Age/Experience



Chapter Six – Offensive Issues

The goal of this chapter is to explore some areas relevant to offense other than its evaluation that have garnered research attention.

Age

Overall Offensive Trajectories

As I grew up watching games on television, I heard on several occasions that players generally peak between ages 28 and 32. Statistically, this guesstimate is both inaccurate and vague. In general, it is earlier, and it is dependent on specific skill. Further, there are methodological problems that invalidate any easy analytic method for determining the peak.

Phil Birnbaum (2009a) addresses two of these problems, both of which are relevant to what statisticians call “selection bias,” defined on Wikipedia as “the selection of individuals, groups or data for analysis in such a way that proper randomization is not achieved, thereby ensuring that the sample obtained is not representative of the population intended to be analyzed.” Suppose you just average the performance of players at different ages, and then use that average at each age as your estimate of offensive production. If you do, you will overestimate the productivity of the average older player, and here is why: The very best players may have lost some of their skills when they reach their mid and late 30s, but they are likely to still be performing at a fairly high level. Weaker players may have lost no more skill than the best ones, but that loss will be enough to end their careers. Phil used the example of Mike Schmidt, whose runs created per 27 outs was 8.9 runs at age 30, and Damaso Garcia, whose RC/27 at the same age was 3.7. At age 35, Schmidt had fallen to 7.3, but Garcia was gone. A naïve attempt to use average performance of players still in the game would result in a higher performance average (Schmidt’s 7.3) at 35 than at 30 (6.3 combining the two). The analogous problem can occur with very young players. Others noting this issue have been Schulz, Musa, Staszewski, and Siegler (1994), Hakes and Turner (2011), and, in his second book, Michael Schell (2005).

As Phil noted, a different path would be the “paired season” method, which is to take all players at each age cohort, compute the average change there is in their performance from one year to the next, and then use that change as an estimate for the change for everybody’s estimate. So, for example, just suppose that the average decrease in RC/27 from age 32 to 33 is one run per game. But, as Fair (2008) pointed out, players are far less likely to retire or be released after a good year than a bad year. If a player has a season in which he performs above his actual ability level due to random processes, than it is more likely that some team will want his services for another season than if he plays below his norm. But if random processes are involved, it is unlikely that he will repeat that season’s performance, so there will probably be a large dip between that and the next year, hastening his departure at that point. As a consequence, players are likely to perform unusually well in their next-to-last season. This leads to a statistical bias in which the next-to-last season should result in greater error in estimation; Fair demonstrated that the error is relatively large. Phil Birnbaum also showed that this error would be a bias toward overestimating declines as a whole, as the soon-to-be-released player is not really as bad as his performance implies.

There is a third problem with methods such as this. As will be described later, different skills increase and decrease at different rates. Just to name two obvious examples, speed is greatest with young players whereas plate discipline often improves such that walks increase with experience. As a consequence, all things being equal, a player whose overall performance relies on the former will probably peak earlier and leave the game before a player who relies on the latter.

It took a long time for the sabermetric community to understand the implications of these issues. In particular, early on there was a tendency to look at overall performance rather than categorize players according to differing specific skills. As with so much else, Bill James led the way in his first conventionally-published Baseball Abstract (1982). Bill’s method was relatively informal, but his findings have been fairly well corroborated since then. He used an informal method he called Value Approximation, which assigns “points” for various annual achievements, e.g., 1 point for a batting average of .250 or more, and one additional point for each BA increase of 25 points, such that a .400 average is worth 7 points. Using all 977 players who appeared in the majors that were born in the 1930s, Bill found that the total “approximate value” of all players in the data set increases in an inverted-U curve that is flatter for older players than for younger, which implies that older players lose ability slower than younger players gain it (more on this below). The curve was highest at ages 26 and 27, with sharp increases before than after; the total was half as much at ages 23 (3 or 4 years before peak) and 33 (6 or 7 years after peak). This method is problematic in that it makes no correction for the number of players in the majors at each age, and a greater number of players as a particular age will increase total approximate value over ages with fewer players. But for what Bill was attempting to show, this is not a problem, because it means that there are more players capable of playing in the majors at those ages; in other words, fringe players peak around 26/27 and so are good enough to be in the majors only around that point. Even so, a better method examines individual player trajectories, and Bill did some of that, with analogous findings.

