Saves Above Expected: A New Contextual Metric For Closers

Mariano Rivera of the New York Yankees led all pitchers with 652 career saves when he retired after the 2013 season. (National Baseball Hall of Fame Library)

 

INTRODUCTION

Chicago Sun-Times sportswriter Jerry Holtzman is commonly credited with devising the save statistic in 1959 to recognize the increasing prominence of relief pitching in the 1950s, although Dodgers statistician Allen Roth had devised a simplistic prototype of the save as early as 1951.1 Before then, the bullpen was mainly a haven for broken down starters who could fool batters only for an inning or two, not a legitimate specialty in its own right. Holtzman changed that, defining the save by giving it a specific set of criteria. When a pitcher finished the game for the winning team, Holtzman outlined two situations in which a save could be awarded. While preserving the team’s lead, the save could only be awarded if the pitcher entered the game with a lead of no more than two runs and pitched at least one inning, or if he entered the game with the tying run at the plate or on the bases.2

Applying MLB’s 1969 definition retrospectively, no pitcher had accrued more than 27 saves in a season before 1960; Joe Page (1949) and Ellis Kinder (1953) shared that record.3 This modest number is unsurprising, since pitchers completed more than 80% of their starts before 1920, more than 50% before 1930, and 40% as late as 1950.4 Almost immediately, managers started reserving their best relief pitchers as “closers,” who were used whenever possible to finish games in which there was an opportunity for a save. In the 1960s and 1970s, relief aces were generally deployed as “firemen” who were brought into high-leverage situations as early as the sixth or seventh inning to get out of jams, then remained in the game to pick up the save. But by the late-1980s, when Oakland’s Tony LaRussa made Dennis Eckersley his closer, relief roles became even more specialized, with the closer confined mainly to the ninth inning of games in which his team led by three runs or fewer. The single-season saves record climbed accordingly, reaching 31 in 1965 (Ted Abernathy), 38 in 1973 (John Hiller), 45 in 1983 (Dan Quisenberry), 57 in 1990 (Bobby Thigpen), and 62 in 2008 (Francisco Rodriguez).5 Meanwhile, complete games declined precipitously, falling below 3% of all starts in 2006 and below 0.6% in 2024.

Despite the fact that the save construct was simplistic and that not all saves are created equal, the save statistic has had surprising staying power among fans, journalists, and Hall of Fame voters. In 1969, the Sporting News began recognizing AL and NL Relievers of the Year.6 The Rolaids Relief Man Award, based on a points system combining wins and saves, began in 1976 and was taken over by MLB in 2014. Some absurdities—like awarding a save to a reliever who pitched only the final inning of a 10–0 rout—were fixed in 1974; now he must pitch at least three innings to qualify for a save in such a lopsided game. Nevertheless, the save construct continues to give the same credit to a modern closer, who enters a game at the start of the ninth inning to protect a three-run lead, as it does to an old-fashioned “fireman,” who enters in the seventh with the bases loaded and no one out and a one-run lead, escapes without allowing a run, and nurses that one-run lead through the eighth and ninth innings. Something is clearly wrong.

Many serious baseball analysts have tried to devise a metric that would better capture the true value provided by relief pitchers.7 The most popular of these is Win Probability Added (WPA), which calculates a pitcher’s specific contribution to the probability of winning a game.8 This metric is useful because (unlike ERA) it assigns a share of responsibility to the reliever for the “inherited” baserunners he allows to score and because it considers “leverage,” i.e., the higher impact on win probability of each run allowed in the later innings of closer games. WPA can also be applied broadly to any pitcher, including starters and relievers who pitch in non-save situations. However, the calculation of WPA is opaque and proprietary; baseball websites like Baseball Reference and FanGraphs offer differing versions.9

The present article proposes a less ambitious but conceptually simpler metric, saves above “expected save probability,” which is designed specifically to adjust for the difficulty of the save opportunities with which a relief pitcher is presented. An expected save probability (ESP) is assigned to each situation in which a pitcher may enter a game, ranging from an easy one-inning bases-empty save opportunity (where the ESP may exceed 90%) to a hairy multi-inning save opportunity (where the ESP may be less than 10%). For multi-inning saves, ESP will increase if the reliever’s team scores insurance runs after he enters the game. The cumulative ESP of a pitcher’s save opportunities is then subtracted from his actual number of successful saves. Although the calculation of Saves Above ESP, which requires meticulous analysis of play-by-play records, is tedious at best, it has an easily understood meaning: What was that pitcher’s success rate in converting his save opportunities compared to what a “generic” MLB average pitcher would have done (on the average) when presented with the same opportunities?

