1974). “The Batter’s Run Average (BRA).” SABR Baseball Research Journal, No. 3, pages 50-57.

Cramer, Richard D. (2019). When Big Data Was Small, Lincoln, NE; University of Nebraska Press.

Deford, Frank (1964). “Baseball is Played All Wrong,” Sports Illustrated, Vol 20, issue 12, pages 14-17.

James, Bill (1978). The 1978 Baseball Abstract. Lawrence, KS: Bill James.

Krabbenhoft, Herm (2009). “Who Invented Runs Produced?” SABR Baseball Research Journal, No. 38, pages 135-138.

Lane, F. C. (1917, January). “Why the system of batting averages should be reformed.” Baseball Magazine, pages 52-60.

Lane, F. C. (1917, March). “The Base on Balls.” Baseball Magazine, pages 93-95.

Lindsey, G. R. (1959). “Statistical Data Useful for the Operation of a Baseball Team.” Operations Research, Vol. 7, pages 197-207.

Lindsey, George R. (1963). “An Investigation of Strategies in Baseball.” Operations Research, Vol. 11, pages 477-501.

Mann, Steve (2005). Interview. http://hendricks-sports.com/interview2.html.

Okrent, Dan (1981). “He Does It by The Numbers.” Sports Illustrated, May 25, 1981.

Palmer, Pete (1973). “On-base Average.” SABR Baseball Research Journal, No. 2, pages 87-91.

Palmer, Pete (1978). “AL Home Park Effects on Performance.” SABR Baseball Research Journal, No. 7, pages 50-60.

Palmer, Pete (2009). “McCracken and Wang Revisited.” By the Numbers, Vol. 19 No. 1, pages 9-13.

Palmer, Pete (2017). “Intentional Walks Revisited.” By the Numbers, Vol. 27 No. 1, pages 16-25.

Pankin, Mark (2004). “Relative value of on-base pct. and slugging avg.” Presented at the annual SABR convention and available at http://www.pankin.com/baseball.htm

Pankin, Mark (2005). “More on OBP vs. SLG.” By the Numbers, Vol. 15 No. 4, pages 13-15.

Pankin, Mark (2006). “Additional on-base worth 3x additional slugging?” Presented at the 2006 SABR convention and available at the Retrosheet research page.

Rickey, Branch (1954, August 2). “Goodby to some old baseball ideas.” Life, pages 78-86 and 89.

https://www.retrosheet.org

Sudyk, Bob (1966, April 16). “Computer Picks Top Clutch Hitters,” The Sporting News, pages 13 and 20.

Tango, Tom, Mitchel G. Lichtman and Andrew E. Dolphin (2006). The Book: Playing the Percentages in Baseball. TMA Press.

Thorn, John, and Pete Palmer (1984). The Hidden Game of Baseball. Garden City, NY: Doubleday.

Wang, Victor (2006). “The OBP/SLG ratio: What does history say?” By the Numbers, Vol. 16 No. 3, pages 3-4.

Wang, Victor (2007). “A closer look at the OBP/SLG ratio.” By the Numbers, Vol. 17 No. 1, pages 10-14.

Notes

1 In the early days of the Statistical Analysis Committee, I suggested that SABR members send their work to Bill James, who had started his Baseball Abstract in 1977 and began the Baseball Analyst with input from his readers in 1982. This ran through 1989. Don Coffin then started the SABR version as the stats committee bulletin and called it By The Numbers. Don published fairly regular issues of the bulletin through 1995. Neal Traven took over in 1997. Phil Birnbaum assumed charge of the bulletin in 1999 and restarted quarterly issues in 2001, although since 2009 the number of bulletins has been reduced to one or two per year, due to lack of contributions. He later became chairman.

2 Dallas Adams, “Team Won/Lost Percentage as a Function of Runs and Opponents Runs,” Baseball Analyst newsletter, April 1983 issue, pages 10-12.

3 The top 17 park factors are all from Colorado, covering every overlapping decade of their existence, with values around 130. In 1996 the Denver ballpark averaged 15 runs per game. Colorado is the only extreme park since the leagues started an unbalanced schedule in 1969, so you have to calculate each team’s road factors separately, since having Colorado as a road park raises the road average by about five points. The only other park over 120 was Philadelphia’s Baker Bowl, which dates back to 1895, but did not become a hitter’s park until around 1915. It was replaced by Shibe Park in 1938. The low end is monopolized by the Dodgers in the 60s and Padres in the 90s at around 85.

For sure, Boras has been outspoken on many topics, garnering controversy on issues such as the timing and contract terms of free-agent signings, the level of team salaries in large affluent markets, the timetable of players graduating from minor to major leagues, the number of innings thrown by pitchers coming off injury, and other labor-management issues. From 2015 to 2018, the Boras Corporation has negotiated well over 200 major league baseball contracts, ranging from many one-year deals to Prince Fielder’s nine-year $214 million mega-contract. The total value of all the contracts is nearly $3.5 billion. The Boras Corporation is not the only agency, though, that has substantial economic interests connected to Major League Baseball players. There are at least eight other agencies that have negotiated contracts worth over a billion dollars since 2015 and obviously have an enormous financial interest in player salaries.

The objective of this study is twofold. First, to examine the number and size of contracts that the largest baseball agencies have negotiated for their clients from the 2015 to 2018 seasons. In doing so we distinguish between single and multi-year team control and free agent agreements. The role of the agent in determining contract terms is central in the latter two cases, especially for free agents since the contract duration and salary are negotiated under open-market conditions. Secondly, to appraise the performance of baseball agencies. Our concentration is to gauge the extent to which player representatives have delivered value to their clients. Do some agencies have the ability to secure salary levels that exceed player performance? By the same token, do some agencies appear to sell their clients short by negotiating salary levels that end up understating their future values?

As alluded to above, batting average has limitations as indicative of a player’s performance. With the aid of new technologies and advanced statistics, baseball has expanded and refined the way in which it evaluates player performance. Arguably the advanced metric that has received the most notoriety and exposure is Wins Above Replacement (WAR), which evaluates a player’s overall worth by calculating the number of wins for which he is responsible compared to a replacement-level player at the same ballpark. Fangraphs, Baseball Prospectus, and Baseball-Reference.com publish WAR statistics on their websites for each major league player. Although there is not a standard WAR measure, the use of WAR has become more pervasive and it is now not unusual to see a reference to a player’s WAR in a newspaper article or baseball blog. WAR has been used to estimate the future value of players and no doubt have played a role in the negotiation of player contracts.

Here, we examine players’ salaries and WAR before and after signing a contract for each agency. WAR serves as a measure of on-field performance. Prior to a contract, WAR tells us about past achievements and is an indication of potential success of the player. Subsequent to the contract, WAR indicates the realization of what is accomplished. When dividing salaries by WAR, we convert a player’s WAR into his monetary value.3 Or, as Fangraphs writer Matt Swartz defines, dollars per WAR is the average cost of acquiring one win above replacement on the free-agent market.4 A player whose WAR is 3 and receives a salary of $15 million provides a lower monetary value or higher cost to his team than a player whose WAR is 2 and receives a salary of $6 million.

We will first review the basic tenets and services provided by sports agencies. Secondly, we will discuss the data employed for the analysis. Thirdly, we will compare and analyze contract data and WAR levels for the clientele of a dozen of the largest baseball agencies. Lastly, we will review our findings and take a look at whether the conclusions found in Gennaro regarding Scott Boras as a super-agent continue to hold a decade or so later.

Brief Background on Sports Agencies

There are around 150 sports agencies representing over 2000 current and former baseball players.5 Some of these agencies are very large and not only represent baseball players and other athletes but also artistic entertainers. A leading example is Creative Artists Agency. CAA represents well known movie and TV stars and baseball, football, basketball, hockey, soccer, golf, and tennis players. Independent Sports and Entertainment and The Wasserman Media Group are global corporate entities representing diverse sport figures including snowboarders, Olympic athletes, coaches, and managers in addition to baseball, football, and basketball players. Other agencies specialize in representing baseball players. Athletes Career Enhanced and Secured, the Boras Corporation, and Beverly Hills Sports Council represent hundreds of baseball players at the major and minor league levels in the United States, Latin America, and Asia. Other agencies represent only a few major league clients. Melvin Roman’s MDR Sports Management specializes in Latin American ballplayers and represents current major leaguers Yadier Molina and Jonathan Villar. Turner Gary Sports has former major league clients Shaun Marcum, Brad Lidge, Chad Bradford and current major leaguers Lonnie Chisenhall, and Shane Greene. Of course, with around 150 agencies, other examples abound.

Whether large or small, each of the agencies has specialists who focus on baseball players, usually with a background in sports, business, and/or law. The MLB Players Association (MLBPA) is the exclusive bargaining agent for players negotiating a major league contract and certifies agents. MLBPA regulates and approves General Certified Agents who can represent or advise players when negotiating a contract, Expert Agent Advisors who may assist in the negotiations, and Limited Certified Agents who can recruit and provide clients maintenance services. MLBPA explains requirements and instructions on how to apply for each type of agent.6 Player-agent representation contracts are signed annually and there are occasional disputes about players opting for signing with new agents.7

Agencies offer a variety of services usually emphasizing professionalism and individual attention in managing, marketing, and negotiating on behalf of the player. Among recent innovations and guidance from MLBPA, agencies are examining players’ social media posts and expunging any offensive or hurtful comments.8 For commission, the agency negotiates the contract, arranges for endorsement deals, and advises the player on financial planning and taxes.9 The multisport agency, Excel Sports, for example, asserts, “From draft day, through arbitration and free agency and into retirement, we are industry leaders not only in contract negotiations, but also in meticulously building some of the most successful athlete brands in the marketplace.”10

MLB Trade Rumors conducted player interviews prior to the 2013 season, asking what attributes players seek in choosing an agent. Not surprisingly, players indicated the importance of interpersonal relationships often developing early in their careers.11 Players look for agents that communicate well and demonstrate an understanding of their individual and family interests and goals. Players require the agents to have the requisite legal and business expertise to represent them in negotiations with general managers and other ballclub executives. They also solicit agencies that have connections with marketing and charitable organizations to establish and enhance their “brand.” Most importantly, the players seek the agencies that will be able to negotiate a contract with the largest payout.

Limited information is available on the precise figures that players compensate their agencies. The available literature suggests that agencies receive a commission of four to five percent of players’ salaries.12 This compares favorably to the National Football League and the National Basketball Association, which limit commissions to three percent of salaries. The commissions exclude fees earned from finding, negotiating, and securing endorsement contracts, where agencies typically earn 10 to 20 percent.13

Sourcing and Explaining the Data

Our main data source is Baseball Prospectus’s Cots Contracts, 2015 through 2018. At the beginning of each season Cots indicates the players on every team, contract terms, and the player’s agency (or agent). Contracts in effect for 2015 include single and multiyear agreements that began as early as 2008. For example, Miguel Cabrera’s eight-year, $152 million contract. Multiyear contracts extend far into the future as well, such as Giancarlo Stanton’s 13-year, $325 million contract from 2015 to 2027, plus an option year. Cots lists the player’s agency each year and we matched those agencies with the start of each contract. For example, Elvis Andrus signed an eight-year, $120 million contract negotiated by the Boras Corporation that began in the 2015 season. In another example, early in his career, Gio Gonzalez agreed to a five-year, $42 million contract plus two years of options running from 2012 to 2016 with Athletes Career Enhanced and Secured as his agency. In 2015, Gonzalez switched agencies to the Boras Corporation. Subsequently, his 2017 and 2018 options were exercised raising the contract to seven years for $66 million. Since Athletes Career Enhanced and Secured negotiated the contract, we list them as the agency of record for the $66 million. Similarly, Creative Artists Agency represented Ryan Braun in his five-year, $105 million extension that started in 2016, although it was negotiated a few years earlier. Where data are available we attribute the player with the negotiating agency and adjust salary when options are exercised (through 2018).14

We source our WAR data from Fangraphs for the years 2005 through 2018. When a contract is negotiated the player, the agency, and the team base the salary and contract length on anticipated future performance. Negotiators often look at past performance to predict what might happen in the future. Rather than using a single year’s WAR, an average of three years prior to the contract is used to represent a player’s achievements and expected performance. For example, in a contract negotiated in 2010, we used average WAR from 2007-2009. For post contracts, we use the average WAR for up to the length of the contract. A 2015 five-year contract would be an average WAR for 2015 to 2019. However, 2019 is not available so in this case we only used four years. To the extent that a player’s productivity declines in outer years of a contract, we may be overstating their productivity. Furthermore, in some instances, particularly post contract years, the number of observations are limited, and in these cases, we opt to use the one or two years of data that might be available. If no pre- or post-WAR are obtainable, then we drop this observation.

An Overview of Agency Contracts

The Boras Corporation is at the head of the class for representing the most MLB players and the size of their contracts. For the 2015 season, the first year of our contract analysis, the Boras Corporation had 75 clients in which they negotiated single or multiple year major league deals starting as early as 2010. Nearly 50 additional agreements were negotiated for each of the next three years for a total of 219 contracts valued at near $3.5 billion or an average contract value of $15.9 million (Table 1). This includes multiple one year or longer contracts for the same player. Boras negotiated three contracts for Carlos Gomez: a 3-year contract in 2014 and single year contracts in 2017 and 2018. For the 2018 season, Boras had 61 MLB clients with single and multiyear contracts originating as early as 2012 (Prince Fielder) and concluding as late as 2025 (Eric Hosmer) and with a total contractual value of $2.1 billion.

Table 1. Big 12 Agencies and Their MLB Players: (Contracts Negotiated 2015–18)

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In addition, Boras has the largest average annual value (AAV) of contracts and the largest number of contracts over $20 million per annum (Table 2). To calculate AAV we divide each player’s contract value by the number of years of the contract. We then calculate an average for each agency. Boras’ players have an AAV of $5 million, exceeding all the other agencies in our database. There are 34 major league players with over $20 million annual payouts, 10 of whom are Boras’ clients. The list includes two players who are no longer active, Mark Teixeira (contract expired in 2016) and Fielder (contract expires in 2020), and eight current players. José Altuve, Jake Arrieta, and J.D. Martinez signed contracts in 2018. Of the 10 players, Bryce Harper is the only one in the group who is under team control. Harper has a one-year contract that expired at the end of the 2018 season. Harper’s new contract with the Philadelphia Phillies that started in 2019, unsurprisingly, set a record: 13 years, $330 million, which is more than $25 million annually.

Table 2. Top Earners Represented by The Boras Corporation

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While the Boras Corporation may be the foremost agency in baseball, it is just one of four sports agencies with over $2 billion MLB player contracts in effect from 2015-2018. And, at least a dozen sports agencies have had contracts over $250 million. In addition to the Boras Corporation (Boras), the agencies are: Athletes’ Careers Enhanced and Secured (ACES), Beverly Hills Sports Council (BHSC), Creative Artists Agency (CAA), Excel Sports Management (Excel), Independent Sports and Entertainment (ISE), Jet Sports Management (Jet), Legacy Sports Agency (Legacy), Magnus Sports (Magnus), Octagon Baseball (Octagon), Sosnick, Cobbe, and Karon (SC), and the Wasserman Media Group (WMG). These agencies do not get as much press coverage as Boras, but along with Boras they account for approximately 40 percent of the total value of all baseball contracts. Furthermore, the dozen agencies account for nearly 75 percent of baseball contracts that exceed $20 million. Table 1 lists each of these agencies with their abbreviated names, the number, contract value, AAV, and the length of the contracts.

The next four largest agencies measured by their total value of contracts are CAA, Excel, ISE, and WSG. CAA has contracts over $2.5 billion, Excel and ISE $2 billion, and WMG $1.7 billion. AAVs are among the highest for these agencies as well, which is not surprising given that they have all but two of the remaining players under contract for our dozen agencies earning over $20 million annually. Interestingly, Zack Greinke (2013 contract) and Yoenis Cespedes (2016 contract) each earned over $20 million and had an opt out which they exercised, Greinke signing a new contract with Arizona starting in 2016 with an AAV of over $34 million and Cespedes re-signing with New York Mets, nearly a year later than his initial contract, for an AAV of $27.5 million.

The average length of contracts is similar across all the agencies around 1.6 years. About 20 percent of contracts are longer than one year. Boras and CAA have the most long-term contracts. They have 24 and 21 contracts four years or longer and four and three contracts eight years or longer, respectively. WMG negotiated the longest contract, Stanton for 13 years, $325 million for 2015-2027, plus the option year. Jet has an average length of 1.8 years for its contracts, a little longer than the other agencies. Jet negotiated several longer-term contracts for players early in their careers, Kyle Seager’s seven-year, $100 million deal and Corey Kluber’s five-year, $38.5 million contract, each with option years, and both signing while they were under team control.