Sticking with Bill’s relevant research for the time being, he later (1985a) looked at all players with at least 200 plate appearances at age 37 (chosen because only about five percent of major leaguers are still playing at that point) who had accumulated at least 1000 PA in their 25-29 and 35-39 age ranges, and compared performance between those ranges. Every index he examined except for BB/PA decreased substantially for those players over time (BA down .20, SA down .51, OBA down .17 despite the increase in walks, RC/game down 1.05, also SB% and HR/AB). Keep in mind that there is selection bias here, such that this data set mostly included players who were unusually good at maintaining their skills (still getting significant playing time at age 37). The implication is that a more general set would decrease even faster.

Other work on composite indices has also noted that overall performance peaks around age 27. Bob Boynton (2004) examined Win Shares totals for every hitter listed in the 8th edition of Total Baseball, and uncovered a peak at age 26. Mark Armour (2018a) contributed a study to the SABR Statistical Committee blog that reveals age 27 as associated with the highest overall bWAR between 1876 and 2017, 26 right behind, and 25 to 29 as the overall peak. Fair’s (2008) study included all players between 1921 and 2004 with at least 10 “full-time” seasons, defined as at least 100 games for position players. For batters, the peak was 27.6 for OPS and 28.3 for OBA. His work provides equations for the trajectories, with that for OPS declining more rapidly than that for OBA, which means power skills fade faster than on-base abilities. Fair’s method assumed the same trajectory for everyone but allowed for estimations of prediction errors for each player for each year, providing the opportunity to look for unusual performance. He noted a sample of players who tended to have positive errors toward the end of their careers, in other words, consistently playing better than what would have been expected given normal rates of decline. There were 17 who had at least four seasons of this sort from age 28 on, including Barry Bonds, Ken Caminiti, Luis Gonzalez, Mark McGwire, Rafael Palmeiro, and Sammy Sosa; prime suspects for drug-fueled performance enhancement. Most of the others were also recent (the only pre-1970’s name was Charlie Gehringer), such as Andres Galarraga and Larry Walker, both almost certainly due to their stints as Colorado Rockies.

As Bill James’s earliest work (1982) mentioned above shows, it is important to note that the data distributions of performance by age are not symmetrical, but rather are what statisticians call “positively skewed.” In plain English, they go up fairly quickly as player performance increases in their early 20s, but go down more slowly, as player skill erodes relatively slowly through the early 30s. As such, although the peak is usually around 27, players will usually create more total offense after than before 27. In his Win Shares book (2002), Bill James explored aging patterns for 148 great position players, those with at least 280 career Win Shares (see the Overall Evaluation chapter for definition) or more with fewer than 10 as pitchers. Grouped together, total Win Shares among these players increased very rapidly through the early 20s until its peak at age 26, and decreased slowly (still at 90 percent at age 32), and then at the more rapid clip of about 10 percent a year thereafter. Nate Silver (2006b) presented the following 1946 to 2004 data concerning mean percentage change in Equivalent Runs from present season to the next at different ages.

|Age |21 |22 |23 |

|Age |Percentage |>95 |Percentage |>95 |Percentage |

|Shoulder/clavicle |4952 |14.7 |Lower back/ |1895 |5.6 |

| | | |sacrum/pelvis | | |

|Upper leg |3942 |11.7 |Ankle |1713 |5.1 |

|Hand/finger/thumb |3409 |10.1 |Head/face |1694 |5.0 |

|Elbow |3185 |9.5 |Lower leg/ |1550 |4.6 |

| | | |Achilles tendon | | |

|Knee |2171 |6.5 |Foot/toes |1429 |4.3 |

| | | |All others |7683 |22.9 |

On to some specific injury types.