In this article, Saves Above ESP will be presented for a sample of twelve relief pitchers, all of whom were deployed in save situations in at least 55% of their relief appearances. The selected pitchers comprise the Top 11 from the all-time saves leaderboard plus Hall of Famer Bruce Sutter, one of the earliest true closers, who compiled 300 saves in an injury-shortened career.10

METHODS

Baseball Reference is the source of all player statistics used in this article, including WAR (Wins Above Replacement) and WPA, and are current as of May 2025.11 However, I have not included games from the 2025 season. In this article, the acronym WAR refers exclusively to pitching WAR. Baseball Reference’s Stathead Game Finder was used to extract the play-by-play accounts of each of a pitcher’s save opportunities.12 The ESP for each save opportunity was calculated as described below.

Greg Stoll’s analysis of Retrosheet data from the 1957 through 2015 seasons was used to estimate the probability of scoring a specific number of runs in any of the 24 scenarios defined by all possible combinations of numbers of outs (0, 1, or 2) and runners on base (none, 1B, 2B, 3B, 1B and 2B, 1B and 3B, 2B and 3B, or bases loaded).13 These data, which represent averages over many teams, ballparks, and eras, and are not specific to the particular park or to the opponent a pitcher may be facing, were used to estimate the probability that a generic MLB-average RELIEVER would achieve a save in the same situation in which a relief pitcher entered a given game.14 For example, consider a pitcher who enters the game at the start of the ninth inning—the most common scenario for closers since 1990. If his team leads by one run, his ESP is 72.7%, since 72.7% of all innings in Stoll’s database were scoreless. By the same logic, the ESP for relief pitchers who enter at the beginning of the ninth to protect a two-run lead would be 87.5%, since 87.5% of all innings in Stoll’s database end with fewer than two runs scored. Similarly, the ESP for relievers who enter at the beginning of the ninth inning to protect a three-run lead would be 94.4%, since 94.4% of all innings in Stoll’s database end with fewer than three runs scored.15 The calculation of ESP is equally straightforward for relievers who enter after the beginning of the ninth inning to protect a lead. At the two extremes, the ESP is 13.4% for a reliever who enters with the bases loaded and no one out to preserve a one-run ninth-inning lead and 99.3% for a reliever who enters with the bases empty and two outs to preserve a two-run ninth-inning lead.

The calculations become more complicated for multi-inning saves, especially when the reliever’s team expands its lead after he enters the game. For example, the ESP for a reliever who enters a game with runners on 1B and 3B with one out in the bottom of the 8th inning with a one-run lead is 41.6%—the product of the probability of emerging unscathed from the 8th inning jam (57.2%) times the probability of pitching a scoreless ninth inning (72.7%). If his team adds an insurance run in the 9th inning, the expected save value becomes 50.0% (57.2% times 87.5%). The ESP for more complicated scenarios can be calculated by combining the probabilities of simpler sub-scenarios.

 

 

RESULTS

Table 1 lists the 12 relief pitchers analyzed in this article by descending order of career saves, along with a few salient standard career stats. Dennis Eckersley’s stats during his 12 seasons as a reliever are shown in a separate line. Not counting Eckersley’s 45.4 WAR as a starter in 1975–86, Mariano Rivera clearly stands out from the crowd in ERA, ERA+, WAR, and WPA, as well as saves. The nine pitchers who began their bullpen careers after 1986 are closely bunched regarding the percentage of save opportunities (defined as saves plus blown saves) converted to saves; their success rates range from 84.6% (Eckersley) to 89.1% (Rivera and Nathan). The others—Sutter (74.8%), Franco (80.8%), and Smith (82.3%)—began their bullpen careers between 1976 and 1984, when closers were often deployed as firemen to get out of jams and had to pitch more than one inning to earn a save. The following stats are also worth noting:

• Rivera is the only one of the 12 listed pitchers with at least 30 WAR as a reliever. For relief pitchers and most other positions, it takes roughly 60 WAR to be a strong candidate for the Hall of Fame.
• The career ERA and ERA+ of Wagner and Papelbon stand out from the mere mortals not named Rivera.
• Hoffman, Nathan, Jansen, Wagner, and Papelbon all perform well on the WPA metric (28-34), although no one comes close to Rivera. This suggests that they were proficient, not only in keeping their own ERA low but also at preventing inherited runs from scoring. Kimbrel, Smith, Franco and Sutter performed relatively weakly in WPA.