In the last column in Table 1 we examine the estimated commission received by each agency. Using the four percent estimate discussed above, Boras’s commission is nearly $140 million based on the salaries of its negotiated contract players. Fielder’s nine-year, $214 million 2012-2020 contract generates over $8.5 million or a shade under $1 million per year. CAA’s total commission is also over $100 million during this time period with the Robinson Canò 10-year, $240 million 2014-2023 contract standing out with over $9.5 million commission or again a shade under $1 million per year. Isolating the 2018 season and the players’ AAV of the negotiated contracts by Boras and CAA, the earned commissions are nearly $20 and $13 million, respectively.

A player’s MLB status—pre-arbitration, arbitration, or free agent—significantly affects the ability to negotiate salary and the length of a contract. The AAV escalates as a player attains more experience and moves into free agency. For our sample of players for the 12 agencies, the average value for team controlled and free agent players increases from $2.5 million to $7.8 million. Clearly, players and their respective agencies have the most negotiating power in the free-agency market and this is reflected in the higher salaries and lengthier contracts. Table 3a shows that Boras has the largest number of free agent contracts (47), the highest total value ($2.2 billion), the highest AAV ($10.6 million), and the lengthiest (2.9 years) contracts.15 Over 60 percent of the value of Boras’s contracts are free agents, adding credence to the often stated comment that Boras’s clients are less likely to sign a long-term contract early in their careers relative to other players. However, there are several notable exceptions mentioned below.

Table 3a. Big 12 Agencies and Their MLB Free Agent Players: (Contracts Negotiated 2015–18)

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Table 3b. Big 12 Agencies and Their MLB Team Control Players: (Contracts 2 years or longer negotiated 2015–18)

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Team control players, who are thought to have the most upside by their teams, may coordinate with their agencies to negotiate multiyear contracts or extensions. In these cases, the role for their representatives is considerably more significant than for a one-year deal. Determining the tradeoffs between a guaranteed return of salary for a fixed number of years plus agreeing to any option years provides a player some security compared to one-year or short-term contracts and subsequently becoming a free agent. This is a paramount decision for a young aspiring player. Boras negotiated multiyear million dollar extensions for Andrus’s eight-year, $120 million contract with the Texas Rangers, Stephen Strasburg’s seven-year, $175 million contract with the Washington Nationals, and most recently Altuve’s $163.5 million, seven-year contract with the Houston Astros. Excel negotiated multiyear million dollars extensions for Clayton Kershaw with the Los Angeles Dodgers and Homer Bailey with the Cincinnati Reds, as did CAA for Adam Jones with the Baltimore Orioles as their free agency approached. In other cases, pre-arbitration players agreed to multiyear contracts. Anthony Rendon’s first contract negotiated by Boras with the Washington Nationals was for four years, plus an option year, in his first major league season. ISE negotiated a five-year contract plus an option year with the Arizona Diamondbacks for Paul Goldschmidt prior to the 2013 season, an illustration of an early major-league contract that buys out free agency years. Successful baseball stars in Japan, Korea, and Cuba have inked initial multiyear contracts without any major-league experience. Two prominent examples include Texas agreeing to terms with Japanese star Yu Darvish, represented by WMG, and Oakland coming to terms with Cuban star Yoenis Cespedes through CAA.

Boras, CAA, and Excel have the most team-controlled players with contracts of two years or longer, subsequently referred to as multiyear team control or team control 2 players (Table 3b). CAA has the highest total value ($1.1 billion) and AAV ($13.7 million) contracts, with Buster Posey’s nine-year, $167 million plus option contract with the San Francisco Giants being a notable example. WMG stands out with the longest average length of contracts (7.3 years) but with only a total of eight contracts in this category. WMG clients include New York Yankees superstar Stanton and former Japanese and Cuban players (Darvish, Kenta Maeda, Yasiel Puig, and both Yulieski and Lourdes Gurriel). The combination of free agents plus team control players account for approximately 85 to 90 percent of agency commissions, although only around 30 percent of the total number of contracts.

Differences in Talent and Salaries across Agencies

The information examined in Tables 1, 2, and 3 demonstrate that Boras has the highest paid players on an average annual basis for all free agent players. They also tend to have lengthier contracts compared to the other large agencies. Along with Boras, CAA and Excel have the most multiyear contracts for players under team control and their AAVs for these players are among the highest. There are at least two reasons to explain the success of these agencies: they may be more adept at attracting highly-skilled players, and they may be more skillful at negotiating more lucrative contracts. To distinguish the two reasons, we must examine player achievements before inking their names on contracts.

We chose WAR to measure performance, since it is a comprehensive measure. The WAR metrics are shown in Table 4 for free agents and team control 2 players from each of the 12 agencies. We find that Boras players earn higher WAR scores pre-contract than most other agencies for both free agents and team control 2 players, suggesting that its clients may be more talented and successful. Altuve, Harper, and Max Scherzer each have an average WAR of over 5 contributing to the relatively higher average for Boras (see Table 2). The two other agencies that average over 3 WAR for team control 2 players are WMG and CAA. Notable WAR achievements elevating metrics for these two agencies are Stanton’s nearly 5 WAR and Cespedes’s nearly 4 WAR, respectively.

Table 4. Player Performance by Agency: Wins Above Replacement Prior to Contract

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In the next two columns in Table 4 we focus on the monetary value of players. Players compensated by a higher salary per WAR prior to signing are more costly. No agency stands out, except for Jet, with most agencies having around $5 million per WAR for free agents and nearly $4 million for team control 2 players. There is some variation that can often be explained by one or two contracts per agency, where the player had limited success but still received a relatively high paying contract. For example, Jet has represented catcher Jeff Mathis. While his most recent agreement is relatively small $4 million for two years, his WAR averaged a meager 0.1 prior to signing. Mathis is considered to be an excellent game-caller, helpful to a pitching staff, and is considered “one of the best at something that cannot be measured but is valued.” 16 In this case, WAR may not be an adequate measure of his value to a team.

In Table 5 we examine players’ success after signing the contract. WAR outcomes are consistently lower than prior to the contracts. This is an expected result particularly for free agents since these players are older and their performances tend to drop off with age. Because of lower WAR, post-contract salaries per WAR increase considerably for free-agent players. The average dollar cost is approximately $10 million. According to Swartz, the dollar-cost estimate of replacing a free agent is worth around $10 million over the 2015-2017 period.17. Our post-contract results are within the $10 million range for Boras and most of the other agencies. The main outlier, the nearly $20 million per WAR for Sosnick-Cobbe’s free agent clients, reflects a small sample size and some players with slightly negative WARs and high salaries, most notably Jay Bruce’s 2018 three-year, $39 million contract with the New York Mets combined with 2018 WAR at replacement level.

Table 5. Player Performance by Agency: Wins Above Replacement Post Contract

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Team control 2 players exceed the achievements and are less costly than free agents; this is the case for every agency in Table 5. Coming to terms with team control 2 players for multiyear contracts relative to free agents appear to be advantageous for teams. The team owners absorb the risk of players getting injuries or subpar performances but the team control 2 clients demonstrate greater monetary value than their free agent counterparts. The team control 2 players likely receive less than free agent market rate compensation and tend to be younger.

Concluding Observations: Gennaro Generally Had It Correct

In Gennaro’s 2011 article he concludes that Boras’s hype as super-agent is justified. Our analysis indicates most of the findings related to Boras’s success continues to prevail. We find that Boras has the largest number of major league players under agreement, with an estimated total contract value of $3.5 billion covering contracts signed between 2015 and 2018 seasons. The firm represents clients with the highest average annual salaries and is among the agencies with the longest contracts.

Boras does appear to be a master at attracting the game’s biggest stars. The company retains many of the most successful free agents. Current clients, such as Harper and Scherzer, often achieve higher WAR scores than other players. Toward the end of the 2018 season, emerging Phillies slugger Rhys Hoskins opted to hire Boras as his agent.18 Boras’s reputation as an agent who encourages his players to wait for free agency rather than sign extensions while under team control often holds. However, there are some key exceptions where Boras has negotiated extensions with players’ existing teams at or near market rates. Two relatively recent examples are the seven-year extensions for Altuve and Strasburg.

In addition to Boras we examine several other big agencies in detail. ACES, CAA, Excel, ISE, and WMG each represent major league players with well over one hundred contracts totaling at least $1.5 billion. Each have at least one star with contracts exceeding six years and $100 million. Included in this list are names like Jon Lester, Posey, Greinke, Miguel Cabrera, and Stanton, respectively.

The dozen agencies in our study appear to be competitive with each other when comparing the negotiated salaries given their clients’ level of performance. Whether we are discussing free agents or multiyear contract team control players, the average annual salary per WAR prior to signing contracts are approximately $5 and $4 million, respectively, for each of the dozen agencies. Post salaries per WAR are mostly greater than pre-salary, indicating that performance levels are often less after signing a contract. This is true for free agents in each of the dozen agencies and half of the 12 agencies of the team control 2 players.

Gennaro indicates that Boras is more successful in negotiating maximum value for his clients, achieving nearly twice their average contract values—both salaries and length of contracts—relative to performances. We find a similar result for free agents. Boras’s clients have nearly 90 percent higher average contract values and 45 percent greater WAR. In contrast though, for multiyear team control players, Boras’s clients attain 20 percent higher average contract values but achieve much higher WAR of 45 percent relative to other agencies. Boras may be more successful at negotiating free-agent contracts but this does not appear to be the case for multiyear team control clients.

We should add one more point: our focus has been on a metric that we can measure, namely, salary and WAR. While salaries are obviously a key component a player seeks in choosing an agency, there are likely many personal and branding factors that are important to players in enlisting agency representation. The ability of the agencies to market their players might vary and generate different streams of income.

BARRY KRISSOFF is an Adjunct Associate Professor of Economics at the University of Maryland Global Campus. His first article in the BRJ, “Society and Baseball Face Rising Income Inequality,” was a finalist for the 2014 SABR Analytics Conference Research Awards in the category of Historical Analysis/Commentary. He continues to look forward to a World Series victory in Washington, DC — maybe this is the year! Contact information: bcybermetric@hotmail.com.

Acknowledgements

The author appreciates the careful and extensive critique and suggestions by John Wainio and two anonymous reviewers. We also benefited from correspondence with the Major League Baseball Players Association.

Notes

1Jorge Castillo, “Scott Boras Says Shifts Are Partly Why Bryce Harper Isn’t Enjoying a Typical Harper Season,” Washington Post, July 5, 2018. https://www.washingtonpost.com/news/nationals-journal/wp/2018/07/05/scott-boras-says-shifts-are-partly-why-bryce-harper-isnt-enjoying-a-typical-harper-season/?noredirect=on

2 Vince Gennaro, “The Scott Boras Factor: Reality or Hype?” Baseball Prospectus, April 15, 2011. https://www.baseballprospectus.com/news/article/13584/baseball-proguestus-the-scott-boras-factor-reality-or-hype

3 Neil Paine, “Bryce Harper Should Have Made $73 Million More.” FiveThiryEight, November 9, 2015. https://fivethirtyeight.com/features/bryce-harper-nl-mvp-mlb/

4 Matt Swartz, “Foundations of the Dollars-per-WAR Evaluation Framework.” Fangraphs, March 26, 2014. https://www.fangraphs.com/tht/foundations-of-the-dollars-per-war-evaluation-framework/

5 MLBTR Agency Database. Major League Baseball Trade Rumors. http://www.mlbtraderumors.com/agencydatabase

6 See MLBPA Agent Regulations: http://mlb.mlb.com/pa/info/agent_regulations.jsp

7 Bob Nightengale and Jorge L. Ortiz. “Scott Boras loses in grievance against Beltran,” USA Today, March 26, 2014. http://www.usatoday.com/story/sports/mlb/2014/03/26/scott-boras-grievance-carlos-beltran-robinson-cano-switching-agents/6934915/

8 Jared Diamond, “Baseball Tries to Clean Up After Social-Media Fouls.” Wall Street Journal, August 22, 2018, page A14.

9 Wendy Thurm, “Longtime Agents Slash Fees, Try to Shake Up Industry.” Fangraphs, August 26, 2014. https://www.fangraphs.com/blogs/longtime-agents-slash-fees-try-to-shake-up-industry/

10 Excel Sports Management. http://new.excelsm.com/representation-baseball/

11  See for example: B.J. Rains “Why I Chose My Agent: David Wright.” Major League Baseball Trade Rumors, March 13, 2013, part of a series of interviews of players. http://www.mlbtraderumors.com/2013/03/why-i-chose-my-agency-david-wright.html

12  See Wendy Thurm; Marie Gentile, “The Average Sports Agent’s Commission,” Houston Chronicle, June 28, 2018 (updated), http://work.chron.com/average-sports-agents-commission-21083.html; and Sports Management Worldwide, “Sports Agency’s Salaries,” https://www.sportsmanagementworldwide.com/courses/athlete-management-sports-agent/salaries.

13  Marie Gentile.

14  If options are not exercised then the contract usually includes a relatively small payout to the player. We did not include these payouts so the value of the contracts may be slightly understated.

15  Consistent with MLB rules, the Cots’ database expresses MLB experience in years and days of service. A player becomes eligible for free agency if he has six years of experience at the beginning of a season. However, some players are listed between six and seven years of service who agreed to an extension before they became a free agent (see Altuve, Cots, 2018, for example). We reviewed Baseball Prospectus contract information to discern which players opted for an extension. These players are not included as free agents but are included in Table 2b.

16  R.J. Anderson, “Baseball believes in Jeff Mathis and the hidden value of game-calling by catchers.” CBSsports.com, February 20, 2018. https://www.cbssports.com/mlb/news/baseball-believes-in-jeff-mathis-and-the-hidden-value-of-game-calling-by-catchers/

17  Matt Swartz, “The Recent History of Free Agency Pricing.” Fangraphs, July 11, 2017. https://www.fangraphs.com/blogs/the-recent-history-of-free-agent-pricing/

18  Steve Adams, “Rhys Hoskins Hires Scott Boras.” MLB Trade Rumors, Setptember 18, 2018. https://www.mlbtraderumors.com/2018/09/rhys-hoskins-hires-scott-boras.html

In the second grade, I developed a fondness for Hall of Fame pitcher Addie Joss. He played from 1902 to 1910. His career was cut short by meningitis. There was no picture of him in my almanac, but I used his 1.89 career ERA and .968 WHIP to construct an image in my head of a sturdy and precise man — stirrups even and pressed, face placid and clean. Only a wild pitcher, I had thought, would grow an unruly beard. Indeed, if Joss were the most precise pitcher ever, he would have no facial hair. I wouldn’t know for sure what his face looked like until I was in middle school when I encountered a Joss tobacco card at a collector’s convention in Chicago. In the image on the card, he was mostly as I’d imagined: straight-faced with a popped jersey collar. But I did not expect his hair parted down the middle, his bangs curled and waxed like some dorky pre-war actuary.

Each time I attend a baseball card show, I’m introduced to another of my hero’s faces and can’t help but imagine that player at work. In my imagined scenes, actions and dialogue are derived from a unique baseball vocabulary: bases load like guns, changeups fall off tables, and frozen ropes earn doubles. This vocabulary has influenced the way I organize and retrieve my memories. In my brain, I file cable news clips of war next to Josh Hamilton’s 2008 Home Run Derby performance, tie my two weeks in the Ecuadorian jungle to Rick Ankiel’s wild fastball, and place my father’s death beside the 1997 World Series, which the Cleveland Indians lost. When I study baseball-related language, I am studying myself — my history, assumptions, and proximity to the world. Language and cognition are inseparable, and so our passions impact our perceptions, thought organizations, and communications.

In their book Metaphors We Live By, cognitive linguists George Lakoff and Mark Johnson claim that “the essence of metaphor is understanding and experiencing one kind of a thing in terms of another.”1 We cannot make sense of our complex inner and outer worlds without conceptual metaphors, through which we decipher and describe non-tactile or ambiguous concepts by comparing them to concrete objects and experiences. Metaphors are not merely “characteristic of language alone,” but “pervasive in everyday life…in thought and action.”2 To strip our lives of metaphor is to live in a single dimension, to know nothing but unnamed, immediate sensations. Metaphors allow us to name and play in confounding depths — everywhere from our psyches to the cosmos — which is, I think, to be human.

Here, I’ll examine orientational, ontological, and structural metaphors used to describe baseball games. As I do, I hope some of the core assumptions and perceptions that are common amongst baseball fans, and perhaps humanity as a whole, become more evident. Most importantly, I hope this basic survey will bolster my — and hopefully my readers’ — ability to intentionally and effectively recognize and construct metaphors, then employ them in communication, to better describe the human experience.

I live vicariously through Dodgers pitcher Clayton Kershaw. We’re about the same age, and both have four-year-old daughters. But Clayton is five inches taller than I, left-handed, and induces major-league whiffs with a swooping, 88-mph slider. At this point in my life, my fastball peaks at 73 — that according to a carnival speed gun. In an alternate reality, I sometimes think, there is a tall, athletic version of myself who throws physics-bending curveballs. I watch every Kershaw start on television. He is in California while I am in Philadelphia. Our time zone difference means that I will likely stay up past midnight once every five days during the baseball season. My wife heads to bed without me on Kershaw nights.