Concussions

As mentioned above, research concerning the impact of concussions is particularly valuable given the potential long-term repercussions. Green, Pollack, D’Angelo, Schickendantz, Caplinger, Weber, Valadka, McAllister, Dick, Mandelbaum, and Curriero (2015) uncovered evidence of 277 “mild traumatic brain injuries” in major and minor league baseball players during 2011 and 2012, resulting in a median of nine days out of action. The vast majority occurred either while in the field (53.4%), batting (27.4%), or baserunning (9.0%). Interestingly, the most prevalent causes differed between the minors (collision between players, 30.8%; hit by pitch, 26.7%; hit by batted ball, 18.4%) and majors (hit by batted ball, 29.3%; collision between players, 22%; hit by pitch and diving for balls, both 19.5%, with latter only 4.5% in minors). Not surprisingly, catchers were the most susceptible (41.5% of the total); among these, 41.2 percent were due to collisions, 35.3 percent to being hit by a batted ball, and 13.2 percent to being hit by a bat. Catchers also dominated Wasserman, Abar, Shah, Wasserman, and Bazarian’s (2015) list of 66 incidents between 2007 and 2013 that met a number of restricting conditions, with 26 instances, followed by 20 outfielders, 13 corner infielders, and only 7 middle infielders. Mean estimates of time missed cited in articles tended to be about a month (Pettit, Navarro, Miles, Haeberle and Ramkumar, 2018; Sabesan, Prey, Smith, Lombardo, Borroto and Whaley, 2018). The fact that mean time missed is far greater than median implies that a substantial number of concussions have resulted in very long absences, as much as a full year.

Turning to performance effects of concussions, Wasserman et al. compared 38 players who missed fewer than 10 days with a set of 68 players on the bereavement or paternity lists and thus missing fewer than 10 days for non-health reasons. With no differences in the two weeks prior to injury, the two weeks after returning to action resulted in significantly worse performance for the concussed (BA, .232 vs. .266; SA, .366 vs. .420; OBA, .301 vs. .320; OPS, .667 vs. .746). These figures were basically the same for the entire sample of 66, including those missing more than 10 days. Fortunately, the performance decrement for the concussion victims had become far smaller in the 4 to 6 week period after return. A return to pre-concussion performance has also been noted by Sabesan et al. (2018), Ramkumar, Navarro, Haeberle, Pettit, Miles, Frangiamore, Mont, Farrow, and Schickendantz (2018), and Chow, Stevenson, Burke, and Adelman (2019). In contrast, Pettit et al. (2018) reported that the likelihood of the concussed playing a full season one (61.5%), three (33.8%) and five (16.9%) seasons after the year of injury was noticeably below players missing time due to bereavement or paternity leave (88.3%, 62.1%, and 36.5% respectively).

Other Injury Types

Although not as prevalent as with pitchers, ulnar collateral ligament tears and resulting reconstruction surgery also occurs to position players. Particularly striking in published reports are its effects on catchers. Camp, Conte, D’Angelo and Fealy (2018a) examined 167 UCL reconstructions on major and minor league position players between 1984 and 2015, with 8 of these second-timers. Surgery was far more prevalent among catchers (46 cases) than infielders (62 across the four positions) or outfielders (58 across the three), and rate of return to action (58.6%) was markedly lower than other positions (infielders, 75.6%; outfielders 88.9%), and pitchers (83.7%). In addition, unlike infielders and outfielders, catchers were less likely to return to play and, if they did, failed to return to pre-injury performance levels (Begly, Guss, Wolfson, Mahure, Rokito, and Jazrawi, 2018), were more likely to require a second procedure (Camp et al.), and had much shorter careers after the procedure than a matched set without it (2.8 versus 6.1 seasons; Jack, Burn, Sochacki, McCulloch, Lintner, and Harris, 2018). Those at other positions did suffer in that half of those in Jack et al.’s data set changed positions upon return, likely down the defensive spectrum. Finally, median time to return to play according to Camp et al. was highest for pitchers (392 days), equal for catchers (342) and outfielders (345), and lowest for infielders (276).