Taken together, these stats seem to suggest that some of the pitchers in Table 1 may be more deserving than others of their lofty ranking in saves. But they do not tell us which of these pitchers were best at preserving a lead. This is the skill that Saves Above ESP is designed to measure.

 

 

Saves Above ESP for our 12 relief pitchers are shown in descending order in Table 2.

The top five pitchers in Saves Above ESP exactly follow the ranking for saves, although the gap between Rivera and Hoffman is far greater—especially when postseason saves are included. However, Wagner, Rodriguez, and Franco drop to the bottom of the ranking when their saves are viewed in the context of their difficulty. This is not too surprising for Franco (138 ERA+ and 19.2 WPA) or Rodriguez (148 ERA+ and 24.2 WPA), but is quite unexpected for Wagner, whose 187 ERA+ was second only to Rivera and whose 29.1 WPA ranked fifth among the 12 relievers. Even Sutter (who had 122 fewer saves) and Eckersley (who did not become a reliever until his age 32 season) rank higher than Wagner.

Although Hoffman holds the highest single-season mark of 8.1 Saves Above ESP in 1998, Rivera’s career high 7.5 Saves Above ESP in 2008 was nearly as good. However, unlike Hoffman, who only had three seasons with at least 4.0 Saves Above ESP, Rivera had six such seasons in his 19-year career. Papelbon, Wagner, and Rodriguez are the only other relievers in Table 2 with at least three such seasons. It is also worth noting that a pitcher’s peak year for Saves Above ESP does not always coincide with his peak year for saves. For example, Francisco Rodriguez’s record-setting 62 saves in 2008 were accompanied by seven blown saves (BS), and resulted in fewer Saves Above ESP than his 47-save (4 BS) 2006 season or his 45-save (5 BS) 2005 season. Similarly, Rivera’s 53 saves in 2004, Smith’s 47 saves in 1991, Jansen’s 47 saves in 2016, Kimbrel’s 50 saves in 2013, Papelbon’s 41 saves in 2008, Eckersley’s 51 saves in 1992, and Wagner’s 44 saves in 2003 represented career highs in saves but not in Saves Above ESP; other seasons with fewer saves had fewer blown saves or (in Smith’s case) more difficult save opportunities and thus more Saves Above ESP.

The extraordinary postseason performance of Mariano Rivera is especially noteworthy. Certainly, he had the advantage of nearly twice as many postseason save opportunities (47) as Jansen (24), his closest competitor. (Eckersley (17) and Kimbrel (11) were the only others with at least 10 postseason save opportunities.) However, Rivera was also even more stingy in the postseason (0.70 ERA) than he was in the regular season (2.20 ERA) and had an 89.4% (42/47) success rate for saves. This is all the more remarkable because Joe Torre frequently asked Rivera to pitch multiple innings to collect his postseason saves. Rivera succeeded in 73% (8/11) postseason save opportunities with ESP <65% resulting in 2.8 postseason Saves Above ESP; a generic reliever would have been expected to save only 5.2 (47%) of those 11 games.

A more detailed examination of the impact of reliever usage (which has changed over time) provides further insight into the divergence of Saves Above ESP from raw save totals, as shown in Table 3.

 

 

Looking quickly at the left half of the table, each of the 12 relievers enjoyed a high success rate in easy (ESP≥65%) save situations, ranging from 92.0% for Rivera to 86.3% for Sutter. Turning to the right half of the table, however, we see that the real disparity is in how these 12 relievers fared in more difficult (ESP<65%) save situations. Lee Smith really thrived under pressure, succeeding in 66/105 difficult save opportunities and amassing 12.4 Saves Above ESP in these games. Dennis Eckersley also did well, amassing 6.2 Saves Above ESP in only 58 difficult save opportunities. Sutter and Rivera (the only twenty-first century pitcher who has been tested much in ESP<65% save situations) also performed well in these challenging opportunities. At the other end of the of the spectrum, Franco struggled in his 80 ESP<65% appearances, converting only 34 saves (42.5%)—6.2 fewer saves than expected for a generic reliever. The other seven pitchers, all of whom pitched mostly in the twenty-first century, were each presented with fewer than 35 difficult save opportunities. Hoffman and Jansen fared pretty well in these situations, while Rodriguez, Wagner, and Nathan fared rather poorly. But the sample sizes are small.

