It is common to hear players, both batters and pitchers, comment on the value of being able to “make adjustments” during a game. For example, pitchers speak of “setting a batter up” by a certain sequence of pitches, which may take several at-bats to accomplish. Similarly, batters often remark that they “look for” a certain type of pitch or in a certain location after considering what the pitcher has thrown before. Although it makes sense that a player will alter his mental approach as a result of earlier success or failure, I decided to go beyond the anecdotal interviews and ask if there were any tangible evidence indicating that this learning actually takes place.

I analyzed every play of every game from 1984 through 1995, which is 24,823 games and more than 1.69 million at-bats. The play-by-play information, which comes from the Baseball Workshop in Philadelphia, is publicly available. In the very near future similar data will be available for earlier seasons from Retrosheet, the organization of which I am proud to be president. The analysis here is limited to matchups between starting batters and starting pitchers, thereby allowing the study of the maximum number of sequential encounters in a given game. Given the realities of modern relief pitcher usage, it is very uncommon for a batter to face the same relief pitcher more than once in a game, and therefore the relievers were excluded. The batting performance of pitchers was also removed.

The next question is how to evaluate performance so that we can make the comparisons in a meaningful way. I chose to calculate the three standard aggregate measures: batting average, on-base average, and slugging average. Sabermetric studies in the last two decades have made it clear that these three reflect different aspects of batter performance and I therefore suspected that they might not all show the same pattern of learning during a game. Table 1 presents the results for all games from 1984 to 1995.

TABLE 1: Batting by Number of Appearances. │ │ All games, both Leagues, 1984-1995

In addition to noting how uncommon it is for a starting batter to face a starting pitcher four times in a game, we see clear patterns of improvement, or learning, in all three values as the game progresses. However, the three averages do not increase at the same rate. On base average rises slowly, only 3.4% from the first to fourth time at bat, while batting average and slugging average go up much more rapidly, 6.6% and 7.9% respectively.

Figure 1 (all figures are at the end of the paper) is the graphical version of the same data and shows some more subtle points. The most rapid change on the entire figure is in slugging average from the first to second time up. In the 1950s Branch Rickey and Allan Roth developed a measurement called “isolated power” to examine extra base hits separately from singles. Isolated power is simply the difference between slugging average and batting average. For all at-bats over the 12 years studied the isolated power is .134 (batting average of .260 and slugging average of .394; see Table 3). For the data in Figure 1, the isolated power values for the four times at bat are .132, .145, .150, and .146. My interpretation is:

1. the first time up batters are more concerned with making contact than hitting with power and;
2. the second and subsequent times up they are adjusting with the result that they are able to swing more confidently and with greater

Of course, we can’t lose sight of the possibility that pitchers are learning during these successive at-bats as well. However, the increases we see in Figure 1 indicate that in a relative sense the batters are ahead of the pitchers in their adjustments.

In an attempt to look for other factors controlling these numbers, I divided the games by league; these results are presented in Table 2.

TABLE 2: AL and NL Batting by Number of Appearances, 1984-1995

A quick glance shows that the two leagues are very similar in all three values, perhaps more so than might be expected, given the reputation of the American League as the more offensively minded. I would like to address this point with the small digression shown in Table 3.

TABLE 3: Correction for Effect of DH and pitchers, 1984-1995

The top portion of this table shows that the AL has more offense by all three measures, confirming the conventional wisdom. The middle portion presents the data for the DH and for pitchers, with the expected huge difference. The bottom part of the table was derived by subtracting the DH from the AL values and the pitchers from the NL data. The results show very close agreement, perhaps surprisingly so, between the two leagues. In fact, comparing the NL with pitchers removed to the entire AL with the DH included gives even closer agreement. My conclusion on this point is that essentially all the difference in offense between the two leagues is accounted for by the DH.

Back to the main point, let’s look at the league differences graphically, as is done in Figure 2 which presents the data from Table 2. Although there are some differences between the leagues, it is clear that they are quite similar.

The next idea I had for subdividing the results was by home and road team, as presented in Table 4. To my surprise, there are rather large differences between the two, both in absolute value of the numbers and in the pattern of changes. The home team has an overall seven-point superiority in all three of the measures used here, as shown in the bottom portion of Table 4. However, the greatest differences are in the pattern of the changes, as shown in Figure 3, which comes from the data in the first two portions of Table 4.

TABLE 4: Home and Road Batting by Number of Appearances, 1984-1995

In all three parameters, the rates of increase are steeper for players on the visiting team than they are for those who are playing at home. In fact, slugging average for the home players actually drops from the third to fourth time at bat. By the fourth time at-bat, the home and road players are almost identical. This pattern is initially surprising, since it is not obvious why the road-team batters should display so much more learning than the home-team batters. However, we must remember that there are two sides to each matchup and consider the pitchers as well.

One of the great differences usually identified between different parks is the mound and it is common to hear visiting pitchers comment that it takes time to adjust. Therefore, it is reasonable to consider that there are two kinds of learning going on. The first is the mental part of the pitcher-batter confrontation, which we have seen to favor the batter, and the second is the physical adjustment by the pitcher to the mound. Presumably the home team pitchers are more familiar with the mound than the road team pitchers are and they should have less of this adjustment to do.

Let us consider the home vs road differences again, remembering that the home and road batters end up with very similar performances. By this argument, the learning displayed by the road-team batters would therefore result mostly from the mental aspects, since the home team pitchers are not affected as much by the mound.

On the other hand, the road-team pitchers are starting the game at a relative disadvantage as they deal with the idiosyncrasies of that particular mound. Therefore, the performance by home-team batters starts off at a higher level, but does not increase as rapidly, because there is less room for improvement before they reach the maximum in the fourth time up. However, it must be true that the road-team pitchers have been successful in their adjustments, or else one would expect that the performance by home-team batters would continue beyond what is actually observed.

There is one additional factor which might affect the batters, and that is the nature of the hitting background. Although the center-field background does vary between parks, there is much less variation here than there is in the mound. One way to examine the effect of the hitting background would be to compare the performance of road-team batters in the first game of each series to the later games in the series. If the background were a significant factor, then one would expect the first game performance to be different. I did not subdivide the results in this way, so this possibility remains unexplored.

Until last Saturday, these were all the ways I had thought of dissecting the data. However, that afternoon I received a call from Jerry Crasnick, who is a sportswriter with the Denver Post. Jerry was calling to discuss my research on the effect of artificial surface, which I presented at last year’s SABR meeting, but during our conversation I mentioned my topic for this year. Jerry told me he had discussed this very subject with Craig Biggio of the Houston Astros and that Craig was firmly convinced that the physical demands of the position cause catchers to pay a huge offensive price.