Jack, Sochacki, Gagliano, Lintner, Harris, and McCulloch (2018) uncovered 21 thumb ligament repairs for position players between 1987 and 2015. All returned to play, an average of four months after the procedure. There were no significant differences before and after surgery or with a matched group in games played, WAR, or UZR.

Biceps tenodesis is a procedure for fixing biceps tendon ruptures. The track record for pitchers receiving this treatment is poor, but appears to be much better for position players. Chalmers, Erickson, Verma, D’Angelo and Romeo (2018) uncovered five such examples between 2010 and 2013; four of whom were able to return to play.

Schallmo, Singh, Barth, Freshman, Mai, and Hsu (2018) explored 18 major league players with serious cartilage damage to the knee between 1991 and 2015, including both pitchers and position players. All returned to action after an average of 254 days, but with significant decrements in OPS for position players and WHIP for pitchers the following season. However, with an average age of 31 years, performance drops could be a result of natural career trajectory, and there is no matched group to make any comparison.

I found three studies concerning hip arthoscopy covering almost the same time periods; Schallmo, Fitzpatrick, Yancey, Marquez-Lara, Luo, and Stubbs (2018; 1999 to 2016), Frangiamore, Mannava, Briggs, McNamara, and Philippon (2018, 2000-2015), and Jack, Sochacki, Hirase, Vickery, McCulloch, Lintner, and Harris (2019, 2000 to 2017). The number of affected players differed among them (33, 23, and 26 respectively), as did the average age of injury (30, 26, and 30 respectively). About 80 percent returned to action. Both Schallmo et al. and Jack et al. claimed lower OPS in the season after compared to the season before, but given the age of their sample, we again may be seeing the impact of natural career trajectories. Frangiamore et al.’s group did not register performance drips (.264 BA the year before, .267 BA the year after), but their data set was a lot younger. I have no idea why the average ages differed so markedly across studies.

The hook of hamate is a hand bone that can be injured while swinging the bat.  Guss, Begly, Ramme, Taormina, Rettig, and Capo (2018) limited their sample to 18 cases with at least 100 major league PAs in two seasons before and after the injury.  There was similar performance in WAR, ISO, OPS and other measures before and after injury and with a control group matched on age and Similarity Score.

Finally, Camp, Wang, Sinatro, D’Angelo, Coleman, Dines, Fealy, and Conte (2018) examined 2920 major and minor league players who missed at least one game between 2011 and 2015 due to being hit by a pitch. Fortunately, only 1.4 percent needed surgery. The hand was the target for 21.8 percent of these, followed by the head (17%), elbow (15.7%), forearm (9.1%), and wrist (7%). Actual injuries were reported for 31 percent of those hit in the head, compared to 9 percent for the forearm and hand and 2 percent or less for other locations. Pitch velocity correlated about .30 with injuries per HBP and almost that much for days missed per injury. Protective equipment helped return to play. If hit on the elbow, an average of 1.8 days were missed if the player was wearing a pad versus 3.5 days without one, and if hit on the head, 7.3 days were missed if the ball hit the helmet versus 12.7 days if it did not.

Performance Enhancing Drugs

Research examining the impact of performance enhancing drugs on hitting began appearing after Major League Baseball was finally embarrassed into attempting to route out the problem. The best rationale for this work of which I am aware is a study by a physicist named Tobin (2008). After reviewing past physiological work on the impact of steroids on weight lifters, he decided to assume an increase in muscle mass of ten percent from its use, leading to an analogous increase in kinetic energy of the bat swing and a five percent jump in bat speed (I don’t understand why that is also not ten percent). Using an equation for bat/ball collision from past work resulted in a four percent increase in the speed of the ball as it leaves the bat. Next on the agenda was a model for the trajectory of the ball. There is apparently disagreement among past workers on the impact of air resistance, with quite different models following from different assumptions about it. Tobin examined the implications of several, with the stipulation that a batted ball would be considered a home run if it had a height of at least nine feet at a distance of 380 feet from its starting point. Computations based on these models resulted in an increase from about 10 percent of batted balls qualifying as homers, which is the figure one would expect from a prolific power hitter, to about 15 percent with the most conservative of the models and 20 percent for the most liberal. These estimates imply an increase in homer production of 50 to 100 percent.