On June 18, 2014, Clayton Kershaw no-hit the Colorado Rockies. Baseball wordsmith Vin Scully provided the color commentary. Scully began his career as a radio announcer. His descriptions of that game were so vivid that pictures weren’t necessary. The baseball, according to Scully, “dips” and “drifts,” gets “punched” and “speared.” In the third inning, a Rockies batter hit a “soft line drive.” Scully, always concerned about his words’ clarity, defined his terms, “The use of the word line-drive is describing the trajectory.” In the eighth inning, when it seemed the Rockies might not get a hit, the camera panned to Kershaw’s wife. Scully, speaking like a proud family member, noted, “There’s Ellen, applauding her hubby.” In contrast to the elated Dodgers, the Rockies looked dejected. Scully used a refrain to describe struck-out Rockies: “Down he goes.” “Down he goes.” “Down he goes.” I imagine the Colorado hitters knew their doom was inevitable, like characters in Vonnegut’s Slaughterhouse Five: “So it goes.” “So it goes.” “Down he goes.” Here, I am concerned about that metaphorical downward movement toward outs.

According to Lakoff and Johnson, many conceptual metaphors are the result of our spatial orientation. Indeed, they “arise from the fact that we have bodies of the sort that we have and that they function as they do in our physical world.”3 Through orientational metaphors, we “organize a whole system of concepts with respect to another.” That is, we make sense of abstract ideas by way of physical perceptions, “up-down, in-out, front-back, on-off, deep-shallow, central-peripheral.”4 We often describe abstract concepts, such as emotions, as physical entities within our perceived spaces: I am feeling down; Things are looking up; Her spirits are high.

Based on linguist William Nagy’s research (1974), Lakoff and Johnson suggest nine spatial concepts which drive orientational metaphors:

• “Happy is up; sad is down.”
• “Conscious is up; unconscious is down.”
• “Health and life are up; sickness and death are down.”
• “Having control or force is up; being subjected to control or force is down.”
• “More is up; less is down.”
• “Foreseeable future events are up (and ahead).”
• “High status is up; low status is down.”
• “Virtue is up; depravity is down.”
• “Rational is up; emotional is down.”5

As these orientational concepts are dependent upon subjects’ immediate environments, they will not be uniform across all cultures. However, most of these concepts appear as driving forces in baseball descriptions.

In his essay collection The Summer Game, Roger Angell — a J.G. Taylor Spink Award winner and long-time New Yorker fiction editor — describes baseball in the 1960s. His book, like the sport during that decade, is dominated by images of the Yankees, Dodgers, Giants, and Cardinals — and hopeful considerations of the pitiful, fledgling Mets. Occasionally, Angell constructs essays by watching games on television, but most of the time, he writes about his first-hand experience as a fan at the ballpark.

Of a 1962 playoff game between the Giants and Dodgers, Angell writes, “One out of every three or four [Dodgers fans] carries a transistor radio in order to be told what he is seeing, and the din from these is so loud in the stands that every spectator can hear the voice of Vin Scully.”6 Like many of my own potent baseball memories, those fans’ recollections — including Angell’s — are forever linked to Scully’s voice, his turns of phrase, his metaphors.

Using language similar to Scully’s refrain from that 2014 Kershaw no-hitter — “Down he goes” — Angell describes an important moment from the ’62 series: “[Maury] Wills stole second, and the Giants’ catcher, in attempting to cut him down, relayed the ball to center field and to the possessor of the best arm on the club, Willie Mays, who then cut down Wills at third.”7 The speedy Maury Wills, like a tree chopped down and removed from the forest, was, when tagged out, removed from the field of play. If health and life are up and sickness and death are down, then we might conclude that the base paths on a baseball field are reserved for wellness and vitality; they are up. As such, it is common for fans, commentators, and writers to describe winning teams as riding high and losers as fallen.

Perhaps some people are attracted to baseball because it is a quick and obvious representation of their struggle to remain upright. We are all bound to the world by gravity and celebrate many human achievements which work against it: first steps and bike rides, stolen bases and home runs. Orientational metaphors, then, which are rooted in near-universal physical perceptions or at least common language related to those perceptions, are strong connecting points between the orator or writer and the audience.

In 1963, the New York Mets lost 111 games. The previous year they’d lost a historic 120. Still, Roger Angell made his way to the Polo Grounds, where he and a boisterous crowd rooted for that lovable but struggling team. Angell writes about those Mets:

Last year when the team trailed the entire league in batting…its team average was .240. So far this year, the Mets are batting .215, and a good many of the regulars display all the painful symptoms of batters in the grip of a long slump — not swinging at first pitches, taking called third strikes.8

Slumps, it seems, are heavy diseases which attach themselves to baseball players, then pull them downward toward outs. On the literal surface, the Mets may have looked strong and confident, but beneath a metaphorical lens, they might have appeared hunched over, straining to stand — let alone hit — in the batter’s box.

Angell suggests that if the Mets’ offensive woes continue, their manager “will be forced to insert any faintly warm bat into the lineup, even at the price of weakening his frail defense.”9 We understand temperature in up-down terms; it rises and falls. Cold is, perhaps, closer to rigidness or death than heat, or at least away from free movement and vitality; it is down. In baseball, a players’ metaphorical temperature is equivalent to their readiness to enter the game and their likelihood to remain upright, which is to help their team win. Players who have consistently performed at an elite level are often described as hot. Struggling players are cold.

While hot-cold metaphors are grounded in our spatial orientations, they also draw from our direct experiences with objects: snow, campfires, coffee, etc. Lakoff and Johnson call such metaphors “ontological.” Through ontological metaphors, we understand abstract concepts as concrete entities. Ontological metaphors might be richer or more specific than orientational metaphors:

One can only do so much with orientation. Our experience of physical objects and substances provides further basis for understanding…Once we can identify our experiences as entities or substances, we can refer to them, categorize them, group them, and quantify them — and, by this means, reason about them.10

Through ontological metaphors, we might understand a struggling baseball team as more than simply fallen, but rather a defective machine — a complex physical entity. One might describe those 1963 Mets as rusty or not firing on all cylinders. Roger Angell describes that team’s manager as a novice mechanic whose “Tinkering [of the lineup] can lead to the sort of landslide that carried away the Citadel last year.”11 As machines are full of unique parts and movements, the ontological metaphors built from them — by way of direct observation or experience — might be intricate and action-packed.

If people construct ontological metaphors through specific, past physical experiences, how might they impact our physical states when called upon in the present? Do fans feel literally cold when their favorite player strikes out, stuck in a frigid slump? In a close game, do fans literally feel hotter when they see their All-Star closer warming up in the bullpen?

In their paper “Cold and Lonely: Does Social Exclusion Literally Feel Cold?” University of Toronto social psychologists Chen-Bo Zhong and Geoffrey J. Leonardelli write, “Metaphors such as icy stare and cold reception are not to be taken literally and certainly do not imply reduced temperature. Two experiments, however, revealed that social exclusion literally feels cold.”12 In one experiment, Zhong and Leonardelli asked sixty-five undergraduate students to recall “a situation in which they felt socially excluded or included.”13 Then, at the request of a supposed maintenance staff member, those students estimated the current room temperature. Consistently, students who had been asked to recall memories of social exclusion estimated lower room temperatures. For those students, social exclusion felt cold. Therefore, metaphorical concepts primed literal, physical sensations. Commenting on their experiment’s results, Zhong and Leonardelli note,

[These Findings] highlight the idea that metaphors are not just linguistic elements that people use to communicate; metaphors are fundamental vessels through which people understand and experience the world around them…It is possible that people use coldness to describe social interaction patterns partly because they observe, at an abstract level, that the experience of coldness and the experience of social rejection coincide.14

Metaphors are bridges by which people connect abstract concepts to literal, physical perceptions. For example, uncertainty is chilling, ambitious plans are lofty, and depression is dim. In this way, abstract and concrete concepts and their connecting metaphors are tied together in our brains. When someone entertains a metaphor, they may also experience any of the abstract or concrete concepts that metaphor was initially built to bridge.

The metaphors that Vin Scully and Roger Angell use to construct images of baseball games in their listeners’ or readers’ minds affect their psychological, emotional, and physical states. I imagine if I were a Rockies fan watching that Kershaw no-hitter on mute, in the absence of Scully’s voice, the images on the screen would frustrate me. Perhaps I’d curse at Colorado pitcher Jorge De La Rosa after he allowed five runs in the third inning. Maybe I’d pound my right fist on my knee when Rockies catcher Wilin Rosario struck out for the third time. But if I turned on the volume and let Scully tell me what I was seeing, he might lull me from mere frustration into depression. Maybe after I heard his refrain, “Down he goes,” I’d hang my head, then hunch my back. Perhaps if he said that the Rockies’ hitters looked “scared and lonely” at the plate, I’d also feel alone, and possibly cold. If Scully called the Rockies’ offense broken, I might be moved to sadness, as I was in the third grade when my dog destroyed my Sammy Sosa rookie card, chewed beyond repair.

One of the most iconic calls of Scully’s career came in Game Six of the 1986 World Series. The Red Sox led the Mets three games to two and were on the verge of their first championship since 1918. In the bottom of the 10th inning of the sixth game, with the score tied 5-5 and Mets infielder Ray Knight on third, Mookie Wilson, a speedy bean-pole-of-a-man, hit a “Little roller up along first.” Before Wilson’s hit, Red Sox first basemen Bill Buckner had positioned himself 20 feet from the bag. As Wilson swung, Buckner shuffled five steps to his left and crouched to receive the ball. At that time, Buckner — strong, handsome, and mustached — was one of Boston’s stars. He’d won a batting title in 1980 and twice led the league in doubles. But at that point in his career, Buckner was not sure-handed and he failed to field Wilson’s grounder. Vin Scully yelled, “Behind the bag! It gets through Buckner. Here comes Knight, and the Mets win it!”

In the months following his error, Buckner would receive death threats from crazed Red Sox fans who blamed him for that World Series loss. His name would become synonymous with failure. But in that moment, Scully did not say “Buckner missed it” or “Buckner made an error,” but rather that the ball went “through” Buckner. Scully deemed the baseball, not a player, the main actor.

Often in baseball commentary, the ball is described as a creature. After a player swings at and misses a 95-mph fastball, an announcer might say that the ball ate the batter up. Or if a batter pushes a perfect bunt down the third-base line, so the ball rolls to a stop before the catcher or third baseman can field it cleanly, a writer may explain that the ball died on the field.

Sometimes, baseballs are described like people which dance, race, baffle, and hum. According to Lakoff and Johnson, such attributions “allow[s] us to comprehend a wide variety of experiences with nonhuman entities in terms of human motivations, characteristics, and activities.”15 Roger Angell personifies the baseball in his description of a 1968 matchup between the Red Sox and White Sox. In the third inning, Chicago’s left fielder Tommy Davis hit “a two-base screamer just inside the bag at third.”16 Maybe Davis swung so hard, made such true contact, that the baseball did not merely hiss as it usually does when rushing through wind, but yelled. Imagine standing at a street corner, an angry man shouting obscenities as he runs in your direction. Can you blame Boston’s third baseman for stepping to the side of that screaming grounder, letting it pass?

Perhaps if baseballs always moved as expected, and weren’t consistently fooling or injuring players, people might see them as fair and honest characters which, when batted, deserve secure send-offs rather than harmful hits. However, baseballs, so far as most baseball people know them, are crafty and unpredictable, worthy of punishment. Broadcasters happily describe batted balls as smacked, crushed, walloped, destroyed, slapped, rapped, struck, banged, pounded, cracked, punched, swatted, belted, and shot. Baseball language is often violent.

Radio commentator John Sterling creates a unique home run call for every Yankee. He often uses alliteration and rhymes. In the past, he called each Derek Jeter home run a “Jeter Jolt,” and with every Chris Carter blast he exclaimed, “Carter hits it harder!” Often Sterling utilizes battle-like phrases: “Bernie goes boom!” “Kelly killed it!” “It’s a nuke from Youk!” “It’s an A-bomb for A-Rod!”

On March 29, 2018, when power-hitting right fielder Giancarlo Stanton hit his first home run as a Yankee, John Sterling exclaimed, “It is gone! In his first Yankee at bat! Giancarlo, non si puó stoparlo! (Giancarlo can’t be stopped!) It is a Stantonian home run. A two-run blast.” Many Yankees fans did not like some of ways Sterling had described that home run. On social media, they questioned Sterling’s poor Italian and dismissed his use of that added suffix in “Stanton-ian.” “Ruthian” is already a common word in the Yankee vernacular, and any comparison between Stanton and Ruth might be blasphemous in the Bronx. But nobody challenged Sterling’s use of the word “blast.” Few people ever question his war words.

Maybe John Sterling, like many baseball fans, not only thought that Stanton’s home run ball resembled a soaring weapon or that the slugger’s buttoned uniform looked like battledress, but has conceptualized the entire sport as war. Maybe he’s mentally organized baseball atop an existing schema of battle, and so he cannot separate the motives and strategies of literal war from his metaphorical understanding of the game. Perhaps a single structural metaphor, baseball as war, drives most baseball commentary.

While orientational metaphors help us to understand abstract concepts in broad physical terms, they “are not,” write Lakoff and Johnson, “in themselves very rich.”17 And though we might personify inanimate objects through ontological metaphors — know ourselves and the world in more complex terms than up and down or in and out — they are limited by their necessary relationship to tangible items. We might only comprehend our inner and outer worlds as specific intangible systems through structural metaphors. Of all conceptual metaphor types,

Structural metaphors…provide the richest source of elaboration. Structural metaphors allow us to do much more than just orient concepts, refer to them, quantify them, etc., as we do with simple orientational and ontological metaphors; they allow us, in addition, to use one highly structured and clearly delineated concept to structure another.18

Perhaps the most common example of a structural metaphor is rational argument as war. Like all animals, humans “fight to get what they want.”19 However, unlike the rest of the animal kingdom, we have instituted rational parameters around conflict and developed “sophisticated techniques for getting our way.”20 We not only participate in reckless fights but structured battles, not only physical altercations but rhetorical situations. In verbal arguments,

Each sees himself as having something to win and something to lose, territory to establish and territory to defend. In a no-holds-barred argument, you attack, defend, counterattack, etc., using whatever verbal means you have at your disposal — intimidation, threat, invoking authority, insult, belittling, challenging authority, evading issues, bargaining, flattering, and even giving “rational reasons.”21

We spend much of our social lives in arguments, many of them subtle and nuanced. Our default rhetorical moves in those arguments are often combat-like, designed to maneuver metaphorical battle flags toward us. As protective animals in a society often framed by war, we might perceive any two-sided contest as a battle, and so, as with rational argument, we may conceptualize and describe baseball as war.

In 1951, New York Giants utility player Bobby Thomson hit a walk-off home run to win the National League pennant, sending his team to the World Series. The following day, the New York Daily News dubbed Thomson’s home run “The Shot Heard ‘Round the Baseball World,” a play on Ralph Waldo Emerson’s 1837 “Concord Hymn,” written to commemorate the beginning of the Revolutionary War. In that poem, Emerson writes, “Here once the embattled farmers stood/And fired the shot heard round the world.”22

In the prologue to his novel Underworld, Don DeLillo imagines J. Edgar Hoover at the Polo Grounds the day Bobby Thomson hit that famed “shot.” In DeLillo’s fictionalized account, just before the Thomson blast, Hoover learns of a secret Russian atomic test, the deployment of an enemy “instrument of conflict…a red bomb that spouts a great white cloud like some thunder god of ancient Eurasia.”23 Hoover is not concerned with the outcome of the baseball game, but “the way our allies one by one will receive the news of the Soviet Bomb.”24 After Thomson’s hit soars into the stands beyond Dodgers left fielder Andy Pafko, the Giants fans and players erupt into victorious mayhem. People toss thousands of newspaper clippings, receipts, and ripped magazine pages into the air. Paper rains over J. Edgar Hoover like confetti. Here, he stands at the intersection of the literal and metaphorical, between the tangible by-products of victory — streamers and joyous chants — and the complex intangibles which often drive war strategy and baseball language: morality, justice, purpose.

Fans who conceptualize baseball as war, their team’s seasons as moral and just conquests, might employ battle terms in discussions about gameplay: Koufax has coerced ten players to swing at his curveball; The manager should have deployed his closer earlier; Henderson evaded the tag at third; The Cubs pitching staff lacks firepower; Hershiser looks tired but will not surrender; That Cabrera double might spark a breakthrough; Griffey is patrolling center field; Acuña was plunked, but took the high ground and did not rush the mound.