The essence of Craig’s comment was that he was “toast” his last time up. Of course, I was immediately inspired to check out this assertion and I reran my programs to record the batting events of catchers separately from those non-catchers. The results are in Table 5, where even a quick glance shows that the patterns for catchers are quite different. The overall totals are lower, which is no surprise, but what strikes me is the very slight increases by the catchers during the game compared to the other batters.

TABLE 5: Effect of Being the Catcher on Batting by Number of Appearances

In fact there are some noticeable decreases in batting average and on-base average between at-bats one and two for the catchers. Over the four plate appearances, catcher batting averages rise only slightly and on-base average actually declines. Slugging average shows the overall increase we have seen all along, but to a lesser degree. Figure 4 shows the same information, where the patterns stand out even more clearly.

Do these results support the idea that catchers are damaged later in the game? In an absolute sense, it appears the answer is no, but compared to other players the answer is clearly yes. What do these results have to do with learning? Assuming that catchers can make adjustments as well as other players, then it appears that their learning as batters is largely overcome by the physical demands of playing behind the plate.

Before I give my conclusion, there is one more point that must be made, which is to note that I presented no information for individual teams or players. It is always true in a study such as this that the results get less clear as the sample size gets smaller. I therefore made the large divisions of league, home vs. road, and fielding position. When the results are divided more finely, to single teams or single batters, there will inevitably be many exceptions that cloud the issue, largely because of their statistical unreliability. I have chosen to avoid this confusion.

In conclusion I note that I began this study with the question that is the title of the presentation: Do Batters Learn During a Game? It is clear that the general answer is: yes, they do. However, it is also clear that the situation is a little more complicated than that and that a better understanding can be obtained by considering other factors, the two biggest of which are the effect of playing at home vs. on the road and of being the catcher.

So the next time you hear a batter say that he improved his performance by making adjustments during a game, there is a good chance you should believe it. On the other hand, if you hear a pitcher say it, then you might be a little suspicious.

DAVID W. SMITH received SABR’s highest honor, the Bob Davids Award, in 2005. He is the founder and President of Retrosheet.

Figure 1

Figure 2

Figure 3

Figure 4

As a baseball artifact, it’s pretty special as it is.

It’s a scorecard from August 5, 1891 — a day when Buck Ewing drove in four runs off Cy Young and the New York Giants managed to hold off the Cleveland Spiders, 8–7, at the Polo Grounds. The book still shows the partial vertical fold its original owner might have created while stuffing it into a pocket as he raced to catch the steam-powered elevated train that would take him back downtown. And the scorecard pages themselves tell of a Cleveland rally thwarted only in the last of the ninth, when Spiders player-manager Patsy Tebeau, rounding third base, passed his teammate Spud Johnson going in the opposite direction — running his team into a game-ending double play.

The program is actually an embryonic yearbook. There are 14 photos and biographies of Giants players, and a wonderful series of anonymous notes under the heading “Base Hits” (“Anson next week. If we win three straights [sic] from him, we will be in first place”). But amid all the joyous nostalgia of a time impossibly distant — stuffed between the evidence that the owner saw Cy Young pitch in his first full major league season — hidden among the ads that beckon us to visit the Atalanta Casino or try Frink’s Eczema Ointment or buy what was doubtlessly an enormous leftover supply of Tim Keefe’s Official Players League Base Balls — we can throw everything out, except the top of page 10.

There, in six simple paragraphs, the scorecard’s buyer is advised how to use it. “Hints On Scoring” tells us, simply, “On the margin of the score blanks will be seen certain numerals opposite the players’ name . . . . The pitcher is numbered 1 in all cases, catcher 2, first base 3, second base 4, short stop 5, third base 6.”

This is no mistake caused by somebody’s over-indulgence at the Atalanta Casino.

The unknown editor offers a few sample plays, including: “If a ball is hit to third base, and the runner is thrown out to first base, without looking at the score card, it is known that the numbers to be recorded are 6-3, the former getting the assist and the latter the put-out. If from short stop, it is 5-3. . . .”

If we need any further confirmation that more has changed since 1891 than just the availability of Frink’s Eczema Ointment, the scorecard pages themselves provide it. In the preprinted lineups, third basemen Tebeau of Cleveland and Charlie Bassett of New York each have the number “6” printed just below their names. And the two shortstops, Ed McKean of the Spiders and Lew Whistler of the Giants, each have a “5.”

We may view the system of numbers assigned to the fielding positions as eternal and immutable. But this 1891 Giants scorecard suggests otherwise, and is the tip of an iceberg we still don’t fully see or understand — a story that anecdotally suggests a great collision of style and influence in the press box, no less intriguing than the war between that followed the creation of the American League.

The shortstop used to be “5,” and the third baseman used to be “6.”

We do not know precisely how and when it changed — there is a pretty good theory — but we do know that by 1909, the issue had been decided. In the World Series program for that year, Jacob Morse, the editor of the prominent Base Ball Magazine, gets seven paragraphs — the longest article in the book — to offer not “Hints On Scoring” but the much more definitive “How To Keep Score.” And he leaves no doubt about it. “Number the players,” Morse almost yells at us. “Catcher 2, pitcher 1; basemen 3, 4, 5; shortstop 6. . . .” The New York Giants themselves had reintroduced scorekeeping suggestions by 1915, and conformed to the method demanded by Morse, as if it had always been that way.

We can actually narrow the time frame of the change to a window beginning not in 1891, but closer to 1896. In the same pile of amazingly simple artifacts as that Giants scorecard is the actual softcover scorebook used by Charles H. Zuber, the Reds’ beat reporter for the Cincinnati Times-Star five years later. Zuber employed a “Spalding’s New Official Pocket Score Book” as he and the Reds trudged around the National League in the months before the election of President McKinley. Inside its front cover, one of the Great Spalding’s many minions has provided intricately detailed scoring instructions. “The general run of spectators who do not care to record the game as fully as here provided,” he writes with just a touch of condescension, “can easily simplify it by adopting only the symbols they need.”

That this generous license was already being taken for granted is underscored by the fact that the Spalding editor suggests “S” for a strikeout, but writer Zuber ignores him completely and employs the comfortingly familiar “K.” But the book’s instructions are not entirely passé. They include the suggestion that the scorer use one horizontal line for a single, two for a double, etc. — which is exactly the way I was taught to do it, in the cavernous emptiness of Yankee Stadium in 1967.