Obviously, the infrequent usage of the most recent relievers (Nathan, Papelbon, Kimbrel, and Jansen) in ESP<65% situations reflects the temporal trend, which has increasingly called for closers to be deployed primarily to start the ninth inning. At that point in the game, ESP is at least 72.7% (the value for a one-run lead). Most closers today rarely encounter a save opportunity with an ESP of less than 65%, except when they are called upon to protect a one-run lead in extra innings with the “zombie runner” at 2B (ESP=37.9%). However, it is curious that Billy Wagner was used only 22 times in his career with ESP<65%. By contrast, Rivera, who (like Wagner) began his career in 1995, was used in 56 ESP<65% situations during the regular season plus 11 during the postseason. The most difficult save of Wagner’s career—with an ESP of 52.8%—came on September 19, 1999, when he entered a 4–3 game against St. Louis with a runner at 1B and one out in the bottom of the eighth inning, and gave up no hits and two walks while getting the final five outs (four coming on strikeouts).16 He faced six more difficult save opportunities in his career—and failed in all of them. At the other end of the spectrum, Lee Smith saved 34 games in more difficult situations than Wagner’s most difficult save, including two (while pitching for the Cubs in 1983–84) with ESP<40%. On May 10, 1983, Smith protected a 3–2 lead over the Dodgers after entering at the start of the 7th inning (ESP=38.4%).17 On July 4 1984, he protected a 2–1 lead over the Padres after entering with runners on 1B and 3B with one out in the 9th (ESP<34.3%).18 Smith’s outstanding success rate in difficult save opportunities explains why he outranks Wagner in Saves Above ESP, despite Wagner’s far superior ERA and WPA.

 

Figure 1. Wagner vs. Rivera and Hoffman (In-Season)

 

Figure 1 compares Wagner’s career progression of in-season Saves Above ESP with Mariano Rivera and Trevor Hoffman, his two closest contemporaries. Hoffman, who is two years older than Rivera and reached the majors two years earlier, got a head start and leaped to a big lead over Rivera with his career year in 1998, but Rivera gradually gained on him and overtook him in 2007, by which time Hoffman was fading. Rivera expanded his lead over Hoffman to 15 Saves Above ESP in the remaining six years of his career. Wagner was two years younger than Rivera (although he also reached the majors in 1995), but backslid with –4.8 Saves Above ESP following an excellent 1999 season (5.6 Saves Above ESP), and still had only 1.7 Saves Above ESP as he entered the 2001 season. He then kept pace with Rivera from 2000–03, slowed down in 2004–07, and was worse than a generic reliever in 2008–10. Although he was deployed in ESP<65% save situations 17 times in 1997–2000, he performed so poorly (3.9 saves below ESP), that he was rarely used again in those circumstances—and never after 2005. While it is always risky to make claims about poor clutch performance by extrapolating from small sample size, those Hall of Fame commentators who criticized Wagner’s rocky postseason record of 1–1 with 3 SV and 1 BS and a 10.03 ERA may have had a point. (Of course, Ty Cobb and Ted Williams also produced below expectations in the World Series, so Wagner is not alone.)

DISCUSSION

One cannot meaningfully assess relief pitchers by their raw save totals or even their raw save percentages without knowing the context of how they were used. The Saves Above ESP metric is designed specifically to provide that context by adjusting for the probability (ESP) that a generic major league average pitcher would successfully close out the game. Adjusting for ESP does not change the fact that saves is a situational metric which (like RBI, Runs, and Wins) depends on the opportunities a player receives. By either metric, a reliever who is asked to protect a one-run lead with the bases loaded and no one out in the ninth inning and limits the damage to a game-tying sacrifice fly is deemed a failure, while another reliever who is called upon at the start of the ninth inning to protect a three-run lead and escapes after giving up two runs and leaving the bases loaded is deemed a success. But while merely counting saves gives the first pitcher a zero and the latter pitcher a one, Saves Above ESP gives the first pitcher a –0.13, and the second pitcher a +0.06. It’s still not completely fair, but fairer than just counting saves.

Saves Above ESP resembles WPA and similar metrics in that it views actual outcomes in the context of an empirical run-scoring probability database. However, it differs fundamentally from these metrics in that it is tied to a specific pass/fail outcome, the save. WPA is more abstractly tied to winning probability. A relief pitcher who relinquishes a lead, stays in the game while his team regains the lead, and then protects that lead may chalk up a positive WPA for that game, but will be charged with a blown save and a decrement in his Saves Above ESP. Saves Above ESP is useful for evaluating pitchers who are used predominantly as closers, but (unlike WPA) sheds little light on the value of old-time relievers like Hoyt Wilhelm, who made only 32% of his pitching appearances in save situations.