The baseball as war metaphor is compelling, but we might not only know the game that way. The sport is many things to many people. To some, baseball is a meticulous, practiced craft performed through improvisation, and so it is jazz. To others, baseball is athletic leaps performed by sculpted men in matching costumes, a ballet. Still, others may know the game as a matrix where player actions resemble numbers which collide and change and reveal or echo mathematical truths. Perhaps the depth and breadth of our passions apart from baseball are among the few limits on our metaphorical conceptions of it.

In her essay “I Remember, I Remember,” poet and essayist Mary Ruefle writes about making a metaphor:

I remember — I must have been eight or nine — wandering out to the ungrassed backyard of our newly constructed suburban house and seeing that the earth was dry and cracked in irregular squares and other shapes, and I felt I was looking at a map and I was completely overcome by this description, my first experience of making a metaphor, and I felt weird and shaky and went inside and wrote it down: the cracked earth is a map.25

Humans are miraculous metaphor-making machines. Our brains are full of beautiful, complex connections between formless mysteries and tactile or structured elements. We construct most metaphors unconsciously. But some people, like Ruefle, can make rich metaphors actively. Active metaphor construction is a practiced craft, honed through repeated and deep deliberations of undefined concepts, and perhaps bolstered by a basic understanding of how humans conceptualize their worlds: orientationally, ontologically, structurally.

When we invent metaphors, we satisfy a primal human urge to decipher and organize thought and experience. Mary Ruefle explains how she felt after constructing that first metaphor, “It was an enormous ever-expanding room of a moment, a chunk of time that has expanded ever since and that my whole life keeps fitting into.”26 I imagine, with each new metaphor I construct, fractal-like synapse paths grow in my brain, connecting emotions, senses, and objects in new, unique ways.

Recently, my mother retired and moved in with my family. She brought boxes full of my childhood things with her: baseball cards, model cars, and wide-ruled notebooks. I did not read or write many stories as a child. My early notebooks mostly contain black and white drawings. On the first page of my fifth-grade notebook, I drew Bob Feller mid-pitch, his left toe pointed high in the air. On the second page, I drew a cartoon of Mark McGwire flexing, the word slugger printed across his chest. On the fourth page, I drew a hodge-podge of baseball players, only identifiable by the last names scrawled above their heads: Thomas, Vizquel, Griffey, Belle, Justice, Maddux, Bonds. Below that player lineup, I identified an important metaphor that many of my experiences keep “fitting into”: baseball is my life.

DANIEL ROUSSEAU is a Philadelphia-based writer. His work has appeared in Cimarron Review, The Briar Cliff Review, and Salon, among others. He has been a finalist for the Frank McCourt Memoir Prize, and his essay “Retrieving Charlie Gehringer” received a notable citation in Best American Essays 2018.

Sources

Angell, Roger. The Summer Game. Lincoln: University of Nebraska Press, 2004.

Delillo, Don. Underworld. New York: Scribner, 1997.

Emerson, Ralph Waldo. “Concord Hymn by Ralph Waldo Emerson.” Poetry Foundation. https://www.poetryfoundation.org/poems/45870/concord-hymn.

Lakoff, George, and Mark Johnson. Metaphors We Live By. Chicago: University of Chicago Press, 2017.

Ruefle, Mary. “I Remember, I Remember.” Poetry Foundation, July 2, 2012. https://www.poetryfoundation.org/poetrymagazine/articles/69829/i-remember-i-remember

Zhong, Chen-Bo, and Geoffrey J. Leonardelli. “Cold and Lonely: Does Social Exclusion Literally Feel Cold?” Psychological Science 19, no. 9 (2009): 838-842.

Notes

1 George Lakoff and Mark Johnson, Metaphors We Live By (Chicago: University of Chicago Press, 2003), 5.

2 Lakoff and Johnson, Metaphors We Live By, 3.

3 Lakoff and Johnson, Metaphors We Live By, 14.

4 Lakoff and Johnson, Metaphors We Live By.

5 Lakoff and Johnson, Metaphors We Live By, 15-17.

6 Roger Angell, The Summer Game (Lincoln: University of Nebraska Press, 2004), 72.

7 Angell, The Summer Game.

8 Angell, The Summer Game.

9 Angell, The Summer Game.

10 Lakoff and Johnson, Metaphors We Live By, 25.

11 Angell, The Summer Game, 50.

12 Chen-Bo Zhong and Geoffry J. Leonardelli, “Cold and Lonely: Does Social Exclusion Literally Feel Cold?” Psychological Science 19, no.9 (2008): 838.

13 Zhong and Leonardelli, 839.

14 Zhong and Leonardelli, 840.

15 Lakoff and Johnson, Metaphors We Live By, 33.

16 Angell, The Summer Game, 21.

17 Lakoff and Johnson, Metaphors We Live By, 61.

18 Lakoff and Johnson, Metaphors We Live By, 61.

19 Lakoff and Johnson, Metaphors We Live By, 62.

20 Lakoff and Johnson, Metaphors We Live By, 62.

21 Lakoff and Johnson, Metaphors We Live By, 62.

22 Ralph Waldo Emerson, “Concord Hymn by Ralph Waldo Emerson,” Poetry Foundation, https://www.poetryfoundation.org/poems/45870/concord-hymn.

23 Don DeLillo, Underworld (New York: Scribner, 1997), 23.

24 DeLillo, Underworld, 30.

25 Mary Ruefle, “I Remember, I Remember,” Poetry Foundation, July 2, 2012, https://www.poetryfoundation.org/poetrymagazine/articles/69829/i-remember-i-remember.

26 Ruefle.

Among the many statistical analyses of baseball that have been published during the last four decades, the single most important in my opinion is The Hidden Game of Baseball (1984) by Pete Palmer and John Thorn. Their research, based on a large-scale regression analysis of baseball statistics, led to the development of summary measures for overall performance (including batting, base running, pitching, and fielding) standardized to account for several factors. These factors included changes over time in the average number of runs scored per game, differences in players’ home parks, and the relative difficulty of a player’s fielding position. This last factor reflects the fact that for two players with identical offensive performance, the one playing a more difficult position (e.g., catcher or shortstop) is more valuable than one playing a less difficult position (e.g., left field).

The beauty of Palmer’s and Thorn’s two primary summary measures — Total Player Rating (TPR) and Total Pitcher Index (TPI) — was that they quantified the performance of players (both pitchers and non-pitchers) in terms of wins contributed to the team relative to average performance. Thus the values of these measures could be positive, zero, or negative, and totals for teams correlated very highly with team performance. Since team performance is primarily a function of how well the team’s players perform, these measures were in fact good predictors of team performance.

Eight editions of Total Baseball were published next, 1989 through 2004, authored by Palmer, Thorn, and others. TB was more comprehensive than previous baseball encyclopedias, and starting with the 4th edition was recognized as the official encyclopedia of Major League Baseball. Total Baseball included other measures of overall performance in addition to those developed by Palmer and Thorn. The 8th edition introduced the term Total Player Wins (TPW), described as: “The ‘MVP’ of statistics, this ranks pitchers and position players by their total wins contributed in all their endeavors, revealing the most valuable performers in a given year.” (Page 2,673.) TPW replaced the terms TPR and TPI used previously. The TPW concept was continued in five editions of the ESPN Baseball Encyclopedia through 2008 where it was referred to as Batter-Fielder Wins (BFW).

As with many print publications, Total Baseball became antiquated in the wake of the Internet. Baseball-Reference.com, developed by Sean Forman, went public in 2000. The B-R.com database was developed originally using the same data underlying the issues of Total Baseball.1 At B-R.com, the concept of TPR has been relabeled Wins Above Average (WAA). While there have been many refinements in computing values of WAA, the basic concept is the same: WAA quantifies the performance of players (both pitchers and non-pitchers) in terms of wins contributed to the player’s team compared with average performance.2

Sources of the data

Most of the data included in this paper are from Baseball-Reference.com, and many were obtained using the Play Index on the website. The Play Index is a feature of Baseball-Reference.com that enables a researcher to develop a wide range of custom tabulations. Without the Play Index, it would not have been feasible to calculate many of the statistics presented here.

Wins Above Average (WAA)

To illustrate how WAA relates values for players with team performance, we can start with the 2018 season, using an average team, the best team, and the weakest team, as defined by their won-lost records. The most average team was the Los Angeles Angels with an 80–82 record. They had a team WAA of +0.2 (essentially zero), composed of a +5.2 for the non-pitching position players and designated hitters — hereafter called “position players” — and a -5.0 for pitchers. Not surprisingly, the best player on the team was Mike Trout with a WAA of  +8.1. With just an average player in place of Trout, the team would probably have won about eight fewer games, which would have produced a 72–90 record. (It should be noted that a team’s WAA is not expected to predict its won-lost record exactly; differences can occur for various reasons, for example how well or poorly a team did in one-run games.)

The best team in 2018 was the Boston Red Sox with a won-lost record of 108–54 and a team WAA of +22.3, composed of +6.2 for position players and +16.1 for pitchers. This value of WAA suggests a won-lost record of about 22 games above .500, or 103–59. While the Red Sox ranked first in the American League in runs scored with 876 and third lowest in runs allowed with 647, the values of WAA indicate that their pitchers were further above average than their position players. The explanation for this apparent inconsistency is one of the features of WAA, which incorporates Park Factor. As usual, Fenway Park in 2018 was more favorable to hitters and less favorable to pitchers than the average park. In 2018, Mookie Betts had a WAA value of +8.9, the highest in the major league. Without Mookie Betts and with an average player in his place, the total WAA value for position players on the Red Sox team would actually have been negative (-2.7, calculated as +6.2 – 8.9).

The weakest team in 2018 was the Baltimore Orioles at 47-115 with a team WAA of  –22.9, composed of –15.6 for position players and –7.3 for pitchers. This suggests a won-lost record about 23 games below .500, or 58–104. As seems frequently to be the case with weak teams (such as teams losing more than twice as many games as they won), the Orioles’ record in games decided by one run was also weak, with 12 wins and 29 losses.

One more example to show how WAA relates player value to team performance: the 1927 New York Yankees. Considered one of the best teams of all time, the 1927 Yankees included six future Hall of Famers: Babe Ruth, Lou Gehrig, Herb Pennock, Waite Hoyt, Earle Combs, and Tony Lazzeri, as well as their manager, Miller Huggins. The team had a won-lost record of 110-44 and a team WAA of +33.4, composed of +26.7 for position players and +6.7 for pitchers. In the 154-game season then in use (where a record of 77–77 was average), this suggests a won-lost record of about 110–44, which happens to agree exactly with the Yankees record that year. Their run-producing ability was led by outstanding seasons for Ruth (+9.9) and Gehrig (+9.3), with major contributions from Combs (+4.4) and Lazzeri (+3.8).

In brief, the WAA concept provides an excellent method that is intuitively appealing for quantifying the performance of players and connects player performance with team performance in a systematic way.

Wins Above Replacement (WAR)

The summary definition of WAR from the Baseball-Reference website follows: “A single number that presents the number of wins the player added to the team above what a replacement player . . . would add.”  (This replacement player would come from the top minor-league level.)  A comprehensive history and discussion of the WAR concept is also provided on B-R.com. As noted in this discussion, “There is no one way to determine WAR. There are hundreds of steps to make this calculation, and dozens of places where reasonable people can disagree on the best way to implement a particular part of the framework. . . . WAR is necessarily an approximation and will never be as precise or accurate as one would like.”

The discussion includes the concept of replacement players and states, “When computing the value of a major league player, average is a poor baseline for comparison. Average players are relatively rare and can be expensive to acquire. . . . Replacement level players, by their very definition, are players easy to obtain when a starter goes down. These are the players who receive non-roster invites at the start of the year, or the players who are 6-year minor league free agents.”

While the computation of WAA and WAR are both complex and involve many steps, the computation of WAR is more subjective. The computation of WAR starts with WAA and adjusts the benchmark from the concept of an average (a straightforward statistical measure), to the concept of a replacement player. The replacement player concept is not at all straightforward, as reflected by the fact that it is calculated differently by different sources (e.g. Baseball Reference, Fangraphs). The calculation is further complicated by the fact that the best actual replacement player available to a team varies because the minor league players available vary from one team to another. An example of this is provided later.

It is clear from the definition of WAR and the discussion of the concept of replacement-level players that the primary motivation for developing WAR is not the performance level of baseball players in general, but rather the performance level as it pertains to replacing a major league player with an available minor league player.

The problem with this approach is that while the replacement-level concept may be very useful with regard to replacing a player, this does not mean that the replacement-level concept is preferable in general, or that WAR is preferable to WAA for general evaluations of player performance. In part because the WAR concept has been used widely to analyze the financial costs of replacing players and because there is an understandable focus among baseball journalists about players’ salaries, team salary totals, the financial worth of free agents, etc., WAR values are cited frequently. In contrast WAA values are rarely, if ever, seen in newspapers and magazines, but appear only (or with few exceptions) in the professional literature on the analysis of baseball performance. A related difficulty is that WAR values are used in the media with no discussion of their limitations.

Limitations of Wins Above Replacement (WAR)

We can start by looking at what using the WAR concept in place of the WAA concept does to our examples relating values for players with team performance. In the case of our average team — the 2018 Los Angeles Angels and their 80-82 record — the team WAR was +35.0 (composed of +26.0 for position players and +9.0 for pitchers). Unlike the team WAA value of +0.2, the team WAR value of +35.0 does not convey that this was an average team. One would have to dig into the technical details of the computation of WAR to find out that the benchmark for an average team is no longer a won-lost record of 81–81 and a .500 winning percentage, but rather a won-lost record of 47–115 and a .292 winning percentage. While a lot of research has gone into determining this benchmark, it has changed over time and reflects a lot of subjective decisions, as noted in the Wins Above Replacement Explainer quoted earlier.

Does the fact that the replacement-level benchmark of a won-lost record of 47–115 is equal to the actual performance of the 2018 Baltimore Orioles mean that they could have gone out and signed a team of replacement-level players and achieved the same result? This is highly doubtful. There is a big difference between the pool of talent at the top minor-league level (noted in the summary definition of WAR) and the talent actually available (the non-roster invites and 6-year minor league free agents, as noted earlier).

Historically, there are many examples of top minor league players who were not free to sign with a major league team of their choice or a team looking for a replacement player. The 1937 Newark Bears (with a .717 winning percentage) in the International League provide one notable example. This team was owned by the New York Yankees and was the top team in its minor league farm system, with several players who were good enough to have been starters on other major league teams in 1938, including batting champion Charlie Keller. He was kept at Newark for the 1938 season because the Yankees had a starting outfield of Joe DiMaggio, Tommy Heinrich, and George Selkirk.

While the fact that there are very few major league players who are not exactly “average” and that they can be expensive to acquire, as noted above, does not mean that the average major league player is not a useful benchmark — or the most useful benchmark — for general player evaluation. While it is nice to deal with distributions of values that conform to the classic bell-shaped curve (in statistical theory, a normal distribution) where the average (more technically,  the mean), median, and mode of the distribution are identical, these distributions exist primarily in statistical theory. A simple example would be the distribution of the expected number of heads in 100 tosses of a coin.

Statistical distributions in the real world are skewed, and the mean is most likely not the most frequent value. The distribution of US households by annual income provides another example. In this case, the distribution is skewed to the right (reflecting the fact that there are cases where the value is extremely high), and thus most cases have values below the mean.

The distribution of values of WAA provides another example. The distribution is skewed to the right with most cases having values below the mean. The primary explanation is that players who are way above average (say a WAA of 5.0+) typically will play in the large majority, if not all, of their team’s games. Players who are way below average (e.g., on pace for a WAA of –5.0 or less in a season) will not get to play very long in the major leagues. In 2018, 448 position players had 100 or more plate appearances, among whom 194 had a positive WAA (+0.1 or higher), 11 had a WAA of 0.0, and 243 (a majority) had a negative WAA (–0.1 or lower). In contrast, the corresponding WAR values of these 448 position players were 338 positive, 9 at 0.0, and 101 negative, reflecting that the benchmark for WAR values is well below the average major league performance.

In 2018, the top 10 position players, all of whom had over 600 plate appearances, had an average WAA of 5.8. Their average WAR was 7.9, suggesting that for full-time players, the average WAR is roughly 2.0 above the average WAA for a single season.

Three major observations about the WAR concept stand out based on the preceding discussion:

1. the WAR concept was developed originally with a focus on replacing a major league player with a minor league player, not on the general evaluation of player performance;
2. the implementation the of replacement-level concept is highly subjective; and
3. the WAR concept distorts the basic statistical properties of distributions such as the average.

These three observations led me to see if anyone had researched the issues raised by these facts. I found research published in 2012 by Adam Darowski comparing WAR and WAA at HighHeatStats.com.3 He showed that in addition to increasing the numerical value of a player’s career by switching from WAA to WAR, this increase is not consistent among players and results in tremendous differences in the ranking of players by their career performance.