The Spalding instructions go on for 11 paragraphs, and the official rules for scoring fill another 20. But remarkably, there are is no guidance about how to numerically abbreviate the shortstop, third baseman, or anybody else who happened to be on the field. There isn’t even the suggestion that a scorer must number the players, or abbreviate the players, according to their defensive positions: “Number each player either according to his fielding position or his batting order, as suits, and remember that these numbers stand for the players right through in the abbreviations.”

In other words — use any system you damn well please. Number the shortstop “5” if you want, or “6.” Or, if he’s batting leadoff, use “1.” Or if he’s exactly six feet tall, try “72.”

If by now you have wondered if the father of scorekeeping and statistics, Henry Chadwick, was not sitting there with smoke pouring from his ears over all this imprecision and laissez-faire, don’t worry — he was. As early as his 1867 opus The Game Of Base Ball he was an advocate of one system and one system only — numbering the players based on where they hit in the order.

I realize that some of the most ardent of you, who have little shrines to Chadwick (in your minds, at least) as the ancient inspiration for SABR itself, must be reeling at the thought. Even if you think using “6” for the third baseman instead of the shortstop is a bit silly, it’s a lot better than Chadwick’s idea, surely the worst imaginable system of keeping score, based on the batting lineup (“groundout to short, 1 to 7 if you’re scoring at home — no, check that, I forgot, the relief pitcher Schmoll took Robles’ spot in the batting order in the double switch, so score it 9 to 7”).

Before we knock down the Chadwick statue outside SABR headquarters, this caveat is offered in his defense. In 1867, random substitutions were not permitted at all, and not until 1889 did they become even partially legal. Within a game, the batting order changed about as frequently as the designated hitter today assumes a defensive position. Chadwick’s insistence on defensive numbering based on offensive positioning still doesn’t make sense on a game-to-game basis, but at least he wasn’t completely nuts.

But, as Peter Morris points out, Chadwick wanted to keep his system even as the substitution rule was changing. That same series of “Hints On Scoring” from the 1891 Giants scorecard first appeared, word for word, in a column in the New York Mail and Express in early 1889.

Weeks later, Chadwick is railing against it in the columns of Sporting Life. This new defensive-based scoring system is, he writes, “in no respect an improvement on the plan which has been in vogue since the National League was organized. If you name the players by their positions, and these happen to be changed in a game, then you are all in a fog on how to change them.”

Chadwick was wrong about the ramifications but right about the coming fog.

Certainly, as the Giants scorecard and Charles Zuber’s Spalding scorebook suggest, confusion would reign through the 1890s and into the new century. The New York scorecards soon reverted to “3B” and “SS” and dropped all hinting on what the bearer was supposed to do. Zuber’s scoring system starts with the first baseman at “1,” has the shortstop as “4,” and the pitcher and catcher as “5” and “6.” Only the Hall of Fame manager Harry Wright seems to have nailed it. In the voluminous scorebooks he kept through to his death in 1893, he has penciled in, in perfect, tiny lettering, the third baseman as “5” and the shortstop as “6.”

So how was this chaos resolved?

This proves to have been the unexpected topic of conversation in the late 1950s between a budding New York sportswriter and one of the veterans of the business. Bill Shannon, now one of the three regular official scorers at Yankee and Shea Stadiums, was talking scorekeeping with Hugh Bradley.1 Bradley had been covering baseball in New York since the first World War, had been sports editor of the New York Post in the ‘30s, and was at the time of his conversation with Shannon a columnist with the New York Journal-American.

Shannon recalls that, out of nowhere, Bradley began talking about a great ancient conflict between rival camps of scorers, one of which favored the shortstop as “5” and the other as “6.” The inevitable clash occurred, Bradley told him, at the first game of the first modern World’s Series.

The World’s Series, of course, had gone out with a whimper and not a bang in 1890. Though the Brooklyn Bridegrooms and Louisville Cyclones had been tied at three wins apiece, disinterest in that war-ravaged season was so profound that attendance at the last three games had been 1,000, 600, and 300, respectively. They didn’t even bother to play the decisive game.

Thus when the series was restored 13 years later, every attempt was made to keep haphazardness and informality out of the proceedings. Not just one official scorer was required, but two — and the two foremost baseball media stars of the time: Francis C. Richter of Philadelphia, the publisher and editor of Sporting Life, and Joseph Flanner of St. Louis, editor of The Sporting News.

Hugh Bradley could not have witnessed it, but he could have heard it second- or third-hand. As the rivals from the two publications filled out their scorecards, somewhere in the teeming confusion of the Huntington Avenue Grounds in Boston, somebody —  probably the more volatile Flanner — peeked.

And he didn’t like what he saw.

Richter was numbering Pittsburgh shortstop Honus Wagner as “5” and third baseman Tommy Leach as “6.”

Questioned by Flanner, Richter supposedly responded that that was the way they kept score where he came from, and why would anybody do it any differently?

The basis of their argument was supposed to have been regional. The shortstop, Bradley told Shannon, was still a comparatively new innovation in the game, and it really defined two different positions. In Flanner’s Midwest, he was positioned much like the softball short-fielders, not truly an infielder and thus not meriting an interruption of the natural numbering of the basemen. In Richter’s East, the shortstop had developed into what he is today — the second baseman’s twin. So what if he didn’t anchor a bag? It was second baseman “4,” shortstop “5,” third baseman “6” and don’t they have any good eye doctors out there in St. Louis, friend Flanner?

Bradley’s recounting of the conflict had voices being raised and dark oaths being sworn before the more malleable Richter gave way, little knowing that he was ceding the issue forever on behalf of generations to come who saw the same logical flaw he had seen.

Bill Shannon’s authority on such matters is near absolute. He can not only recount virtually every game he’s ever seen, but can also run down the personnel histories of the sports departments at the dearly departed of New York’s newspapers. He believes in the long-gone Bradley’s saga of near-fisticuffs between Richter and Flanner — while ‘Nuf Sed McGreevey and his Royal Rooters worked themselves into a frenzy before the first pitch of the 1903 Series — because of its likely provenance.

One of Bradley’s writers when he was sports editor of the Post in the ‘30s was Fred Lieb, himself almost antediluvian enough to have witnessed the Flanner-Richter showdown. Shannon suspects Bradley got the story from Lieb, and that Lieb had gotten it from his fellow Philadelphian Francis Richter.