Turning to on-field evidence, some fairly weak studies have been performed that fail to reveal as much about the effect of performance enhancers as their authors claimed. Muki and Hanks (2006) examined career trends in home runs per at bat for the top hundred career home run hitters, which at that time went down to George Brett’s 317. They claimed that these trends were significantly different (usually decreasing with age) for the 64 members of this group whose careers ended in 2000 or earlier than those (usually increasing with age) for the 36 whose careers either ended later or who were still active at the time of the study. However, Caillault (2007) pointed out that the 19 of the latter 36 who were still active had not yet had the opportunity so to speak for their trend to turn downward. In addition, Muki and Hanks gave every season equal impact on their trend analysis (including, for example, one totaling 13 at bats for Harmon Killebrew), leading to untrustworthy trends.

Baseball Prospectus’s Nate Silver (2006a) studied the 40 batters and 36 pitchers Organized Baseball suspended for PED use during 2005, comparing indices adjusted for age and level of play before (i.e., 2004 and 2005 before suspension) and after (rest of 2005) suspension. For position players, Silver noted decreases upon return from suspension that were tiny although, due to small sample sizes, “on the verge of being statistically significant” (page 335; batting average, -.010; on-base average, -.014; slugging average, -.006; Cliff Blau pointed out to me that this implies isolated power actually went up); for pitchers, decrements were insignificant (+0.3 walks, -0.1 strikeouts, and +.02 home runs per 9 innings, and ERA jump of +0.13). Keep in mind that these results could be due to performance layoff rustiness rather than stopping the use of PEDs; this is an easy comparison to do via using matched players missing time from injury. For an analyst as skilled as Silver, this is disappointedly weak work.

A far more rigorous examination was conducted by Schmotzer, Switchenko, and Kilgo (2008, 2009). The authors began by accepting the specific conclusions of the Mitchell Report, i.e., the fingered players for the exact years specified, which included 33 players (over 79 seasons) for steroid use and 26 players (over 70 seasons) for human growth hormone use. Through a series of models with different assumptions and either including or not including the extreme outlier Barry Bonds, they compared these to 1277 non-accused players (over 6508 seasons) who totaled at least 50 plate appearances in a season between 1995 and 2007. Their measure of choice was a version of Runs Created 27 adjusted for the age of the player (i.e., across all players of a given age, the difference between mean RC27 for the age cohort and mean RC27 across all age groups). For steroids, estimated increase in RC27 ranged from 3.9 percent to 18 percent, with their favorite model estimating 7.7 percent without Bonds and 12.6 percent with. The researchers obtained analogous enhancements for home runs and isolated power, but a decrease of up to twenty percent in stolen bases. In contrast, most of the models for HGH predicted no impact, consistent with physiological research they cite. Moskowitz and Wertheim (2011), studying the 249 minor league players who tested positive and were suspended for PED use between 2005 and fall 2010, concluded that this group was 60 percent more likely to be promoted to higher levels in the minors the next year than non-suspended players. Incidentally, shorter and lighter players were more likely to be caught than taller and heavier, a likely function of the fact that the former would have greater motivation to add power to their game.

De Vany (2011) presented data that he saw as contradicting the claim that steroid use was widespread in baseball. For him, the feats of Mark McGwire, Sammy Sosa, and Barry Bonds are indeed unusual, reminiscent of Babe Ruth’s domination of home run hitting during the 1920s. However, he found the ratio of home runs per at bat, per hit, and per strikeout as remaining the same between 1959 and 2004. I think it is safe to say that his methods were not subtle enough to find the obvious.