His primary example of a player whose career ranking benefits from using his WAR value rather than his WAA value is Pete Rose. This is because Rose had many average or below- average seasons as measured by his WAA value — especially in the latter years of his long career — that still added to his WAR value or did not reduce it significantly. Darowski asks, when considering a player for the Hall of Fame, does one ask if “he was so much better than the AAA players of his day” or if “he was so much better than everyone else?” Darowski favors the latter criterion, and given this choice, divides a player’s WAR value into two categories: his WAA wins (due to being above average compared with other major league players) and his “showing-up wins” (due to being below average among major league players but better than the minor-league benchmark). There are some cases where a major league player’s performance was so far below average that his WAR value was negative (e.g., Pete Rose in 1981 and 1982, at ages 41 and 42, with WAA values of -3.4 and -4.0, and WAR values of -1.1 and -2.1, respectively.)

The term “showing-up wins” may seem a bit harsh and/or cynical since most players in any given year are likely to have WAA values below average, as explained previously. This does not mean that they do not deserve to play in the major leagues. However, Darowski’s term is used here because the focus is on overall performance compared to other players overall (e.g., does the player deserve to be considered for the Hall of Fame), not on who the team might replace him with if he is no longer available (e.g., injured or opts for free agency).

Table 1 is titled “WAA and WAR Comparison for the top 65 Position Players in Career WAA and in Career WAR: 1871-2018.” (See below.) I limited the lists to 65 players — about the number that can be included reasonably in a one-page table. The table is designed to illustrate how WAR values relate to WAA values for top players by dividing their WAR wins into WAA wins and showing-up wins, as suggested by Darowski. The two lists include 74 players: 56 players who appear on both lists, 9 players who appear on the WAA list only, and 9 players who appear on the WAR list only.

While the lists of the top 65 position players in WAA and in WAR include many of the same players, there is a pronounced and systematic bias. In general, players with less than the average number of career plate appearances show a drop in their ranking when switching from WAA to WAR, and vice versa. Among the top 10 players in WAA, Rogers Hornsby and Ted Williams (each with fewer than 10,000 plate appearances) drop from 5 to 9 and from 6 to 11, respectively. Among players in the top 65 in career WAA and with fewer than 8,000 career plate appearances, there were the following changes (all declines) in career ranking when switching from WAA to WAR: Dan Brouthers, 28 to 39; Joe DiMaggio, 30 to 42; Mike Trout (active), 37 to 99; Arky Vaughan (40 to 54); Johnny Mize, 45 to 61; Lou Boudreau, 50 to 104; Chase Utley, 53 to 95; Joe Jackson, 56 to 110; Gary Carter, 57 to 68; Billy Hamilton, 60 to 103; and Jackie Robinson, 62 to 114.

Among players whose rank is higher using WAR instead of WAA, Pete Rose, with the all-time record of 15,890 plate appearances, stands out (40 compared with 134). Other players with differences in rank of 20 or more include: Robin Yount, 43 versus 74; Paul Molitor, 45 versus 73; Sam Crawford, 48 versus 94; Reggie Jackson, 51 versus 89; Derek Jeter, 57 versus 114; and Rafael Palmeiro, 59 versus 122. Most of these players had over 12,000 career plate appearances.

WAA and WAR player rankings from Table 1 are shown in a scatter diagram in Figure 1 for 74 players. These include the 56 players who are among the top 65 in both WAA and WAR, the 9 players who are among the top 65 in WAA only, and the 9 players who are among the top 65 in WAR only. The Coefficient of Rank Correlation (rho) = 0. 62. As would be expected, among the 56 players on both lists, the maximum difference in rankings between WAA and WAR is relatively small; it is 17 for both Larry Walker (WAA of 39 and WAR of 56) and Brooks Robinson (WAA of 58 and WAR of 41). For the other 18 players (those who are in the top 65 on just one of the two measures, WAA or WAR, but not both), the differences in rankings are typically much larger. The largest difference in ranking is 94 for Pete Rose (WAA of 134 and WAR of 40). The largest difference in the opposite direction is 62 for Mike Trout (WAA of 37 and WAR of 99). (This difference may well decrease as Trout’s career progresses.)

The systematic bias noted above can be quantified by comparing the statistical relationship between career plate appearances and the change from WAA ranking to WAR ranking for the 18 players who appear on just one of the two lists. For example, Derek Jeter with 12,602 plate appearances rises 57 places (WAA rank of 114 to WAR rank of 57), and Lou Boudreau with 7,025 career plate appearances drops 54 places (WAA rank of 50 to WAR of 104). For these 18 players, the coefficient of correlation (r) between career plate appearances and change in ranking = 0.96. This means that the coefficient of determination (r squared) = 0.92. Thus 92 percent of the variation in the changes in going from WAA ranking to WAR ranking for these 18 players is due entirely to differences in their numbers of career plate appearances. This supports Darowski’s conclusion as described previously.  This is not to question the WAR concept for the purpose that it was developed, but to show that the WAR concept has a pronounced bias when it comes to evaluating overall career performance, including deciding which players should be considered for the Hall of Fame.

The focus in this analysis is on differences in rankings of players by WAA and WAR, as reflected in the discussion above and in Figure 1; however, it may be of interest also to summarize the statistical relationship among the values (as opposed to the rankings) of WAA and WAR. While this not a classic case of trying to quantify the effect of an independent variable (X) on a dependent variable (Y), such as the effect of education on income), WAA is designated here as the independent variable (X), and WAR is designated as the dependent variable (Y), reflecting the fact that WAR adjusts the performance benchmark from that of an average major league player to a top minor league player. Using linear regression, the least-squares line (in the form of Y = a + bX) showing this relationship is WAR = 28.358 + (1.112)(WAA). Consistent with this relationship, for the 74 players, the mean value of WAA is 56.3 and the mean value of WAR is 91.0. The largest difference between a predicted value (using the least-squares line) of WAR and the actual value of WAR for any of the 74 players is for Pete Rose. Given his WAA value of 29.7, his predicted WAR value is 60.7 compared with his actual WAR value of 79.7.           

Finally, it is interesting also to look at the percentage of a player’s wins in his WAR value that are due to “showing up,” as defined by Darowski and as discussed above. It is below 30 percent for some of the greatest players of all time: Babe Ruth (22.6 percent), Rogers Hornsby (23.2), Ted Williams (23.6), Barry Bonds (23.9), Mike Trout (24.3, active), Mickey Mantle (27.9), Willie Mays (29.5), and Honus Wagner (29.9). At the other extreme, the percentage of a player’s wins as defined by his WAR value that are due to showing up, is above 50 percent for several players among the top 65 in career WAR, led by Pete Rose at 63.5 percent.

Summary and Recommendations

The data presented in this paper show that the Wins Above Replacement (WAR) concept seriously distorts the evaluation of player performance in Major League Baseball by systematically understating the value of players with relatively short careers and overstating the value of players with relatively long careers (as measured by plate appearances) and are consistent with the findings of Adam Darowski. It is recommended that the evaluation of player performance be shown using values based on the Wins Above Average (WAA) concept and that use of the WAR concept be restricted to its original focus on replacing a major league player with a minor league player.

Table 1

Figure 1

(Click images to enlarge)

CAMPBELL GIBSON, PhD, is a retired Census Bureau demographer. His first article in the BRJ was “Simon Nicholls: Gentleman, Farmer, Ballplayer” published in Vol. 18 (1989).

Acknowledgements

I appreciate the comments and suggestions of two anonymous reviewers, especially the suggestion to add a scatter diagram.

Notes

1 It should be noted that the database for Baseball-Reference.com is much larger than that original Total Baseball dataset, including comprehensive statistics for minor league baseball, and that the database and website are updated almost continuously. The WAR values and statistical values pulled from Baseball-Reference.com reflect what was current on February 1, 2019, and will have changed by the time of publication of this article.

2 For a detailed explanation of these measures, see The Hidden Game of Baseball. For a shorter explanation, see the 8th edition of Total Baseball, pages 976-979.

3 http://www.highheatstats.com/2012/07/wins-above-replacement-war-vs-wins-above-average-waa/.

Traditionally, ballplayers would travel to Havana during the offseason to play winter ball—not just major league players, but also Negro Leaguers, many of whom played in Latin America before Jackie Robinson broke the color barrier in 1947 because of the more equitable treatment they received outside of the United States. However, Castro decreed that foreign imports were no longer allowed on any of the island’s diamonds.

For over four decades of this period of self-imposed isolation, the Cuban national baseball team, equipo Cuba, went nearly undefeated in international tournaments. Cuban baseball players competed in rickety stadiums that lacked any of the amenities associated with modern venues, but the crowds were large and loud every night. “Sports activities offered the citizen a means of individual expression, a way to compete, to achieve, and to accomplish something. In a non-capitalist, anti-individualistic society, such an opportunity was rare.”2

Castro exploited the incredible play of equipo Cuba as evidence of the socialist regime’s success and as a source of national pride. The creation of development academies for amateur athletes tethered baseball players to the state and made amateur baseball in Cuba a government-run operation.

Based on a cost-benefit analysis of the value of defection, I argue that strong familial and community ties prevented Cuban players from abandoning the national team after the 1959 revolution. However, after the fall of the Soviet Union in 1991 and legalization of the possession of the US dollar two years later, prominent players began defecting to the Major Leagues as those bonds started to break. A dearth of economic opportunities on the island triggered widespread player disillusionment with party ideology. Therefore, players such as Yoenis Céspedes, Aroldis Chapman, and Yasiel Puig who, had they been born decades prior, would have remained in Cuba, analyzed the incentives of defection and decided that exponentially higher salaries in MLB were worth the price of leaving the island.

My study examines the time between Castro’s takeover and the legalization of the US dollar on the island in 1993. The revolution altered how players were developed and subsequently indoctrinated with the socialist creed. When René Arocha, a pitcher on equipo Cuba, defected in 1991, he ushered in a new era of Cuban baseball in the US, but I have found that this moment alone was not enough to encourage a widespread exodus of baseball players. Instead, it was a combination of limited economic freedoms caused by the dissolution of the Soviet Union (and their financial support to the island) that led to the proliferation of equipo Cuba players filling spots on Major League rosters. Defection “began happening in earnest after the collapse of the Soviet Union because the Cuban economy, which was in shambles already, took a further dip and the players saw that their future was bleak.”3

Despite the government establishing academies for amateur volleyball, boxing, and soccer, baseball was the most popular sport on the island and deeply ingrained in the national consciousness. Castro wanted to make baseball his own in the same way he sought to reorder healthcare and education. Juan Linz explains in his book, Totalitarian and Authoritarian Regimes, that “the destruction, or at least decisive weakening of all the institutions, organizations, and interest groups existing before a new elite takes political power and organizes its own political structures is one of the distinguishing characteristics of totalitarian systems.”4 Castro stripped the game of its association with the United States and ushered in a new era—one completely under his control. Cuban baseball historian Roberto Gonzalez Echevarria notes that Castro took “a tremendous tradition, one that all Cubans agree is the essence of their identity, of being Cuban, and fused it with a state structure which supports the playing of the game, that creates the young ballplayers, finds them, uses them and develops them.”5

The timeless rules of baseball were unaltered so that when equipo Cuba played in international competitions they would not be at a disadvantage, but Castro eliminated many of the commercial features of sports. Even in 1959, corporate sponsors had taken over most major-league ballparks with Coca-Cola signs dotting the outfield walls from New York to Los Angeles. Castro, in his crusade against all things capitalist, saw to it there were “no paid advertisements in Cuban ballparks, just political slogans.”6 Instead of team owners, the Communist Party operated all organizations and stadiums throughout the island. Baseball therefore became not only a form of recreation, but also a means through which to raise the next generation of party loyalists.

Castro implemented a system where ballplayers were developed locally, in a similar fashion to the state-sponsored sports programs of the Soviet Union. Every two to three years, depending on their abilities, young athletes were promoted to different academy levels to foster their talents. Parents were encouraged to place particularly gifted children in special sports schools for early training at the regime’s expense. Youngsters with potential were thus offered luxuries: better food, comfortable living quarters, modern facilities, opportunities to travel and compete, and even special bonuses such as a car or pocket money.7

The government had a strong influence over amateur Cuban athletes at a very impressionable age. While in the US a Little Leaguer might dream of playing shortstop for the Yankees, in Cuba there was no higher honor than being named to the national team. When players were between thirteen and sixteen, the top athletes attended Escuelas de Iniciación Deportiva (EIDE). At these sports initiation schools, students divided their day between the field and classroom. Competition was incredibly fierce at each level. “Those baseball players who show exceptional promise at the EIDEs are sent on to the Escuela Superior de Perfeccionamiento Atlético (ESPA). There is one ESPA in each of Cuba’s fourteen provinces, plus one for the city of Havana.”8 Since players attend EIDEs and ESPAs in the province where they were born, strong bonds developed between a player and his community. The state made an intentional investment in its athletes both physically and ideologically with the expected dividend someday being their high level of play in international tournaments.

Wearing a jersey with “Cuba” emblazoned across your chest as a member of the national team was a tangible representation of the state, so Castro micromanaged the officials and players of equipo Cuba. This party oversight meant that in addition to having baseball prowess, a player had to also follow doctrine and ideology as outlined by the regime. Castro expected that anyone affiliated with equipo Cuba would properly represent the island—no errors were tolerated on or off the field.

Cubans had great pride and respect for their players who seemed to embody the ideals of the revolution. Player defections caused significant grief and heartbreak to fans who viewed many athletes like sons or brothers. Sigfredo Barros, a Cuban journalist, explained that “no one in the United States taught Arrojo to throw a sinker; he was taught that here in Cuba. Or the slider to Orlando, or Livan’s 93-mph fastball, or to field balls like Ordóñez does. We taught them those things here.”9 The references to Rolando Arrojo, brothers Orlando and Livan Hernandez, and Rey Ordóñez, all of whom defected from Cuba in the 1990s, underscore the pain many Cubans felt when players abandoned the national team.

Baseball, and its accompanying values, proved an effective vehicle for Castro to advance the objectives of his new socialist order. “The sports hero exemplifies the ideal disciplined worker, loyal revolutionary, and obedient soldier.”10 While there were few economic or social victories the government could cite, the Olympic gold medals in Barcelona in 1992 and Atlanta in 1996 equipo Cuba won seemed to vindicate the methods of the Communist Party. Castro merged sport with nationalism and ensured that the game advanced his authoritarian mission.

In a society of alleged equality, one man stood above all others. Every aspect of the Cuban regime, and baseball in particular, was meant to glorify the prowess of Fidel Castro. On the rare occasions when he spoke to American journalists, he cited multiple occasions when he was scouted as a pitcher by major league teams and even offered a contract. While most of these stories have been debunked, the narrative he constructed of himself as a legendary baseball player speaks to the importance of the game in earning the respect and devotion of Cuban citizens.

These four decades of spectacular play by equipo Cuba and backing by the Soviet Union resulted in a golden era for Cuban baseball. While Cuban players didn’t enjoy the same material comforts as their counterparts in the United States, for some the admiration and love communities lavished on them overcame the financial gap. Carlos Rodriguez Acosta, the current Commissioner of Cuban Baseball, explained that “almost all of our athletes, not only in baseball, but in all of our sports, are all very aware of what they represent and why they’re so great. They’re great because they’ve benefited from a free education system, because sport is the right of the people, because they don’t rely on sport to make a living, because health care is free and because they are given everything.”11 Rodriguez Acosta’s rhetoric was a hallmark of the curriculum each player learned at all levels of the state-sponsored development academies.

Just as they were instructed in how to properly throw a curveball or steal second base, party ideology was taught to Cuban baseball players. Ronald Wintrobe explains in his essay “The Tinpot and the Totalitarian: An Economic Theory of Dictatorship” that “the Party encourages and directs loyalty by maintaining and propagandizing an exclusive ideology that promotes the Party’s goals and helps establish and codify its reputation.”12 Every victory against the US was not just a win for equipo Cuba, but a triumph over capitalism and the Western world order. For a time, there were many Cuban athletes who believed unconditionally in Castro and the socialist state.

Omar Linares was one of those players and arguably the most talented third baseman in Cuban baseball history. He was the “poster boy for the deep-seated loyalty of the great majority of late-twentieth century Cuban diamond stars.”13 For over two decades he trumpeted the benefits of the Cuban baseball system, always remembering to pay homage to the state and development academies that taught him the game. “Linares often described his decision to remain in Cuba, making the equivalent of $20 a month plus a few perks not available to the average Cuban, as based upon the gains he and his family made through the revolution.”14

Since Linares was frequently approached by major-league teams to play in the US and could have left the island, albeit under covert methods, on multiple occasions, Linares’s cost-benefit analysis at the time favored remaining in Cuba. While the degree of his support of the system may have been amplified to serve the goals of the state, his comments to foreign journalists and Granma, Cuba’s official government newspaper, seem to be authentic representations of his feelings. After equipo Cuba beat the Baltimore Orioles in 1999 in an exhibition game, Linares proclaimed, “Commander-in-chief, the mission you gave us has been completed,” and he ended his battle report to the comandante en jefe with the words “Socialismo o muerte! (Socialism or death!) Patria o muerte! (Homeland or death!) Venceremos! (We will triumph!)”15 Linares, like other amateur Cuban baseball players, received no financial incentives for winning a championship. Nevertheless, he played with a tenacity and joy that transcended economic concerns.