For now, that’s all we’ve got — a pretty good-sounding anecdote. There is nothing yet found in the files of The Sporting News, New York Times, Washington Post, or even in any of the contemporary Spalding or Reach annual guides. No Flanner-Richter screaming match, no ruling on whether the shortstop or the third baseman was “5,” no verified explanation as to how we got from the hints in the 1891 Giants scorecard to the instructions of the 1909 World Series program, no smoking gun proving when it became this way, as if there had never been any other way.

Needless to say, further research is encouraged and its results solicited.

In the meantime, dare I even mention that the 1891 Giants book also identifies the right fielder as “7” and the left fielder as “9”?

KEITH OLBERMANN anchors MSNBC’s nightly newscast, Countdown, and co-hosts a dally hour with Dan Patrick on ESPN Radio. A SABR member since 1984, he still regrets not acting on his intention to sign up during a visit lo Cooperstown in 1973.

Notes

1 Bill Shannon died in 2010, after this article was initially published.

A team’s season record is massively influenced by luck. Suppose you take a coin and flip it 162 times to simulate a season. Each time it lands heads, that’s a win, and when it lands tails, that’s a loss. You’d expect, on average, to get 81 wins and 81 losses. But for any individual season, the record may vary significantly from 81-81. Just by random chance alone, your team might go 85–77, or 80–82, or even 69–93.

Suppose you were able to clone a copy of the New York Yankees, and play the cloned team against the real one. (That’s hard to do with real players, but easy in a simulation game like APBA.) Again, on average, each team should win 81 games against each other, but, again, the records could vary significantly from 81–81, and the difference would be due to luck.

As it turns out, the range and frequency of possible records of a .500 team can be described by a normal (bell-shaped) curve, with an average of 81 wins and a standard deviation (SD) of about six wins. The SD can be thought of as a “typical” difference due to luck — so with an SD of six games, a typical record of a coin tossed 162 times is 87–75, or 75–87. Two-thirds of the outcomes should be within that range, so if you were to run 300 coin-seasons, or 300 cloned-Yankee seasons, you should get 200 of them winding up between 75 and 87 wins.

More interesting are the one-third of the seasons that fall outside that range. If all 16 teams in the National League were exactly average, you’d nonetheless expect five of them to wind up with more than 87 wins or with fewer than 75 wins. Furthermore, of those five teams, you’d expect one of them (actually, about 0.8 of a team) to finish more than 2 SDs away from the mean — that is, with more than 93 wins, or more than 93 losses.

This is a lot easier to picture if you see a real set of standings, so Table 1 shows a typical result of a coin-tossing season for a hypothetical National League where every team is .500.

In this simulated, randomized season, the Mets in the East and Diamondbacks in the West were both really .500 teams — but, by chance alone, the Mets finished ahead of Arizona by 27 games!

As it turns out, this season is a little more extreme than usual. On average, the difference between the best team and the worst team will be about 24 games, not 27. Also, there should be only one team above 93 wins (we had two), with the next best at 89.

Real Seasons

So far this is just an intellectual exercise because, of course, not every team is a .500 team. But even teams that aren’t .500 have a standard deviation of around six games, so a similar calculation applies to them.

For instance, suppose you have a .550 team, expected to win 89 games. That’s eight games above average. To get a rough idea of the distribution of wins it will actually get, you can just add those eight games to each row of Table 1. So, if our .550 team plays 16 seasons, in an extremely lucky season it’ll finish 102–60, and in its unluckiest season it will go only 75–87 — still a swing of 27 games (although, as we said, 24 is more typical). It’s even possible that those two seasons will be consecutive, in which case the team will have fallen from 102 wins down to 75 in one season — and only because of luck!

If, in an average season, one team will drop 12 or more games out of contention for no real reason, and some other team will gain 12 games, it’s pretty obvious that luck has a huge impact on team performance.

Which brings us to this question: is there a way, after the fact, to see how lucky a team was? The 1993 Philadelphia Phillies went 97–65. But how good were they, really? Were they like the top team in the chart that got 13 games lucky, so that they really should have been only 84–78? Were they like the bottom team in the chart that got 14 games unlucky, so that they were really a 111–51 team, one of the most talented ever? Were they even more extreme? Were they somewhere in the middle?

This article presents a way we can find out.

Luck’s Footprints

A team starts out with a roster with a certain amount of talent, capable of playing a certain caliber of baseball. It ends up with a won-lost record. How much luck was involved in converting the talent to the record?

There are five main ways in which a team can get lucky or unlucky. Well, actually, there are an infinite number of ways, but those ways will leave evidence in one of five statistical categories.

1. Its hitters have career years, playing better than their talent can support.

Alfredo Griffin had a long career with the Blue Jays, A’s, and Dodgers, mostly in the 1980s. A career .249 hitter with little power and no walks, his RC/G (Runs Created per Game, a measure of how many runs a team would score with a lineup of nine Alfredo Griffins) was never above the league average.

Griffin’s best season was 1986. That year he hit .285, tied his career high with four home runs, and came close to setting a career high in walks (with 35). He created 4.16 runs per game, his best season figure ever.

In this case, we assume that Alfredo was lucky. Just as a player’s APBA card might hit .285 instead of .249 just because of some fortunate dice rolls, we assume that Griffin’s actual performance also benefited from similar luck.

What would cause that kind of luck? There are many possibilities. The most obvious one is that even the best players have only so much control of their muscles and reflexes. In The Physics of Baseball, Robert Adair points out that swinging one-hundredth of a second too early will cause a hit ball to go foul — and one-hundredth of a second too late will have it go foul the other way! To oversimplify, if Griffin is only good enough to hit the ball randomly within that .02 seconds, and it’s a hit only if it’s in the middle 25% of that interval, he’ll be a .250 hitter. If one year, just by luck, he gets 30% of those hits instead of 25%, his stats take a jump.

There are other reasons that players may have career years. They might, just by luck, face weaker pitchers than average. They may play in more home games than average. They may play a couple of extra games in Colorado. Instead of 10 balls hit close to the left-field line landing five fair and five foul, maybe eight landed fair and only two foul. When guessing fastball on a 3–2 count, they may be right 60% of the time one year but only 40% of the time the next.

I used a formula, based on his performance in the two seasons before and two seasons after, to estimate Griffin’s luck in 1986. The formula is unproven, and may be flawed for certain types of players — but you can also do it by eye.

Here’s Alfredo’s record for 1984-1988:

Leaving out 1986, Griffin seemed to average about –22 batting runs per season. In 1986, he was –5: a difference of 17 runs. The RC/G column gives similar results: Griffin seemed to average around three, except in 1986, when he was better by about one run per game. 425 batting outs is about 17 games’ worth (there are about 25.5 hitless at-bats per game), and 17 games at one run per game again gives us 17 runs.