Gould and Kaplan (2011) performed a study specifically about Jose Canseco, inspired by Canseco’s claims concerning his personal impact on the steroid use of teammates. Based on data from 1970 through 2009, the authors concluded that after playing with Canseco, “power-hitters” (poorly operationally defined by position; first base, outfield, designated hitter, and for some reason catcher) increased their home runs by an average of 20 percent and their RBIs by 12 percent in years subsequent to playing Canseco, with no analogous impact for non-power-related performance measures such as walks and batting average. Yet, there was no analogous impact for other players, including some known or highly suspected to be steroid users (Giambi, McGwire, Palmeiro). Finally, even Canseco’s impact disappeared starting in 2003, when steroid testing became prevalent. Although the authors do not specifically state that they trust everything Canseco said about others’ steroid use, it is implied between the lines.

Finally, Ruggiero (2010) attempted to predict who was and was not a user based on whether performance differed substantially from career trajectory in specific seasons, particularly toward the end of careers. Mark McGwire, Ken Caminiti, Jason Giambi, and Len Dykstra had seasons that made them look guilty, Sammy Sosa and Gary Sheffield did not, and the data were unclear for Jose Canseco and Barry Bonds.

In summary, there is good evidence that steroid use substantially increases power, but attempts to finger specific players are not trustworthy. There is no good evidence that HGH has analogous effects.

A related issue of great concern is the motivation for PED use. Moskowitz and Wertheim (2011) noted that, of the 274 professional baseball players who tested positive between 2005 and fall 2010, natives of Hispanic countries were proportionally overrepresented by about 100 percent and natives of other countries underrepresented analogously. Although it is possible that usage is actually comparable but Hispanics are less successful in hiding it, the likely explanation for this is players from Hispanic nations are generally quite poor, and are willing to take a risk in this regard given that baseball is probably their own realistic route out of poverty. In fact, there was a clear linear relationship between per capita gross domestic product for specific countries and likelihood of a positive test. In particular, Puerto Rico, with somewhat higher GDP than the other Hispanic cultures, had a somewhat lower likelihood. Incidentally, the same relationship existed among U.S. players alone, with wealth measured by the average in the players’ location of birth. In addition, Venezuela and the Dominican Republic had higher rates than Mexico and Colombia. I wonder if, in order to connect with MLB organizations, players from the former two countries are more often at the mercy of middle men (the “buscon”) who may pressure the youngster (most are mid-teens) to use PEDs. Incidentally, almost all suspensions for recreational drug use were for U.S.-born players.

Another finding was the linear relationship between national income levels and the age in which the positive test occurred. The average ages were as follows: for Dominicans and Venezuelans 20-21, for Mexicans and Puerto Ricans 25, U.S. states 27, Japan, Taiwan, Canada, and Australia 30. Some of this variation is due to the average age in which players start playing professional baseball in the U.S., but according to Moskowitz and Wertheim not all of it. The differing incentives are likely the desire to make the majors in the first place among the Hispanics and the desire for marginal players to maintain a career for the others.

Protection

It is time to puncture another baseball myth. From on-the-air chatter it is clear that traditional baseball people presume that fielding a lineup with two good hitters in a row “protects” the first of them, meaning that the pitcher is more willing to chance getting him out (and so perhaps give him hittable pitches) than pitching around him (making it likely it he walk and thus be a baserunner for the second to drive in. A weaker second hitter would provide less incentive for the pitcher to pitch around the first. Bill James was the first to question this presumption, reporting a little study by Jim Baker in the 1985 Abstract (page 258) showing that in the previous six seasons, Dale Murphy had actually hit for a better BA with frequently-injured Bob Horner out of the lineup (.283) than in (.269). David Grabiner (1991) examined the performance of 25 American League batters during 1991 who were generally followed in the order by a batter with a .450 slugging average and determined that on average they performed a bit better when unprotected by that .450 slugger. James Click (2006a) noted that batting performance of a given batter was unaffected by the quality of the next batter in 2004. In fact, although almost certainly a random finding, performance was worst of all for the best of five categories of “next batters,” dropping by 13 OPS points.