After the fall of the Soviet Union, however, poverty became so dire that all Cubans, athletes especially, could no longer ignore the cost of remaining in a socialist state. The período especial (special period), which was the excuse used for broken machinery and lack of goods and services, disproportionately impacted baseball players. While some Cubans sold cigars to tourists or took on side work to secure extra cash, members of equipo Cuba were closely monitored by the party and unable to engage in any illicit activities. As “Cuba’s domestic GDP collapsed by an estimated 37 per cent, and 50 per cent of the economy lost purchasing power,”16 leaving the island was less of a political stance and more of a means of survival. In addition, “the years of productivity for an athlete, for anyone who depends on his or her body or performance is limited. So, the urgency to be able to use that talent is much greater than in the case of someone who has a much more intellectual type of job. These players felt that urgency after the Cuban economy dipped, and there was a sense of despair, now communism was a religion without a Rome or a Jerusalem.”17

Beginning in 1991, Cuban baseball players began to fully understand that other opportunities existed only ninety miles away. Once removed from the watchful eye of the party, Cuban defectors became more comfortable voicing their critiques of the government. Jorge Diaz, a defector and former member of equipo Cuba, explained, “in Cuba we won three straight championships. They would treat you to a beer, they’d pay for a night at the hotel with your family, but nothing more. One would ask for things that one needed and they would deceive you.”18 While national pride and love of country were ties that had kept players on the island, the tether snapped when baseball players were no longer able to scrape by on meager government handouts.

Baseball players’ repudiation embarrassed the Cuban government. Castro considered members of equipo Cuba to be the face of the revolution. When they turned their backs on the country that raised them, it suggested to the Cuban people that the party could be challenged. As defections have become far more common today (although the risks remain with tales of danger and bravery thoroughly outlined by the US media), the strength of the national team and its grip on amateur players has waned. Instead of staying in Cuba, top players have sought wealth and fame in Major League Baseball.

Notable Cuban Defectors’ MLB Career Earnings

(Click image to enlarge)

Inextricably linked to baseball defectors is the relationship between the United States and Cuba. “It has long been a part of American media policy to cheer on the Cuban baseball defector as a political and ideological story.”19 In this charged climate, there is more at stake than a championship or standing on the Olympic podium. Robert Huish explains in his essay, “The (Soft) Power of Sport: The Comprehensive and Contradictory Strategies of Cuba’s Sport-Based Internationalism,” that “Cuban sport should be understood as part of a broader development agenda, as well as an opportunity or avenue through which Cuba pursues its national interests.”20 When players leave the island, they are fighting party ideology and therefore constitute a threat to the regime.

The Cuban state baseball apparatus is faced with the dual problem of “players with little possibility of advancement and the unwillingness to provide the necessary economic stimulus for players to remain in the country.”21 While during the Mariel exodus thousands of Cubans left the island, it was the players on equipo Cuba who were disproportionately ostracized. “Those who migrated from Cuba to the United States were labeled gusanos (worms or traitors) by the Cuban revolutionary authorities and by many compatriots who remained on the island.”22

While great wealth and fame can await some talented baseball players who leave Cuba, it is still a harrowing journey that is difficult to execute alone. Joe Cubas has represented a number of Cuban defectors and is the mastermind behind the now famous “Joe Cubas Plan” which has become the blueprint for the entire baseball smuggling industry. After ferrying players off the island and establishing residency in a third country (thus circumventing regulations for MLB free agents and the embargo), he encourages high-priced bidding wars among the 30 major league clubs.23

While Cuba under Castro exhibited many of the textbook characteristics of authoritarian regimes and baseball was used by the state as a means through which to promote ideology, it is clear that defection is linked to economic considerations. After years of dynastic success on the world stage, the death blow to equipo Cuba was not due to a lower quality of play on the field or poor coaching but rather the political climate. The Special Period changed the variables players weighed when deciding to defect with the promise of financial security and a better quality of life trumping any debt they may have felt to their homeland.

Despite the many former equipo Cuba stars who now play for storied MLB franchises such as the Yankees, Red Sox, and Dodgers, the Cuban government refuses to acknowledge their achievements or forgive their transgressions. There is a fear that normalizing conversations about teams in the United States will encourage defection. Under this mentality, if the Cuban people were to know of defectors’ successes, it would undermine the socialist mission. Celebrating players in MLB, a business that adheres to the rules of the free market, would be tantamount to touting the benefits of capitalism.

The reign of amateur Cuban baseball from 1959 until the early 1990s is unlikely ever to be seen again. Today, “playing conditions, fan enthusiasm, and ballplayer morale have sunk to all-time lows. The national team heroes are no longer the country’s biggest news.”24 Names such as Omar Linares become the subject of debate among an older generation as the next wave of Cuban athletes set their eyes on defecting to join the major leagues. While players in Cuba’s top baseball league still only earn a few hundred dollars a month, MLB stars such as Yuli Gurriel and José Abreu rake in tens of millions of dollars over their careers.25 These major league standouts who, in a different era, under Fidel Castro, would have given anything to be a member of equipo Cuba now find themselves very far away from the island that first introduced them to the game.

After planning the World Series Trophy Tour for the Chicago Cubs in 2016, KATIE KRALL received a SABR membership from her twin sister as a present for her work with the team. In February 2018, she was selected as part of the inaugural class of the Major League Baseball (MLB) Diversity Fellowship. The program is designed to promote women and people of color into front office executive roles. Krall works in the League Economics & Operations department at the Commissioner’s Office in New York City and assists with player transactions, contracts, on-field discipline, and salary arbitration.

Notes

1. Milton H. Jamail, Full Count: Inside Cuban Baseball, Southern Illinois University Press, 2000, 29.
2. Julie Marie Bunck, “The Politics of Sports in Revolutionary Cuba,” Cuban Studies, Vol. 20, 1990, 127.
3. “Stealing Home: The Case of Contemporary Cuban Baseball.” http://www.pbs.org/stealinghome/debate/defections.html
4. Juan J. Linz, Totalitarian and Authoritarian Regimes, Rienner, 2009, 68.
5. “Stealing Home.”
6. Jamail, 110.
7. Bunck, 120–21.
8. Jamail, 39.
9. “Stealing Home.”
10. Bunck, 119.
11. “Stealing Home.”
12. Ronald Wintrobe, “The Tinpot and the Totalitarian: An Economic Theory of Dictatorship,” American Political Science Review, 1990, 867.
13. Peter C. Bjarkman, “Omar Linares,” Society for American Baseball Research, 2016. http://sabr.org/bioproj/person/ab3866fa.
14. Jamail, 32.
15. Jamail, 142.
16. Robert Huish, et al, “The (Soft) Power of Sport: The Comprehensive and Contradictory Strategies of Cuba’s Sport-Based Internationalism,” International Journal of Cuban Studies, Vol. 5 #1, 2013, 31.
17. “Stealing Home.”
18. “Stealing Home.”
19. Peter C. Bjarkman, Cuba’s Baseball Defectors: The Inside Story, Rowman & Littlefield, 2017, 54.
20. Huish, et al., 27.
21. Jamail, 7.
22. “Stealing Home.”
23. Bjarkman, Cuba’s Baseball Defectors, 159.
24. Bjarkman, Cuba’s Baseball Defectors, 199.
25. Mercer, Greg. “The Baseball Stars Who Ignore MLB to Stay Loyal to Cuba…and Canada.” The Guardian, Guardian News and Media, 9 Aug. 2018, http://www.theguardian.com/sport/2018/aug/09/the-baseball-stars-who-ignore-mlb-to-stay-loyal-to-cuba-and-canada.

The passengers on this small scale adventure include Sr. Ismael Séne, our magnificent intellectual host with his photographic memory, knowing all things baseball, old and new, Peter Bjarkman, the English-speaking master of Cuba’s modern game, our driver, and the camera wielding author, who planned this jaunt with no guarantee of success.

The inspiration for our one-day trip was a group of photographs from the winter ball season of 1927–28. They were taken at a ballpark in Güines, a small city of now 70,000, 50 km. or so southeast of Havana. The photos — a group of sixteen 7”x5” prints, mounted on decorative 10”x8” boards — started turning up in the capital city a few years earlier in an astounding state of preservation, arriving in small groups, until almost the entire collection was assembled (16 of 18 are present). The sauna-like climate on the island is rampantly destructive to paper, and photos usually suffer. Though I had been doing photo research in Cuban baseball for over fifteen years at that point, no picture had ever before appeared of Estadio Tropical Cerveza (Tropical Beer Park), nor had I seen reference to it, nor had I seen any mention of the photographer, Raphael Santiago of Calle M. Gomez 120, Güines, whose name was embossed in each print.

The most exciting feature of this group of photographs was not the record of the physical features of the park, nor the parade of old automobiles entering through the decorated gateway, nor the close up views of the well dressed fans, nor even the pre-game warm-up activity in front of the stands. Instead, it was a team shot of the Cuba Baseball Club, an integrated professional team from the top league in the country. This club, one of the most amazing to take the field in all of baseball history, was composed of big names from Cuba and an all star contingent from the US Negro Leagues.

Managing “Cuba” was Armando Marsans, one of the first Cubans to wear a major league uniform in the twentieth century, playing eight years in the American, the National, and the Federal Leagues. Marsans’ pitching staff features Willie Foster, newly of the Baseball Hall of Fame, Willie Powell, small and sturdy right-hander, along with Cuban Basilio “The Witch” Rosell. Sharing the infield and the outfield were Judy Johnson and Oscar Charleston, monster stars both in the Negro Leagues and in Cooperstown, Walter “Steel Arm” Davis, from the Chicago American Giants, Cubans Pelayo Chacón, who played in Cuba from 1908 to 1932, Cando Lopez, Francisco Correa, and José Perez. The catcher was Larry Brown, whose defensive skills and strong arm were legendary.

We were hoping we could find the site of this forgotten ballpark, as then the photos would take on more meaning, and we might even find some ghostly evidence of these long lost players. So, we headed south, past Cotorro, San Jose de las Lajas, and other suburban towns that ring the south side of Havana. Shortly after leaving the hubbub behind, we were passing horse carts on our two-lane road, along with reeking, wheezing agricultural trucks and 1930s tractors. In short order our tan colored Lada was driving along the main thoroughfare into town, where we stopped at Güines’ stadium, almost sparkling with its bright green grass and fresh coat of red and ochre paint. The stadium hosts a good number of games annually, involving the Havana Province’s three national series teams, Industriales, Metropolitanos, and Habana during the winter season, which usually runs from November to April. There was no ball game on this day, but the guard on duty was not sure where the old field had been, so he directed us into the center of town for more information.

On we went making inquiries, and found that, indeed, there was an old ballpark outside of town, though no one seemed to know its former name. Heading eastward for a short while, the houses soon grew farther apart, the city street grid disappeared, and after a few twists and turns we were parking across the street from what had been Estadio Tropical Cerveza. The old entrance had been replaced by a now weather-beaten, stylized gateway, which was connected to a high cement wall painted white. That outer, higher wall joined with the outfield wall to the north, and together they encircled the entire field. “352” was painted on the outfield wall where the cement baseline intersected it, matching symmetrically the right field line. Another shorter cement wall had been constructed within and parallel to the perimeter structure, separating the field from the spectators, to which were attached two cement above-ground dugouts. The grass was short, the pitching rubber and home plate still in place, so some kind of ball was still being played here. The baselines were composed of poured cement strips about 4 inches wide, sitting a little above ground level, no doubt a hazard for hustling runners and fielders playing close by. What we were looking at was a cement construction ballpark in total disrepair. Between the eras of the totally wood-framed Beer Park and the present day ruin, a reconstruction project had occurred, transforming the field into a 1930s-40s art deco style structure, one probably used extensively throughout the 1950s. In between the two parallel cement walls, now separated from the playing field, the crumbling cement foundations for the old grandstands were still clearly in place, forming patterns in the ground like concrete footprints.

By using the photos to match our locations on the field we were able to figure out where all the seating areas had been placed, where the cars parked, areas designated for pre-game warm-ups, and the location of the other field structures where four teams had posed. Since palm trees grow for hundreds of years, we thought we might match the trees in the photos with the trees of today, but younger palms had intervened.

We strolled about for most of an hour noting features that other photographs in the group revealed, like the location of the benches in front of the grandstands, or where the Cuba team players warming up five in a row intersected with their opponents, or the fact that the paved street we parked on did not exist in 1928, or how very large the park had been and still was. Back at the time of the photos, Tropical Cerveza could likely have held 10,000 fans. The photos from 1927 indicate that a crowd of such a large size could have witnessed the Cuba team in Güines.

We got an historical buzz, if not an ectoplasmic visitation. But as I turned my head to leave, I could have sworn that I saw from the corner of my eye long, tall Willie Foster, arms and legs in motion, throwing warm up tosses to Larry Brown, with Oscar Charleston shouting exhortations from the beyond.

MARK RUCKER is a photographic historian and a longtime SABR member. He was co-founder of SABR’s Nineteenth Century Research Committee with John Thorn, and has been involved in publishing since the mid-1970s. His companies Transcendental Graphics and The Rucker Archive provide access to rare and surprising images from long ago.

On the way to Güines, heading South from Havana, we encountered the past in the form of a horse cart. 

In the 1926–27 season the front gate of Estadio Cerveza Tropical was an elaborate entrance to the field, flanked by the proud owners of the facility.

The front gate of the old field at Güines in 2007, where Peter Bjarkman establishes the scale of the present day entrance.

Cars entering the complex for a game late in 1926.

In front of the grandstands, a pitcher from one of the Güines teams warms up before the contest. The crowd that has packed the grandstands is ready to start.

Today all that is left of the grandstands are the cement structures left in the ground. The camera is in a location which would have been behind the old stands.

The Cuba Base Ball Club warms up before a game at Güines in 1926. This remarkable team fielded stars at almost every position. Here we see warming up at Güines (L-R) Pepín Perez, Pelayo Chacón, Walter Davis hitting fungos, and behind his bat is Oscar Charleston. The four pitchers in the distance to the right are Willie Foster, Willie Powell, Basilio “Brujo” Rosell, and an unknown southpaw.

Long gone are the cheering crowds in the bleachers, the shouts of the vendors, and the crack of the ball off the bat. Instead, we see cinder block dugouts and cement walls, in the seldom-used field on the eastern outskirts of Güines.

A gathering of rooters posed for a photograph near the grandstand at Güines without revealing their team affiliation. Not even a logo. But they do provide a before photo for the after, which was taken in the same spot in 2007.

The fans in Güines came in all ages and sexes. This entertaining shot of los fanaticos, who filled the grandstand at Estadio Cerveza Tropical, shows the broad base of support the game had even in small towns in Cuba.

Where the fans once jumped and shouted, only the foundations are left.

Cuba Baseball Club poses during their visit to the Estadio in Güines. This stellar crew played together for only one year, and did not win the pennant. They were: Top row (L-R) Willie Foster, Larry Brown, Cando Lopez, Oscar Charleston, Willie Powell, unknown, Cuco Correa. Front row Pelayo Chacon, Judy Johnson, Rogelio Crespo, Basilio Rosell, Walter Davis.

Not surprisingly, geography is also an important determinant for the organization of university baseball, resulting in three regional groupings: the Canadian Collegiate Baseball Association (CCBA) operating from the Atlantic to Ottawa, the Ontario University Athletics (OUA) baseball group in Ontario, and the Canadian Colleges Baseball Conference (CCBC) in the west which lumps together colleges and universities in order to form a viable league.3

Finally, the monetary reality for university baseball is that while teams are often organized and compete at a varsity level, the vast majority are only partially-financing “competitive clubs” because U Sports and its provincial members (e.g. the OUA) do not recognize baseball as G1 (varsity) sport.4 In Canada, this distinction is particularly important. In the absence of either official university association recognition or NSO backing — in this case Baseball Canada — U sports, Canada’s university sport governing body, will neither recognize nor organize a national championship for university baseball.5

The Problem

Given these geographic, financial and bureaucratic impediments, university baseball in Canada has historically been siloed into three groupings offering their own championships: the OUA’s provincial championship, the CCBC’s conference championship in the west, and the CCBA’s “national” championship encompassing teams from Ottawa, Quebec, and the Atlantic. While the CCBA has been the closest thing to a bona fide “Canadian University World Series” it still has not been able to solve the problem of a truly national and inclusive tournament.6

The formation of two coach-driven conferences in the OUA (West and East) was deemed necessary for the 2019 season in order to make room for new arrivals Carleton and Ottawa. This makes it difficult for all teams to play each other the same number of times given the short 16-game Fall conference schedule. As a result, seeding for the open provincial tournament on the basis of teams’ win-loss records is an inherently flawed endeavor.