The formula hits almost exactly, giving us 16.7 runs of “luck.” That’s coincidence, here, that the formula gives the same answer as the “eye” method — they’ll usually be close, but not necessarily identical.

Griffin is a bit of an obvious case, where the exceptional year sticks out. Most seasons aren’t like that, simply because most players usually do about what is expected of them. The formula will give a lot of players small luck numbers, like 6 runs, or –3, or such. Still, they add up. If a team’s 14 hitters each turn three outs into singles, just by chance, that’s about 28 runs — since it takes about 10 runs to equal one win, that’s 2.8 wins.

And, of course, the opposite of a career year is an off-year. Just as we measure that Alfredo was lucky in 1985, he was clearly unlucky in 1984, where his 2.46 figure was low even for him.

2. Its pitchers have career years, playing better than their talent can support.

What’s true of a hitter’s batting line is also true of the batting line of what the pitcher gives up. Just as a hitter might hit .280 instead of .250 just by luck, so might a pitcher give up a .280 average against him instead of .250, again just by luck.

Using Runs Created, we can compute how many runs per game the pitcher “should have” given up, based on the batting line of the hitters who faced him (this stat is called “Component ERA”). And, just as for batters, a career year (or off-year) for a pitcher will stick right out.

Here’s Bob Knepper, from 1980 to 1984:

Leaving out 1981, Knepper seemed to average a CERA of about three-and-a-half. But in ‘82, he was at 4.14. That’s about .7 runs per game, multiplied by exactly 20 games (180 innings), for about 14 runs lost due to random chance.

The formula sees it about the same way, assigning Knepper 17 runs of bad luck.

A pitcher’s record necessarily includes that of his fielders — and so, whenever we talk about a pitcher’s career year, that career year really belongs to the pitcher and his defense, in some combination.

3. It was more successful at turning baserunners into runs.

The statistic “Runs Created,” invented by Bill James, estimates the number of runs a team will score based on its batting line. Runs Created is pretty accurate, generally within 25 runs a season of a team’s actual scoring. But it’s not exactly accurate, because it can’t be.

Run scoring depends not just on the batting line, but also on the timing of the events within it. If a team has seven hits in a game, it’ll probably score a run or two. But if the hits are scattered, it might get shut out. And if the hits all come in the same inning, it might score four or five runs.

The more a team’s hits and walks are bunched together, the more runs it will score. That’s the same thing as saying that the better the team hits with men on base, the more runs it will score. Which, again, is like saying the better the team hits in the clutch, the more runs it will score.

But several analyses, most recently a study by Tom Ruane of 40 years’ worth of play-by-play data, have shown that clutch hitting is generally random — that is, there is no innate “talent” for clutch hitting aside from ordinary hitting talent. So, for instance, a team that hits .260 is just as likely to hit .280 in the clutch as it is to hit .240 in the clutch.

And if that’s the case, then any discrepancy between Runs Created and actual runs is due to luck, not talent.

And so when the 2001 Anaheim Angels scored 691 runs, but the formula predicted they should score 746, we chalk the difference, 55 runs, up to just plain bad luck.

4. Its opposition was less successful in turning baserunners into runs

If clutch hitting is random, it’s random for a team’s opposition, too. So when the 1975 Big Red Machine held its opponents to 70 fewer runs than their Runs Created estimate says they should have scored, we attribute those 70 runs to random chance. The Reds’ pitchers were lucky, to the tune of seven wins.

5. It won more games than expected from its Runs Scored and Runs Allowed

The 1962 New York Mets achieved the worst record in modern baseball history, at 40–120. That season they scored only 617 runs and allowed 948 — both figures the worst in the league.

There’s another Bill James formula, the Pythagorean Projection, which estimates what a team’s winning percentage should have been based on their runs scored and runs allowed. By that formula, the Mets should have been 7.6 games better in the standings than they actually were — that is, they should have been 47–113.

Any difference between expected wins and actual wins has to do with the timing of runs — teams that score lots of runs in blowout games will win fewer games than expected, while teams that “save” their runs for closer games will win more than their projection. But studies have shown that run timing, like clutch hitting, is random. Teams don’t have a “talent” for saving their runs for close games, and therefore any difference from Pythagorean Projection is just luck.

So we judge that seven of the Mets’ 1962 losses were the result of bad luck, and that based on this finding, they weren’t quite as bad as we thought. Of course, 47–113 is still pretty dismal.

Putting It All Together

Earlier, we mentioned the 1993 Phillies. How lucky were they? Let’s take the five steps, one at a time:

1/2. Career Years or Off-Years

Everything came together in 1993, as individual Phillies hitters had career years, to the tune of a huge 131 runs.

Lenny Dykstra had a monster year, hitting 19 home runs (his previous high was 10) with a career-high .305 average. He was 37 runs better than expected. Rookie Kevin Stocker was lucky by 19 runs — he hit .324, but would never break .300 again. John Kruk and Pete Incaviglia were a combined 33 runs better than expected. Of the hitters, only Mickey Morandini, at –9, had an off-year of more than three runs.

The pitchers, for their part, were lucky by 39 runs, led by Tommy Greene, who had the best year of his career, 37 runs better than expected. Other than that, the staff performed pretty much as expected. A full list:

3. Runs Created by Batters

The Phillies scored 24 more runs than expected from their batting line.

4. Runs Created by Opposition

The Phillies’ opponents scored almost exactly the expected number of runs, exceeding their estimate by only one run.

5. Pythagorean Projection

Scoring 877 runs and allowing 740, the Phillies were Pythagorically unlucky. They should have won 3.1 more games than they did — at 10 runs per win, that’s about 31 runs worth. Adding it all up gives:

• Career years/off years by hitters: +131 runs
• Career years/off years by pitchers: +39 runs
• Runs Created by batters: +24 runs
• Runs Created by opposition: -1 run
• Pythagorean projection: -31 runs
• TOTAL: +162 runs (16 wins)
• Actual record: 97-65
• Projected record: 81-81

We conclude that the 1993 Phillies were a dead-even .500 team that just happened to get lucky enough that it won 97 games and the pennant.

This shouldn’t be that surprising. The Phils finished last in the division in 1992, and second-last in 1994, with mostly the same personnel. You can argue, if you like, that the players caught a temporary surge of talent in 1993, which they promptly lost after the season. But the conclusion that they had a lucky year makes a lot more sense.