Another limitation of Saves Above ESP is that ESP is based on simple empirical averages of runs scored in various game situations over a 59-year period, which includes the run-starved 1960s and the steroid-inflated high-rolling 1990s and early 2000s. It doesn’t consider whether the opposing hitter is Barry Bonds or Mario Mendoza or whether the game is in Miami or Denver. In the absence of a database that tabulates game situations in easily accessible form, it is also tedious to calculate ESP—to the point of becoming impractical—for old-school “firemen” like Gossage and Fingers, who encountered a wide variety of scenarios, each requiring its own probability calculation. For most modern closers, one can merely copy and paste the ESP for the 70–80% of their save opportunities in which they entered the game to start the ninth inning. Even if it were practical to automate the calculation of Saves Above ESP for the entire careers of multi-inning firemen, this would still fail to capture the value of their frequent usage in high-leverage non-save situations. WPA (which has its own limitations) is more useful in that regard, and also permits comparison of relievers to starters.

The Saves Above ESP metric validates the lofty rating of the top five on the saves leaderboard but scrambles the ranking of the reliever in the #6–11 positions. John Franco, Francisco Rodriguez, Billy Wagner, each of whom successfully converted only 2–4% more of their save opportunities than would have been predicted for a generic MLB average pitcher, fare relatively poorly in Saves Above ESP, ranking below Bruce Sutter who had more than 100 fewer career saves (Table 2). The low ranking of Billy Wagner is particularly surprising given his sparkling 2.31 ERA, 0.998 WHIP, 11.9 SO9, and solid 21.9 WPA. For what it’s worth, Wagner performed poorly in difficult save opportunities (ESP<65%) to the point where his managers essentially stopped using him in such situations in the latter half of his career. The new metric also elevates the rankings of Jon Papelbon and Joe Nathan, who were both one and done in the 2022 Hall of Fame voting.

Note that the Saves Above ESP construct compares a closer’s success in save situations to the performance of a generic MLB average pitcher, not to a hypothetical “replacement level” pitcher. Thus, it is more analogous to an unadjusted version of Wins Above Average (WAA) than to WAR. Someone like John Franco, who had 10 saves above “average” over the course of a 22-year career, was still quite a good pitcher—just not a credible Hall of Fame candidate. Also, we should appreciate the magnitude of Mariano Rivera’s 60.1 Saves Above ESP over the course of his career—especially his 7.5 Saves Above ESP in postseason play. Rivera probably won the Yankees several more pennants and World Series then they would have won with a merely good reliever like Franco as their closer.

After the election of Billy Wagner in 2025, the Hall of Fame now contains nine relief pitchers—the six included in this article plus Rich Gossage, Hoyt Wilhelm, and Rollie Fingers. Some have argued that the role is under-represented in the Hall.19 However, it is hard to see any of the all-time saves leaders discussed in this article who are not already in the Hall of Fame as more than borderline candidates. Indeed, I would argue that Rodriguez and Franco clearly don’t belong. Perhaps, calculating Saves Above ESP for relievers with lesser career save totals but with high WPA, ERA+, and/or standardized peak WAR, may help uncover some hidden gems.20

CONCLUSIONS

The usefulness of the save statistic is greatly enhanced by adjusting for the difficulty of the save opportunities that a relief pitcher encounters. In general, relief pitchers who pitched before 1990 had a more difficult job than modern relievers, who are most often inserted with no one on base and asked to hold a lead for just one inning. Pre-1990 relievers generally received fewer save opportunities than their present day counterparts and were often inserted with runners on base and required to preserve a lead over multiple innings. Comparing a relief pitcher’s save rate to the average expected save probability (ESP) of his save opportunities levels the playing field for relievers who pitched in different eras and for managers with differing bullpen usage patterns.

DAVID J. GORDON, MD, PhD is a retired biomedical scientist and longtime Cubs fan, who joined SABR in 2016 and has a keen interest in baseball history and in metrics that can be applied across historical eras. Since 2016, he has authored eight BRJ papers and three books: Baseball Generations, A Historical Account of the Best Players of Each of Seven Eras Spanning 1871–2019; The American Cardiovascular Pandemic: A 100-Year History, a chronicle of how advances in cardiovascular science have reversed the twentieth century tide of heart attack mortality; and Baseball’s Shooting Stars, which tells the stories of 30 players who had a single Hall of Fame quality season that they could never replicate. More recently, he has collaborated with John Contois on a book about MLBs greatest hitting pitchers, which should be available in bookstores in early 2026.