Of course, in the CCBA, the Northern and Atlantic conferences never played each other in the regular season and held their own playoff eliminations to determine seeds for their joint national championship. It is unclear how this will function in the future with the departure of Carleton and Ottawa.

Between initial submission and final revision of this paper, the CCBA announced it would cease operations in July 2019. Three Quebec teams (Concordia, Montreal, and McGill) have been, at least temporarily, orphaned and unaffiliated in the 2019 season. The remaining Atlantic conference teams have formed as the new Atlantic Collegiate Baseball Association (ACBA).7 This realignment has, for now, severed any connection between the Atlantic clubs and their former competition in central Canada.

These developments only exacerbate a longstanding problem. Even if former Atlantic Conference CCBA (now ACBA), Quebec, OUA, and CCBC university conference teams somehow found a way to work together to create a national championship of university baseball — a unified Canadian University World Series (CUWS) — how would eligible teams be seeded when inter-conference play is rare or absent and no agreed upon playoff format or elimination system currently exists or is ever likely to be implemented?

A Potential Solution

The purpose of this article is to explore the feasibility of an RPI ranking system for Canadian university baseball.8 In the absence of playoff eliminations, and where inter-conference play is sparse, an RPI-based ranking system has, for example, proven useful — albeit controversial — in the US college basketball context.9

The Rating Percentage Index (RPI) is the most commonly used method for ranking a large number of teams that play a relatively small schedule. Most famously adopted in the NCAA, RPI is used to rank teams nationally when most teams never have an opportunity to play one another. The premise of the RPI is that since most teams do not play each other, it would be unfair to rank teams based on wins and losses as in the NFL, NBA, and MLB, or based on a points system as in the NHL. Instead, RPI uses the strength of a team’s schedule in order to judge the quality of their play.

RPI is a mathematical calculation of a team’s strength of schedule. It is the sum of three components: Winning Percentage (WP), Opponent’s Winning Percentage (OWP), and Opponent’s Opponent’s Winning percentage (OOWP), each of which is weighted differently. The Formula for RPI is as follows:

RPI = (0.25 * WP) + (0.5 * OWP) + (0.25 * OOWP)

A team’s WP is the percentage of games that a team wins, expressed — in a form similar to batting average — as a decimal to three digits. This is calculated by dividing the total team wins by total games played. WP accounts for 25% of the RPI calculation. The following is an example of a WP calculation:

• Team A: 4-0
• Team B: 1-3
• Team C: 1-3

• Team A WP = Number of Wins / Number of Games Played = 4 / 4 = 1.00
• Team B WP = Number of Wins / Number of Games Played = 1 / 4 = 0.25
• Team C WP = Number of Wins / Number of Games Played = 1 / 4 = 0.25

And so, we add 25% of each total to each team’s respective RPI. That is, 0.25 for Team A and 0.0625 for Teams B and C.

A team’s OWP considers the winning percentage of teams faced. The calculation is a bit longer than that of WP. It averages the winning percentages of teams faced for every game not including the outcomes of games including the team whose OWP is being calculated. OWP accounts for 50% of the RPI Calculation. Using the same example for the WP Calculation:

• Team A: 4-0
• Team B: 1-3
• Team C: 1-3

Team A goes 2-0 against Team B. Team A goes 2-0 against team C. Team B goes 1-1 against Team C. To calculate Team A’s OWP, we must first find the WP of teams B and C excluding games involving Team A:

• Team B WP: 0.500
• Team C WP: 0.500

Now we may calculate Team A’s OWP:

= Team B WP (0.500) * 2 (games played between Teams A and B)

+ Team C WP (0.500) * 2 (games played between teams A and C) / Games Played by team A

= (1.000 + 1.000) / 4

= 0.500

Thus, Team A’s OWP is 0.500 and 0.250 is added to their RPI. This process can be replicated to find Team B (OWP of 0.500, 0.250 added to RPI) and Team C’s (OWP of 0.500, 0.250 added to RPI) OWP.

A team’s OOWP considers the OWP of teams faced similar to how OWP considers the WP of teams faced. The calculation is similar in length of the OWP calculation, however, at this point in the RPI process the work has already been done and we must only average out the OWP’s of the opponents. OOWP accounts for 25% of the RPI Calculation.

Expanding on the previous example in order to Calculate OOWP:

• Team A: 4-0
• Team B: 1-3
• Team C: 1-3

• Team A OWP: 0.500
• Team B OWP: 0.500
• Team C OWP: 0.500

• Team A OOWP = Team B OWP (0.500) * 2 (games played between teams A and B) + Team C OWP (0.500) * 2 (games played between teams A and C) / Games Played = (1.000 + 1.000) / 4 = 0.500
• Team B OOWP = Team A OWP (0.500) * 2 (games played between teams B and A) + Team C OWP (0.500) * 2 (games played between teams B and C) / Games Played = (1.000 + 1.000) / 4 = 0.500
• Team C OOWP = Team A OWP (0.500) * 2 (games played between teams C and A) + Team B OWP (0.500) * 2 (games played between teams C and B) / Games Played = (1.000 + 1.000) / 4 = 0.500

Thus, each team’s OOWP is 25% of 0.500, and so 0.125 is added to their RPI.

In this example, the OWP and OOWP for each team would all have worked out to be the same, this will not be the case in every scenario, of course, but the point here is to demonstrate how to calculate these numbers. The separating factor for the teams in this particular example of RPI rankings would, of course, be their winning percentages (WP) given that all other factors were equalized. The RPI rankings for the example used would look like this:

• Team A RPI = (0.25 * WP) + (0.5 * OWP) + (0.25 * OOWP) = (0.25 * 1.0) + (0.5 * 0.5) + (0.25 * 0.5) = 0.25 + 0.25 + 0.125 = 0.625
• Team B RPI = (0.25 * WP) + (0.5 * OWP) + (0.25 * OOWP) = (0.25 * 0.25) + (0.5 * 0.5) + (0.25 * 0.5) = 0.0625 + 0.25 + 0.125 = 0.4375
• Team C RPI = (0.25 * WP) + (0.5 * OWP) + (0.25 * OOWP) = (0.25 * 0.25) + (0.5 * 0.5) + (0.25 * 0.5) = 0.0625 + 0.25 + 0.125 = 0.4375

Method

In order for our RPI calculations to be useful we make certain assumptions. First, there must be some inter-conference competition to link teams in the standings. This is the only epistemic basis for ranking teams across Canada from 1 to 20. As a result of this presumption, CCBC teams are excluded from our analysis because while not all teams need to play one another, some teams must cross over. The CCBC, more importantly, plays in the Spring-Summer while the remainder of teams play in the Fall. This does not, however, preclude their participation in a CUWS.10

Second, we have used post-facto results culled from CCBA competition at national championships in 2016, 2017, and 2018. Normally, the RPI would be used to determine if teams qualified for such a tournament in the first place but, as we have noted, we needed the data for our model.

Third, regardless of overall ranking, a Canadian University World Series would likely adhere to some regional representation. Under the CCBA, seeds were awarded on the basis of finishes by Northern and Atlantic playoffs providing for an equal representation from both conferences. In U Sports competition, all national championships also proceed from regional playoff eliminations. In the following section, we follow these same assumptions for interpolating seeds for hypothetical 2016, 2017, and 2018 CUWS.

In the Tables below we rank all participating teams in the OUA and CCBA from 2016 to 2018 by season. We use all available data culled from GameChanger, Pointstreak, and OUA Presto results. We also include all available inter-conference, pre-season, and playoff scores.

Results

Applying the RPI calculation to our dataset by season we arrive at the following rankings for 2016, 2017, and 2018.

Table 1

Table 2

Table 3

(Click images to enlarge)

The results at the top end of the spectrum are not surprising. Teams that had excellent win-loss records and success in play-offs also placed very high in the overall rankings. McGill won three CCBA championships in this period and had the best overall win-loss record. They had won 30 consecutive league games until Carleton beat them in 2018.11 Not surprisingly, McGill ranked first in RPI in each season. The 2016 OUA champs, Western, ranked second in that year while perennially strong programs such as Laurier (2018 OUA champs) and Brock also ranked in the top five each season. Other notables include 2018 CCBA finalist New Brunswick and 2017 OUA champs University of Toronto who also finished in the top five in the years they made championship appearances.

There are some surprises from 6th to 10th however. Contrary to the common assumption that the Atlantic conference, which is made up of smaller schools, is not as strong as the Northern conference or the OUA, Atlantic teams Acadia or Saint Mary’s ranked above CCBA Northern teams like Concordia and Carleton in RPI. This can be better understood by paying closer attention to the way RPI is calculated in our discussion on limitations. Other RPI calculations, for example, have taken into account conference strength. We do not do so in this analysis.

By way of illustration, we also seeded eight teams in a series of hypothetical Canadian University World Series for each of the 2016, 2017, and 2018 based on RPI and regional/conference representation. We selected the highest RPI ranked team by region. As was the practice in the CCBA, one spot is reserved for the host team. We simply reproduced those same hosts in our model. As the more isolated CCBC (West) did not play inter-conference games, included two-year colleges in its schedule, and was excluded from our calculations, we seeded the highest finishing four-year university team at the CCBC championship tournament as the western representative. Finally, as was the practice in the CCBA national championship, we made room for wild card entries. In our case, after regional seeds were determined, we took the next two highest RPI ranked teams that had not already been seeded.

Table 4

Table 5

Table 6

(Click images to enlarge)

Once again, given overall win-loss records, playoff success, and standings, the teams represented in these make-believe national championships of university baseball are not controversial representatives. Each of these teams had very strong records with a history of success in their respective conferences.

Despite determining seeds based on conferences/regions and including host teams, most of the teams in each of the three successive hypothetical World Series we seeded had very high RPI rankings. If we eliminate the Western seed (CCBC), for which we have no RPI score, and the host team, for which placement is automatic, of the remaining qualifying teams, 6 of 6 (or 100%) in each of 2016, 2017 and 2018 were ranked in the top eight for RPI. Thus, despite regional seeding considerations, the CUWS consisted of the top teams in the country.

Of course, these hypothetical seeds are partially a post-facto mockup. Any agreed upon process that accepted a unified Canadian University World Series would set its own parameters around qualifications, regional representations, and even the number of teams included. We have simply adopted the closest approximation of existing practices in our model. In the process, however, the RPI seems to largely confirm the strength of baseball programs across the country as demonstrated in actual playoff and championship results over the last three seasons.

Limitations

As effective and convenient as RPI is for comparing teams, it also has one foundational flaw: no ranking system can compare how two teams would stack up against one another quite like having those teams play head-to-head. There is no way to fix this. Unless, of course, the University of New Brunswick in the Atlantic flies to St. Catharines in Central Canada to play Brock in a weekend double header, or Queen’s University in Eastern Ontario wants to travel to Wolfville, Nova Scotia to play Acadia. As we mentioned, this is highly improbable as it involves significant interprovincial and trans-Canada travel. Moreover, for win-loss records to be the basis of rankings, the schedule would have to be balanced and complete so one could properly seed teams based on head-to-head competition. In the absence of such a schedule, we have the RPI.

Yet, what many analysts particularly dislike about the RPI formula is that so much weight is placed on the question: “How good are the teams you play?” There are three accompanying limitations associated with this weighting that affects the rankings we have presented in this paper: (1) conference strength, (2) the use of post-facto results, and (3) the importance given to pre-season games. We deal with each of these below.

1. Conference strength

As mentioned, seventy-five per cent of the RPI calculation has nothing to do with the team itself and everything to do with how the teams it played performed, and how the teams that those teams played performed. A key problem with the formula is that a team can be rewarded more “RPI points” after losing to a great team than after defeating a bad team. This is because, as mentioned, 75% of the calculation is all about the rest of the league, and not the team in question.

From 2016 to 2018, OUA teams played CCBA Northern Conference teams 26 times in pre-season or inter-league competition. The vast majority of these games involved five-time CCBA champion McGill and, to a lesser degree, perennial runner-up Carleton: teams that posted high win percentages in league play. Not surprisingly, the CCBA Northern teams had a win percentage of .654 (16-8-2) against OUA competition over that three-year period.

Due to the limited amount of inter-conference competition, teams in the Atlantic were statistically firewalled from being beaten by their Northern conference opponents except in the CCBA national tournament. Moreover, the Atlantic conference typically had a less skewed differential in win percentage between teams resulting in higher OWP and OOWP compared to the Northern conference and OUA. Finally, Atlantic teams repeatedly benefited from taking turns losing, yes losing, to undefeated non-conference CCBA affiliate team Holland College that was included in results and standings but ineligible for playoff competition because of its 2-year college status. This causes significant problems for making sense of the final rankings.

By way of example, Saint Mary’s ranked higher in RPI than every Northern conference team except McGill in 2016 and 2017. Acadia did the same in 2018.  Yet from 2016-2018 Acadia and Saint Mary’s were a combined 1-11 (.083) vs. Northern conference teams at the CCBA national championship, and were outscored 126-18.12  Despite these asymmetrical head-to-head results, Saint Mary’s (6-6) still outranked Carleton (14-10) Montreal (7-5), and Concordia (11-13) in RPI in 2017.

Conference asymmetry is a common issue faced by US ranking analysts who have built models to correct for Strength of Schedule (SOS) in RPI calculations.13 The RPIs are calculated here without SOS correction, though there is evidence to support the need for such corrections in future ranking systems. This is especially true considering the CCBC, like the Atlantic conference, does not play any inter-conference games with other Canadian university teams and includes non-university teams in its schedule.

2. Post-facto results

In this analysis we have used results that include CCBA nationals competition to allow for some inter-conference reliability (between Northern and Atlantic conferences of the CCBA) and to lend credibility to the notion that ranking Canadian university baseball teams from 1 to 20 is possible.

Of course, while we required these results to allow for a more robust statistical dataset, the results are based on games that should have ostensibly only taken place after RPI results were considered in deciding the teams receiving seeds to the championship. RPI scores in the future could not make use of these results except if calculations straddled two seasons as a rolling average or, more preferably, if teams intentionally played select inter-conference games as has already been happening in the OUA for 2019.

3. Pre-season games

Inter-conference games between OUA and CCBA Northern teams have been inconsequential on standings, rank, or seeding. Unlike their relevance in US college competition they have no bearing on how Canadian university baseball teams place, and in the absence of a unified national championship they are treated as exhibition games with little more than pride in the balance.

As a result, these games are often considered warm-ups for the season, when coaches test position players and pitchers, do not field their top lineups, and sometimes allow games to end in a tie. Given this reality, one could argue their use in our analysis is a dubious choice but, once again, without the inclusion of these results there would be no theoretical basis to rank OUA teams alongside CCBA teams.

Of course, if RPI was applied to these games and these results mattered for ranking seeds for a CUWS, this would surely change the nature of competition in these contests.

Conclusions

We have demonstrated the feasibility of using an RPI system for ranking Canadian university baseball teams across the country. No secondary ranking system can replace head-to-head play and qualifying playoffs, but in a short Fall season with limited inter-conference play the RPI could be useful for the future development of Canadian university baseball.

The RPI, as we have calculated it in this analysis, has limitations. It does not take into account conference strength, especially when inter-conference play is limited. It over-states the importance of pre-season and exhibition games and uses post-facto playoff results. All of these issues are correctable in future calculations of RPI, especially if there is a coordinated effort to make the results more reliable through planned inter-conference scheduling, as has been long-established in the NCAA.14

Despite its limitation, RPI is a relatively effective ranking system. While some organizations, such as NCAA basketball are using newer metrics,15 other programs such as state high school football associations are adopting the RPI.16 Indeed, there are just as many critics of these newer metrics as the RPI.17 Eight years ago, sabermetrics experts considered a potential ranking index (the PING) for NCAA baseball before regionals, super-regionals, and an accepted national qualification path to Omaha and the College World Series was established through head-to-head competition.18

Comparing a team’s strength of schedule through RPI is the best available, independent method for comparing teams that cannot play one another. Future formulas could take into account conference strength and control for non-conference results. In the end, the RPI offers a tested and objective method for ranking Canadian university baseball teams toward ascertaining their qualification for a potential Canadian University World Series.

GEORGE S. RIGAKOS is Professor of the Political Economy of Policing at Carleton University, where he also manages the university’s baseball program.

MITCHELL THOMPSON is a second year statistics student majoring in mathematics at Carleton University.

Notes

1 Canadian Collegiate Baseball Association. 2019. “History.” BaseballReference.com Accessed June 11, 2019. https://www.baseball-reference.com/bullpen/Canadian_Collegiate_Baseball_Association

2 Canadian Collegiate Baseball Association. 2019. “History.” Accessed July 25, 2019. http://ccba-abcc.pointstreaksites.com/view/ccba-abcc/about/history

3 The University of Windsor, across the river from Detroit, participate in the US-based National Club Baseball Association (NCBA) but were granted entry to the OUA provincial tournament from 2017. Similarly, the University of British Columbia (UBC), based in Vancouver, also plays across the border in the National Athletic Intercollegiate Association (NAIA) and does not compete against Canadian baseball teams. As neither team plays against Canadian university opposition they are omitted from this analysis.