The Best and Worst “Career Years”

Which players had the worst “off-years” between 1960 and 2001? Here’s the chart:

It’s an interesting chart, but also shows a limitation of the formula — it can’t distinguish between players who were lucky, and players who had a real reason for their performance problem.

Take Steve Blass, for example. His well-documented collapse in 1973 was not because he was just unlucky, but that he suddenly was unable to find the strike zone. While succumbing to “Steve Blass disease” is, I guess, a form of bad luck, it’s not really the kind of luck we’re investigating, which assumes that the player has his normal level of talent, but things just don’t go his way. If you’re doing an analysis of the 1973 Pirates, you might want to subtract out those 50 runs, based on the known understanding that they weren’t really bad luck.

Dave Stieb in 1986 — the worst “unlucky” season of the past 40 years — is another interesting case. Stieb was arguably the best pitcher in the AL in 1984 and 1985; he was legitimately bad in 1986, but went back to excellent in 1987 and 1988. What happened in 1986? Bill James suggested that Stieb had lost a little bit of his stuff, and was slow to accept his new limitations and pitch within them. I looked over a couple of game reports in the Toronto Star from that year, and the tone seemed to be puzzlement at Stieb’s bad year — there was no suggestion that Stieb was injured or such.

Here are the luckiest years:

Steve Carlton’s awesome 1972 season, when he went 28-10 for a dismal .378 team, comes in as the luckiest of all time. Norm Cash is second, for his well-documented cork-aided out-of-nowhere 1961 (note that the system is unable to distinguish luck from cheating). And it’s interesting that Sammy Sosa appears on both lists.

You would expect that the luckiest season of all-time would be one like Cash’s, where an average player suddenly has one great year. But, instead, Carlton’s 1972 is a case where a great player has one of the greatest seasons ever. Of course, it’s a bit easier for a pitcher to come up with a big year than a hitter, because there’s a double effect — when his productivity goes up, his impact on the team is compounded because he gets more innings (even if only because he’s not removed in the third inning of a bad outing). On the other hand, a full-time hitter gets about the same amount of playing time whether he’s awesome or merely excellent.

Again, you can visit these cases to see if you can come up with explanations other than luck — Mike Norris, for instance, is widely considered to have been mortally overworked by Billy Martin in 1980, destroying his arm and, in that light, perhaps 60 runs is a bit of an overestimate.

Lucky and Unlucky Teams

The lists of players are interesting but probably not new knowledge — even without this method, we were probably aware that Norm Cash had a lucky season in 1961. On the other hand, which were the lucky and unlucky teams? I didn’t know before I did this study. Not only didn’t I know, but I didn’t even have a trace of an idea.

Table 7 shows the 15 unluckiest teams between 1960 and 2001. The unluckiest team over the last 40 years was the 1962 New York Mets – the team with the worst record ever. This is not a coincidence — the worse the team, the more likely it had bad luck, for obvious reasons.

(Click image to enlarge)

Most of the Mets’ problems came from timing — poor hitting in the clutch, opponents’ good hitting in the clutch, and poor hitting in close games. That poor timing cost them about 15 wins. Bad years from their pitchers cost them another seven wins, which was partially compensated for by two wins worth of good years by their hitters.

On the other hand, the 1979 Oakland A’s had good timing — seven games of good luck worth. But their players had such bad off-years that it cost them 27 games in the win column. Of their 33 players, only five had career years of any size. The other 28 players underperformed, led by the 2–17 Matt Keough (43 runs of bad luck), off whom the opposition batted .315.

The 1995 Blue Jays were actually the unluckiest team by winning percentage — they were –196 runs in a shortened 144-game season. They wound up tied for the worst record in the league when in reality their talent was well above average.

But the 1998 Mariners could probably be considered the most disappointing of these 15 teams. Their talent shows as good enough to win 95 games, surely enough for the post-season — but they had 19 games worth of bad luck, and finished 76–85. It’s not on the chart, but the Mariners were unlucky again the next season, by 13 games this time — they should have been a 92-win wild-card contender in 1999, but again finished down the pack at 79–83.

The luckiest team (Table 8), by a runaway margin, was the 2001 Seattle Mariners, who won 116 games. And they did most of it through career years.

(Click image to enlarge)

Of the lucky runs, 127 came from the hitters (in this study, second only to the 1993 Phillies), and the pitchers contributed 116 of their own (fifth best). Thirteen separate players contributed at least one lucky win each — Bret Boone (40 runs), Freddy Garcia (38), and Mark McLemore (23) topped the list. Only one player was more than 10 runs unlucky (John Halama, at -11). Despite all the luck, the Mariners were still an excellent team — with average luck they would have still finished 89–73.

The 1998 Yankees are considered one of the best teams ever, and it’s perhaps surprising that they emerge as the second luckiest team. Like the 2001 Mariners, the ’98 Yankees got most of their luck from their players’ performances — about eight games each from their hitting and pitching. In talent, they were 92–70, which is still a very strong team. Indeed, of the 15 luckiest teams, the 1998 Yankees show as the best.

The Miracle Mets of 1969 were 17 games lucky — but this time most of their luck was timing luck — 10 wins in Runs Created, and about two wins in Pythagoras. Still, they were a respectable 83– 79 team in talent.

The worst of these lucky teams was the 1960 Pirates. Bill Mazeroski’s famous Game Seven home run brought the World Series championship to a team that, by this analysis, was worse than average, at 76–78. The 97–57 Yankees, whom they beat, had been eight games lucky themselves, but were still the most talented team in the majors that year, at 89–65.

The Best Teams Ever

Which teams were legitimately the best, even after luck is stripped out of their record? Perhaps not surprisingly, the list is dominated by the “dynasty” teams:

The 1969, ’70, and ’71 Orioles all appear in the top 15, as do four Braves teams from the ‘90s. The ill-fated victims-of-Bucky-Dent 1978 Red Sox come in at number 15. (The list may not appear to be in the correct order because of rounding — but it is.)

The 1975 Reds made the list, but the 1976 Reds don’t (they came in at number 42). Interestingly, the unheralded 1977 Reds, whose nine games of bad luck dropped them to 88–74, appear at number 12. The 1978 Reds, with a projected talent of 96–65, were 21st. This suggests that the Big Red Machine stayed Big and Red longer than we think, but bad luck made it look like the talent had dissipated.

I’ve never heard the 1974 Dodgers described as among the best of all time, but they’re fifth on the list. It was Steve Garvey’s first full season, and the Dodgers had a solid infield and legitimately strong pitching staff.