 

Notes

1. Emma Baccellieri, “Rise and Fall of the Save,” Sports Illustrated, June 3, 2019, https://vault.si.com/vault/2019/06/03/rise-and-fall-save.

2. MLB.com, Definition of the Save, https://www.mlb.com/glossary/standard-stats/save.

3. Baseball Reference, Yearly League Leaders and Records for Saves, https://www.baseball-reference.com/leaders/SV_leagues.shtml.

4. Baseball Reference, League Year-By-Year Pitching Averages, https://www.baseball-reference.com/leagues/majors/pitch.shtml.

5. Baseball Reference, Yearly League Leaders and Records for Saves.

6. Baseball Reference Bullpen, “Reliever of the Year Award,” https://www.baseball-reference.com/bullpen/Reliever_of_the_Year_Award.

7. Jim Kaplan, “The New Way to Spell Relief,” Sports Illustrated, April 12, 1982, https://vault.si.com/vault/1982/04/12/the-new-way-to-spell-relief; Doug Dreinen, “New Ways to Spell Relief,” in 1998 Big Bad Baseball Annual Master Press.

8. Baseball Reference, Win Expectancy (WE) and Run Expectancy (RE) Statistics, Win Expectancy (WE) and Run Expectancy (RE) Stats Baseball-Reference.com; Piper Slowinnski, “WPA,” FanGraphs, February 16, 2010, https://library.fangraphs.com/misc/wpa/; Don Malcolm, Ken Adams, Brock J. Hanke (eds), Masters Press; Dave Studeman, “The One About Win Probability,” The Hardball Times, December 27, 2010, https://tht.fangraphs.com/the-one-about-win-probability/.

9. Stathead Baseball, Player Pitching Season and Career Stats Finder: WPA for Pitchers with at least 50% of Appearances in Relief. https://stathead.com/baseball/player-pitching-season-finder.cgi?request=1&match=player_season_combined&order_by=p_wpa_def&year_min=1947&games_started=60&role=reliever&games_relieved=50; FanGraphs.com, WPA for Relief Pitchers, https://www.fangraphs.com/leaders/major-league?pos=all&lg=all&qual=y&type=3&season=2025&month=0&season1=1871&ind=0&team=0&rost=0&players=0&stats=rel&sortcol=2&sortdir=default&pagenum=1.

10. Baseball Reference, Career Leaders and Records for Saves, https://www.baseball-reference.com/leaders/SV_career.shtml.

11. Baseball Reference, https://www.baseball-reference.com/bullpen/Wins_Above_Replacement.

12. Stathead Baseball, Player Pitching Game Stats Finder, https://stathead.com/baseball/player-pitching-game-finder.cgi.

13. GregStoll.com, “Expected Runs in an Inning,” https://gregstoll.com/~gregstoll/baseball/runsperinning.html#about.

14. Baseball Reference, https://www.baseball-reference.com/#site_menu_link.

15. With the introduction in 2020 of the “zombie runner” rule, which places a runner at 2B at the start of every extra inning, the ESP for a standard extra-inning three-out save has become 37.9% for a one-run lead, 73.1% for a 2-run lead, and 87.5% for a three-run lead.

16. Baseball Reference, Houston Astros vs. St. Louis Cardinals Box Score: September 19, 1999, https://www.baseball-reference.com/boxes/SLN/SLN199909190.shtml.

17. Baseball Reference, Chicago Cubs vs. Los Angeles Dodgers Box Score: May 10, 1983, https://www.baseball-reference.com/boxes/LAN/LAN198305100.shtml.

18. Baseball Reference, Chicago Cubs vs. San Diego Padres Box Score: July 4, 1984, https://www.baseball-reference.com/boxes/SDN/SDN198407040.shtml.

19. Elaina and John Pakutka, “More Relief Pitchers Belong in the Hall of Fame,” SABR Baseball Research Journal, Fall 2023, 52 (2): 113–23, https://sabr.org/journal/article/more-relief-pitchers-belong-in-the-hall-of-fame-which-ones/.

20. David J. Gordon, “Standardized Peak WAR,” SABR Baseball Research Journal, Spring 2023, 52 (1): 49–58; https://sabr.org/journal/article/balancing-starter-and-bullpen-workloads-in-a-seven-game-postseason-series/. The reader is encouraged to refer to the online rather than the print version, since the latter has several significant errors, including the omission of a table and two key figures.