4 U Sports is Canada’s national governing body for university sport, equivalent to the NCAA, and formerly named Canadian Intercollegiate Sport (CIS).

5 National Sport Organizations (NSOs) in Canada are legislatively recognized bodies for the management of amateur sport in the country. There are currently 58 NSOs in Canada — Baseball Canada oversees amateur baseball.

6 George Rigakos, “A beginner’s guide to Canadian university baseball.” Canadian Baseball Network. (December 16) Reposted. Accessed June 11, 2019. https://www.curavensbaseball.com/a-beginners-guide-to-university-baseball-in-canada/

7 The demise of the CCBA and the appearance of the ACBA were announced through social media on Facebook July 25, 2019. https://www.facebook.com/CanadianUniversityBaseball/photos/a.2070884913221857/2258906037753076/?type=3&theater and the takeover of the former CCBA account by ACBA on Instagram: https://www.instagram.com/atlanticcba/

8 “How to Calculate RPI and What it Means to Handicappers.” madduxsports.com. Accessed February 3, 2019. http://www.madduxsports.com/library/cbb/how-to-calculate-rpi-and-what-it-means-to-handicappers.html

9 Alex Kirshner, “Yes, USC should have made it to the NCAA tournament.” SBNation. (March 11) Accessed July 9, 2019. https://www.sbnation.com/college-basketball/2018/3/11/17104676/usc-snub-ncaa-tournament-march-madness-2018

10 In 2018, the University of Calgary applied for membership in the CCBA and was accepted but ultimately could not participate as no other western team agreed to play them in a qualifier — a condition set out by the CCBA. The principle author of this paper is also the former President of the CCBA who received the application and membership cheque from the University of Calgary. A provisional agreement was worked out where if at least four members of the CCBC also joined the CCBA the top finisher in the preceding year would be invited to the CUWS. While these conditions were never satisfied, such staggered seedings are not alien to Canadian baseball. The same principle is applied during Baseball Canada’s Sr. men’s championship and in much international baseball competition. For university baseball, of course, the limitations are obvious. Depending on turn-over senior student-athletes graduate and freshmen arrive, the complexion and competitiveness of the team will also change.

11 CU Ravens Baseball. 2018. “McGill’s historic winning streak snapped by Carleton at 30 games.” (September 10). Reposted from CCBA. Accessed July 8, 2019. https://www.curavensbaseball.com/mcgills-historic-winning-streak-snapped-by-carleton-at-30-games/

12  Their only win came in 2016 when Saint Mary’s upset McGill in round-robin play 3-2.

13 James, Crepea, “Pac-12 weighing 20 game basketball schedule, massively raising non-conference standards.” Oregon Live. (May 1) Accessed July 8, 2019. https://www.oregonlive.com/collegebasketball/2019/05/pac-12-weighing-20-game-basketball-schedule-massively-raising-non-conference-standards.html

14 Of course, it cannot go unstated that some teams will attempt to manipulate their inter-conference schedule to best boost their RPI. See: Jesse Newell, “How KU basketball won the scheduling game… again.” The Kansas City Star, June 29, 2018. Accessed September 12, 2019. https://www.kansascity.com/sports/college/big-12/university-of-kansas/article214096929.html

15 Marc Tracy,  “R.I.P. to the R.P.I.: Selection committee breaks out new math,” New York Times, March 15, 2019, Accessed July 8, 2019. https://www.nytimes.com/2019/03/15/sports/ncaa-bracket-selection-sunday-net-rating.html

16 C. Carnahan, “Football RIP ranking system clears final hurdle for 2019.” Orlando Sentinel,January 28, 2019. Accessed June 1, 2019. https://www.orlandosentinel.com/sports/highschool/os-sp-hs-fhsaa-football-0129-story.html

17 Neil Greenberg, “The NCAA’s lousy new metric is going to make March Madness even crazier,” Washington Post, December 18, 2018. Accessed July 8, 2019. https://www.washingtonpost.com/sports/2018/12/18/ncaas-lousy-new-metric-is-going-make-march-madness-even-crazier/?noredirect=on&utm_term=.8a5887a2f735

18 Philip Yates, “The PING ratings: A method for ranking NCAA baseball teams,” SABR Baseball Research Journal, Fall 2011. Accessed July 9, 2019. https://sabr.org/research/ping-ratings-model-rating-ncaa-baseball-teams

Thanks to MLBAM, I have the precise time down to the second that each pitch was thrown in every game in 2018 — with the exceptions of the two games played in Puerto Rico and the three in Mexico — a total of 717,410 pitches. That works out to just under 148 pitches per team per game.

First I need to clarify exactly which pitches I studied. “Time between pitches” is the amount of time after a pitch before the next pitch is thrown. This only applies to consecutive pitches to the same batter. Therefore, the last pitch thrown to each batter does not apply because there is no “next pitch” to him. When these “last pitches” are excluded, the total number of relevant pitches drops to 511,728, which is still an impressive sample size. The overall average interval for all pitches across all situations in 2018 was 23.8 seconds. Of course, there are many interesting ways to subdivide this number.

In addition to the interval between pitches, I studied the time taken for the following:

• Between pitches
• Mound visits
• Between batters
• Between innings
• Substitutions
• Replay challenges
• Injuries
• Ejections

I also looked at the length of each inning since many have reported slower play in later innings.

Table 1 has the basic data for time elapsed after each different pitch result for bases empty situations and those with a runner on first alone.

The bases are empty for 58% of all pitches, so the first column confirms Malone’s conclusion that when the ball is not hit, the proposed 20-second clock would solve a problem that doesn’t actually exist. These are averages, so of course some values are less and some more, but overall the bases-empty situation provides little opportunity for a rule intervention to speed up the game; pitchers are already meeting this standard.

Table 1 also shows that the time increases after a foul ball compared to pitches when no contact is made. This is not surprising. Every foul ball results in a new ball being put in play, which takes more time than continuing to use the same ball. There is greater variation here, as well, since a ball fouled at the plate will not slow things nearly as much as a long foul into the stands.

There is a man on first alone 18% of the time and the second column presents the average intervals in this situation. All other situations combined add up to 24% of pitches. It is conventional wisdom that the game slows down when someone gets on base and these numbers certainly support that position. The average increase is 8.1 seconds across all pitch results. 

Pickoffs

We must consider another major feature of having a man on first, namely pickoff throws. I documented 11,194 throws to first in 2018, 10,755 by pitchers and 439 by catchers. The pickoffs added an average of 25 seconds to each pitch interval although there was a wide variation. When the overall average time for pickoff attempts is subtracted from the 28.4 second interval for a runner on first, then the time between pitches drops to 22.9 seconds. In other words, pickoff attempts at first account for about two thirds of the increase found with having a runner on first. To complete this thread, the other runner situations differ very little, with a combined effect of adding about 1 additional second to the time for a runner on first only.

Mound Visits

Mound visits were restricted in 2018 for the first time with a limit of six per game for each team.  This limit has been reduced to five for 2019. I began noting mound visits in July of 2018. The average time consumed by a mound visit is 81.5 seconds, even though the rules are clear that the visit itself is limited to 30 seconds. The 81 second interval is the actual time between pitches whereas the 30 second clock starts when the manager or coach has left the dugout and does not include the return trip to the dugout, accounting for the wide difference between the rule and the reality. Player visits to the mound are also counted, but the rules do not specify how to time those. If a mound visit ends up in a pitching change, then it does not count against the limited number for the game and I did not count them in my average time.

Time Between Batters

The average time between batters within an inning is 54 seconds. Again this is the time from the last pitch to the previous batter and the first pitch to the next one. I noticed interesting differences in this time for different innings as shown in Figure 1.  The horizontal line is the average for all innings to allow easier comparison.

The value is low in the early innings and then it rises with a peak in the 7th to over 62 seconds, which is almost 15 seconds more than the quickest time in the second inning. The increased time in later innings makes sense as the game pressure mounts and it is reasonable for both batter and pitcher to take a little extra time to get ready. All extra innings are combined as 10. The one point that stands out is in the 9th which has a remarkable drop from the 8th and 7th innings. Two years ago in New York I showed that 47% of games had a margin of three or more runs when the 9th inning started and the team in the lead won 97% of those games. I suggest that the drop I found here reflects the reality there is less deliberate preparation by either the batter or the pitcher since so many games are clearly decided by this point. If a game goes beyond 9 innings, then it is reasonable that the time increases since the games are obviously closer.

Time Between Innings

I found the average time between innings to be 2 minutes and 42 seconds. This is interesting in light of the MLB pace of play rules put into effect for 2018 which set different limits based on the nature of the television broadcast of the game, as shown in Table 2:

I did not look at postseason games. According to MLBAM, there were 62 games designated as national television games in 2018 as opposed to 2368 local television games. The average time between innings for the locally televised games was 2 minutes and 41 seconds and for the nationally televised games it was 2 minutes and 55 seconds, a difference of 14 seconds. In any case, the observed times are well beyond the stated limits, especially for the locally televised games. However, we have to consider when the official clock is started at the end of each half-inning. MLB issued very precise descriptions of how the timing is to be done including different starting details when a relief pitcher is entering the game. The average time between innings also changed significantly by inning, as shown in Figure 2. 

The horizontal line presents the average for all inning changes and the other two lines show the  changes after the top and bottom of an inning. There are two striking features to me in this figure.  First, the times get progressively longer as the game proceeds just as the breaks between batters do, and second, the break after the top of the 7th inning is much longer than all the others. In fact, it is 17 seconds longer than after the bottom of the 7th. Everyone will immediately realize this reflects the “7th inning stretch,” but there is another wrinkle. You may recall that most teams now play “God Bless America” during the 7th inning stretch at Sunday games. There are three notable exceptions: the Yankees play this song in the 7th inning of every game, while the Blue Jays and A’s don’t play it at all. There were 391 games played on Sundays in 2018, to which I added the Yankees non-Sunday games and subtracted the Toronto and Oakland games. That gave a total of 430 games with God Bless America and 2002 games without it, presumably all of which included the traditional singalong of “Take Me Out to the Ballgame” (except for the Orioles who play “Thank God I’m a Country Boy”). The breakdown for these games in shown in Table 3.

The extra one minute and 11 seconds consumed by “God Bless America” is pretty dramatic since it is played in 17.7% of all games. Once again we need to remember that the times I found are from the last pitch to the last batter of the inning to the first pitch of the first batter in the next inning. However, it is clear that the actual times do not correspond to the carefully prescribed timing procedures promulgated by MLB.

Substitutions

Substitutions are another kind of event that takes extra time, of course. The most common type is a pitcher change. Table 4 has what I considered.

As expected, the mid-inning substitution of a pitcher takes the greatest amount of additional time: over two minutes more than a new pitcher at the start of an inning. One of my surprising results from my previous study is that the number of mid-inning pitching changes has not changed almost at all in the last 25 years, even though the total number of relievers per game has increased steadily since 1975. This is because most pitching changes are made at the inning break rather than mid-inning.

Replay Challenges

We now live in the age of replay challenges and they constitute another significant interruption. MLB reports the time taken for each review but by their definition the timing of the challenge starts when the umpires commit to the review. My numbers again are the actual elapsed seconds before the next batter or pitch. Once again there is a difference between challenges at the end of an inning, the end of a batter appearance or the middle of a batter appearance. These details are in Table 5.

The “End of Batter” and “End of Inning” data have to be looked at carefully, since there is already time consumed by these events. The numbers I report in Table 5 have had these challenge times removed. The properly weighted average for these events is 3:05. MLB reports an average of 1:28. Again, their timing starts with the request and ends with the decision from New York, but my measured average time for the interruption is more than double their reported time.

Time to Play Each Inning

The time taken to play a given inning also changes during the course of a game, partly reflecting pitcher subs, but not entirely. Figure 3 shows the values for each inning from the first pitch of the inning to the last.

The data for the visiting team are in the bottom line and for the home team in the top line. It is interesting that the home innings take longer on average in all cases, with a difference of 12 seconds in the 1st to 35 seconds in the 7th — an average of 22 seconds. There is a drop of 36 seconds in the average from the 1st inning to the 2nd and then a fairly steady rise through the 7th. Note that this pattern mimics the differences between batters that we saw before. When these individual half-inning values are summed, we find that the average 8.5 inning game has 2 hours and 12 minutes of actual playing time and the average 9 inning game has 2 hours and 20 minutes of play.

Individual Pitchers

I also looked at the time taken by individual pitchers since one would reasonably expect variation here. In order to reduce noise in the data, I only considered pitchers who threw at least 100 pitches of the “interval” type I examined here with the bases empty. There were 575 pitchers who met this criterion with the average ranging from 15.3 to 28.4 seconds between pitches.

I also looked at the ERA and WHIP (walks plus hits per inning) of these 575 pitchers to see if there were any relation between pitching success and time between pitches. There was no relation. The longest time is 8 seconds slower than overall average, which is not trivial over the course of an entire game, but it is more important to ask how often these slow times occur. Figure 4 shows a distribution that is probably expected, with the large majority of pitchers showing little variation from the mean. In fact, the pitch intervals of 18 to 23 seconds cover 80% of all pitchers.

Individual Batters

It is a logical extension to check individual batters, once again limiting the analysis to those who saw at least 100 “interval” pitches with the bases empty and excluding all pitchers. There were 513 batters in this group. Their range was 17.4 to 25.9 seconds, which is narrower than I found for pitchers. I examined batter success in terms of OPS in relation to the pitch interval and once again there was no relation.

Individual Umpires

The other party in each pitch is the plate umpire. The range here is amazingly narrow, from 19.3 to 20.5 seconds, barely a one-second difference. We can safely conclude that the identity of the umpire is of virtually no significance in the time taken between pitches

Ejections

There were 87 ejection episodes in 2018 which saw the banishment of 189 players, coaches, and managers. In many cases two or more were ejected at the same time. These ejections consumed an average of one minute and 52 seconds.

Injuries

Injuries to players and umpires were very different in their time consequences. I catalogued 528 stoppages of play for an injury to a player and these took an average of two minutes and 19 seconds. Umpire injuries are rarer — only seven in 2018. However, these took an average of nine minutes and 3 seconds. Almost all of these involved the home plate umpire hit by a foul ball, necessitating his replacement to don additional gear, which takes significant time.

Summary and Highlights

• Bases empty: 20.3 seconds
• Man on first: 28.4 seconds
• Throws to first: 25 seconds
• Mound visits: 81 seconds
• Between batters: 54 seconds
• Between innings: 162 seconds
• 7th-inning stretch: 15 additional seconds
• “God Bless America”: 71 additional seconds
• Pitcher change start inning: 14 additional seconds
• Pitcher change mid-inning: 138 additional seconds
• Challenges between plays: 162 seconds
• Challenges between innings: 266 seconds
• Fastest to slowest pitchers: 12 seconds
• Fastest to slowest batters: 7 seconds
• Injuries to players: 2:19
• Injuries to umpires: 9:03

Conclusion

As demonstrated here, there are many different factors that add to the time of games. However, the answer to the question in the title is NO, time between pitches is not the cause of long games. Time between pitches makes only a minor contribution to total time.

Table 6 breaks down the average “regulation length” game, that is, those which are either 8.5 or 9 innings.

The “calculated” times were obtained by summing the observed average times for each half inning as well as the individual average times between innings. The nearly perfect match between the actual and calculated game times gives me great confidence that I considered the proper factors. As a final point, I looked on a per game basis at the various interruptions I identified. These are contained within the calculated play time and are listed in Table 7.

These regulation-length games average 3 hours and 1 minute, so the 17.1 minutes of interruptions comprise an average of 9.5% of the total time.

We are left with the question of where MLB could intervene to shorten games and I see no obvious target for rule changes that could mitigate this situation. There is a pending new rule requiring relievers to face a minimum of three batters instead of one, but these data suggest that will have little to no impact. It seems that the inherent structure of the game has changed to the current rate at which events flow and we should expect that to continue.

DAVID W. SMITH joined SABR in 1977 and has made research presentations at over 20 national SABR conventions. In 2001 at SABR 31, he won the USA Today Sports Weekly Award for his presentation on the 1951 NL pennant race. In 2016 he won the Doug Pappas Award for his presentation on closers. In 2005 he received SABR’s highest honor, the Bob Davids Award, and in 2012 he was honored with the Henry Chadwick award. He is founder and president of Retrosheet and an Emeritus Professor of Biology at the University of Delaware.

Notes

1 David W. Smith, “Why Do Games Take So Long?” SABR Baseball Research Journal, Vol. 47, No. 2 (Phoenix: SABR, Fall 2018). See also Retrosheet: https://www.retrosheet.org/Research/SmithD/WhyDoGamesTakeSoLong.pdf