Arguably the biggest surprise on this list isn’t the presence or absence of any particular team, but that only three teams over the last 40 years were talented enough to win 100 games. This is legitimate — if there were lots of 100-game teams, we’d see a substantial number getting moderately lucky and winning 106 games or more. Also, it’s consistent with a different study I did back in 1988, which found that, theoretically, a team that wins 109 games is, on average, only a 98-game talent. But there is no assurance that this is correct — it’s possible that my algorithm for “career years” overestimates the amount of luck and underestimates the amount of talent.

Here are the worst teams ever:

With expansion, it’s a lot easier to create a team that loses 100 games than a team that wins 100 games. The 100-game loser list is 23 teams long.

Interesting here is the repeated presence of the expansion San Diego Padres, with four teams in the top 15 abysmal list. It’s actually worse than that — the 1970 team finished 19th, and the 1974 Padres were 29th. For six consecutive years San Diego fielded a team in the bottom 30. That they have not been recognized as that futile a team probably stems from the fact that, unlike the expansion Mets, they never had enough bad luck to give them a string of historically horrific records. From 1970 to 1973, their luck was positive each year.

Missing from this list are the 1962 Mets — as we saw, they really should have been 61–99, for 19th worst ever.

The bottom 14 teams are all from the ‘60s and ‘70s, suggesting — or confirming — that competitive balance has improved in recent decades.

How often does the best team win?

In 1989, a Bill James study found that because of luck, a six- or seven-team division will theoretically be won by the best team only about 55% of the time.

I checked the actual “luck” numbers for all 96 division races from 1969 to 1993 (excluding 1981), and found that 59% (57 of 96) were won by the most talented team — very close to Bill’s figure.

Of the 39 pennant races that went to the “wrong” team, the most lopsided was the 1987 National League East. The Cardinals finished first by three games — but were a 78-game talent, fully 16 games worse than the second-place Mets.

Also of note: the 1989 Mets should have finished 15 games ahead of the Cubs instead of six back. The 1992 White Sox should have won the division, beating the A’s by 14 games, instead of finishing third. And the hard-luck Expos were the most talented team in the NL East in 1979, 1980, 1981, 1982, and 1984. They made the postseason only in 1981. In 1982, they were good enough to have finished first by 11 games.

In his 1989 article Bill James speculated that a sub-.500 team could conceivably win the World Series, though it was unlikely. He wrote, “Did we see it in ’88?” For the record, the 1988 Dodgers come out as an 82–80 team — close but not quite. The ’82 Cardinals came the closest in the four-division era — they won the Series with 81.2-game talent.

But the 1960 Pirates fit the bill. Without luck, they were 76–78. Nineteen games of good fortune pushed them to 95–59, the World Series, and set the stage for Bill Mazeroski’s heroics. Table 11 shows every World Series team from 1960 to 2001.

Table 11 makes it evident that, to win the World Series, it’s not enough to be a good team — you have to be lucky, too. Of the 41 champions, 35 of them had a lucky regular season. Of the six unlucky teams, only the 1974 A’s and the 2000 Yankees were unlucky by more than three games.

Before 1969, all the winning teams were lucky, some substantially. Between 1969 and 1993, in the four-division era, luck was a little less important. Since 1995, the champions were, on the whole, only marginally lucky (with the exception of 1998).

This makes sense — back in the one-division league, one lucky team could blow away nine others. Now that team eliminates only three or four others, and even then, those other teams have a shot at the wild card. And the lucky team now has to win three series against superior opponents, instead of just one, which increases the chance that a legitimately good team, instead of just a lucky one, will now come out on top.

From 1995 to 2001, every champion was at least a 90-game talent (adjusting 1995 for the short schedule). Before the wild card, champions with talent in the 80s were very common.

(Click image to enlarge)

Table 12 lists the luckiest and unluckiest seasons for every major-league team from 1960 to 2001. The Blue Jays and the Red Sox have had good success over the years, but never had a huge season where they won 108 games or something and ran away with the division. That seems to be because they never had the kind of awesome luck you need to have that kind of record. The Jays were never more than 7 games lucky, and Boston never more than 9.8.

For the flip side, look at the San Diego Padres — they were never unlucky by more than 9.4 games. As we noted earlier, that perhaps spared them the reputation as one of the worst expansion teams ever — with a bit of bad fortune, their record could have rivaled the Mets for futility.

And the negative sign in Tampa Bay’s “best luck” column is not a misprint — in the first four years of their existence, they were unlucky all four years.

Finally, take a look at the Twins. Their luckiest season immediately followed their unluckiest. As a result, they went from below .500 in 1964 to 102 wins in 1965 — even though they actually became a worse team!

Summary

What can we conclude from all this? First, luck is clearly a crucial contributor to a team’s record. With a standard deviation of six or seven games, a team’s position in a pennant race is hugely affected by chance — seven wins is easily the difference between a wild-card contender and an also-ran.

Second, you have to be lucky to win a championship. As we saw, 85% of world champions had lucky regular seasons.

Third, teams with superb records are likely to have been lucky. Very few teams are truly talented enough to expect to win 100 games. The odds are very low that the 2005 White Sox (99–63) and Cardinals (100–62) are really as good as their record. Despite all this, it should be said that while luck is important, talent is still more important. The SD due to luck was 7.2, but the SD due to talent was 8.5. It’s perhaps a comfort to realize that talent is still more important than luck — if only barely.

PHIL BIRNBAUM is editor of By The Numbers, SABR’s Statistical Analysis newsletter. A native of Toronto, he now lives in Ottawa, where he works as a software developer.

The Algorithm

This is the algorithm to calculate a player’s career-year or off-year luck for a given season. The procedure is arbitrary. I used it because it seems to work reasonably well, but it no doubt can be improved, probably substantially. But, hopefully, any reasonable alternative algorithm should give similar results in most cases.

Of course, any algorithm should sum to roughly zero, since over an entire population of players the luck should even out.

Batters

A batter’s luck is calculated in “runs created per 27 outs” (RC/27). To calculate a batter’s luck for year X:

1. Take the player’s average RC27 over six years: two years ago counted once, last year counted twice, next year counted twice, and two years from now counted once. Weight the average by “outs made” (hitless AB + CS + GIDP) so that seasons in which a batter had more playing time will have a higher weight. Adjust each RC27 for league and park.
2. Add a certain number of “outs made” at the league average RC27:

   –  if the player had more than 2,100 outs made in the six seasons, add 100 league-average outs made;
   –  if the player had fewer than 1,200 outs made in the six seasons, add 900 league-average outs made; and
   –  if the player had between 1,200 and 2,100 outs made, subtract that from 2,100 and add that number of league-average outs made.

   The purpose of this step is to regress the player to the mean. Just as a player who goes 2-for-4 in a game probably isn’t a .500 hitter, a player who hits .300 in 1,200 outs made is probably less than a .300 hitter. This adjusts for that fact.

3. If the player had less than 1,600 outs made over the six seasons (not including those added in step 2), subtract 0.0006 for each out made under 1,600. In addition, if the player had less than 800 outs made over the six seasons, subtract another .0006 for each out made under 800.

   The purpose of this step is to recognize that players with fewer plate appearances are probably less effective players.

4. Add .09 if the player had more than 1,600 outs made (not including those added in step 2).
5. This gives you the player’s projected performance, expressed in RC27. To figure the luck, subtract it from the actual RC27, multiply by outs made, and divide by 27. So if a player projects to 4.5, his actual was 5.5, and he did all that in 270 outs that year, then (1) he was lucky by 1.0 runs per game; (2) he was responsible for 10 games (270 outs divided by 27); so (3) he was “lucky” by 10 runs.

Pitchers

A pitcher’s luck is calculated in “component ERA” (CERA), which is the number of runs per game the opposition should score based on its batting line against him. To calculate a pitcher’s luck:

1. Take the player’s average CERA over six years: two years ago, last year counted twice, next year counted twice, and two years from now counted once. Weight the average by “outs made” (IP divided by three) so that seasons in which a pitcher had more playing time will have a higher weight. Adjust each CERA for league and park.
2. Add a certain number of “outs made” at the league average CERA:
   – if the player had more than 900 outs made in the six seasons, add 900 league-average outs made;
   – if the player had fewer than 400 outs made in the six seasons, add 400 league-average outs made; and
   – if the player had between 400 and 900 outs made, add that number of league-average outs made.
3. Temporarily add this year’s outs made to the total of the six seasons (not including those added in step 2). If that total is less than 1,200, add 0.0006 for each out made under 1,200.
4. Add .35.
5. If the player started more than 70% of his appearances, add .1.
6. If the player had more than 300 outs made this year, but less than 300 outs made total in the six seasons from step 1, ignore the results of the previous five steps, and use the league/park average CERA instead. (That is, assume he’s an average pitcher.)
7. This gives you the player’s projected performance, expressed in CERA. To figure the luck, subtract the actual CERA, multiply by outs made, and divide by 27. So if a player projects to 3.50, his actual was 4.50, and he did all that in 270 outs that year, then (1) he was unlucky by 1.0 runs per game; (2) he was responsible for 10 games (270 outs divided by 27); so (3) he was “unlucky” by 10 runs.

But there still is a host of other potentially interesting issues I want to explore. Are there significant differences even among similar classes of hitters? Are there situational factors that need to be taken into consideration? For example, if there are much lower error rates with no one on, do leadoff batters reach base this way less frequently than cleanup hitters? How big a factor is batter speed? Or whether the batter bats from the right or the left side? Do some parks have much higher errors rates than others, due either to the influence of official scorers or environmental factors such as rocky infields, poor lighting, and unusual wind currents?

On August 11, 1903, the A’s were visiting the Red Sox, then playing in the old Huntington Avenue Grounds. At the plate in the seventh inning was Rube Waddell, the colorful southpaw pitcher for the A’s, who was known to run off the mound to chase after passing fire trucks, and to be mesmerized whenever an opposing team brought a puppy onto their bench to distract him. Waddell lifted a foul ball over the right-field bleachers that landed on the roof of a baked-bean cannery next door.

The ball came to rest in the steam whistle of the factory, which began to go off. As it was not quitting time, workers thought there was an emergency and abandoned their posts. A short while later, a giant cauldron containing a ton of beans boiled over and explod­ed, showering the Boston ballpark with scalding beans. It is prob­ably safe to say that this was the most dramatic foul of all time.

Certainly so! When laughter subsided, I remarked that I’d contributed a multi-part series of articles for the Red Sox maga­zine in 2003, recounting every game of the 1903 season, which culminated in the first victory in a modern World Series for the Boston Americans. (The team was not named the “Red Sox” until owner John I. Taylor designated that name on December 18, 1907, while selecting new uniforms for the 1908 season.) I’d not come across any mention of an explosion raining baked beans onto the crowd – it’s the kind of thing you’d remember – but I certainly wanted to learn more.

I wrote Tim and asked him where he’d learned about this inci­dent, and he referred me to Mike Gershman’s book Diamonds. On page 70, there it was, a story the very respected Gershman titled, “The Great Beantown Massacre.” Mike gave as his source Charles Dryden, whom he described as “for years Philadelphia’s leading baseball writer.” Dryden’s rendition was even more dramatic:

In the seventh inning, Rube Waddell hoisted a long foul over the right-field bleachers that landed on the roof of the big­gest bean cannery in Boston. In descending, the ball fell on the roof of the engine room and jammed itself between the steam whistle and the stem of the valve that operates it. The pressure set the whistle blowing. It lacked a few minutes of five o’clock, yet the workmen started to leave the building. They thought quitting time had come.

The incessant screeching of the bean-factory whistle led engineers in the neighboring factories to think fire had broken out and they turned on their whistles. With a dozen whistles going full blast, a policeman sent in an alarm of fire.

Just as the engines arrived, a steam cauldron in the first factory, containing a ton of beans, blew up. The explosion dislodged Waddell’s foul fly and the whistle stopped blowing, but that was not the end of the trouble. A shower of scalding beans descended on the bleachers and caused a small panic. One man went insane. When he saw the beans dropping out of a cloud of steam, the unfortunate rooter yelled, “The end of the world is coming and we will all be destroyed with a shower of hot hailstones.”

An ambulance summoned to the supposed fire conveyed the demented man to his home. The ton of beans proved a total loss. (Dryden’s story ran in the Philadelphia North American on August 12, 1903.)

What a great story! Naturally, I wanted to learn more. I was surprised I hadn’t come across such a dramatic event while read­ing 1903’s daily game stories in the Boston Herald. I’d read all the usual books about the Red Sox and hadn’t heard this one before. I couldn’t find anything on ProQuest, which made me wonder even more. So I took myself off to the Microtext Reading Room at the Boston Public Library. Surely Dryden would not have been the only sportswriter to have noticed 2,000 pounds of boiling baked beans splattering the bleachers at the ballpark, or the dozen fac­tory whistles shrieking alarm.