Mark Pankin (1993) provided a much more rigorous examination of the “protection” hypothesis. Based on 1984-1992 data, Mark determined that BA and SA for batters of various strengths were unaffected by the strength of the batter after them. In addition, stronger hitters get more walks when batting in front of weaker hitters, which seems to be the opposite of a protection effect. There is an exception, in that everyone hits better and gets more walks before the pitcher bats. John Charles Bradbury and Douglas Drinen (2008) continued in this vein, contrasting the “protection hypothesis” with an “effort” hypothesis in which pitchers put more effort into retiring the first hitter to try ensuring that he won’t be on base for the second. The protection hypothesis implies that a good on-deck hitter will decrease the walks but increase the hits, particularly for extra bases, for the first hitter; the effort hypothesis predicts decreases in all of these indices. Retrosheet data from 1989 to 1992 supported the effort hypothesis; on-deck batter skill as measured by OPS was associated with decreased walks, hits, extra-base hits, and home runs, with the association increased by a standard platoon advantage for the on-deck hitter. This support, however was weak, as a very substantial OPS rise of .100 for the on-deck hitter amounted on average to a drop of .002 for the first hitter. The authors mention an additional and important implication; contiguous plate appearances appear not to be independent, contrary to so many of the most influential models for evaluating offense. However, if their data are representative, the degree of dependence may be too small to have a practical impact on these models’ applicability. David C. Phillips (2011) performed the most thoughtful study of protection to date, with analogous implications. He realized that a study of protection based on player movement within a batting order (e.g., moving a cold hitter to a different spot in the lineup) leads to ambiguous findings, because any change in the performance of that hitter could be due to the change in subsequent batter or to random changes in that player’s performance irrelevant to who is batting behind. In response, Phillips went back to Jim Baker’s original thinking by looking at differences in performance for a given player remaining in the same lineup position based on changes in the next batter caused by injury. Based on Retrosheet data from 2002 through 2009 and limited to protectors with an OPS of at least .700 for a minimum of 200 plate appearances (in other words, hitters good enough to count as potential protectors), Phillips noted that injuries to protectors resulted in an overall OPS decrease of 28 points at that lineup position due to a weaker replacement. With the weaker replacement, the hitter being protected tended to receive a lot more intentional walks but fewer extra base hits (but no more hits, as additional singles compensated), indicative of the expectation that a non-protected hitter will be pitched around more often. These two tendencies pretty much cancelled one another out, resulting in little overall protection effect.

Streakiness

What Counts as Evidence for the Existence of Streakiness?

Another question that has led to controversy is the best explanation for batting streaks and slumps. There is no question that there are stretches in which batters perform better (streaks) and worse (slumps) than their average performance. The question is whether streakiness in batting is due to real differences in player skill level over time, such that it can be explained by some physical or psychological factor relevant to performance (e.g., “Player A is seeing the ball really well right now”; “Player B’s mechanics are messed up right now”) or is just the result of random processes. To bring back the first chapter example, take coin flipping. Over a long stretch of flips, we would expect about half to be heads and half to be tails. However, over short periods, we are likely to get something much different. The following is the result of a series of flips of a quarter done as I write this:

HHHTTHTTHHHTTTTHTHTTTTHHTHTHTTHTTHHHHHHTTHTTTTHTTHHHHHTHTT

1 6 11 16 21 26 31 36 41 46 51 56

Of the 58 tosses, 28 were heads and 30 were tails, almost the expected fifty/fifty split. Yet, it might not look like the result of a random process, because of the “streakiness” in the data. Note the “streak” of heads from flip 34 to flip 39, and the “slump” of heads from flip 12 to 22 (only 2 of 12). Stretches like these always occur naturally in random processes. Similarly, a hitter who tends to get hits in thirty percent of his at bats in the long run (the equivalent of 6 hits every 20 at bats) is bound to have stretches during which he gets hits in fifty percent of his at bats (say, 10 for 20) and others in which he gets hits in ten percent of his at bats (say, 2 for 20).

And even if it appears that streaks and slumps occur by chance statistically, two options still remain: they are statistical artifacts only, or they have “real” causes that occur randomly. Players’ claims that they are real cannot be trusted, as they are examples of the after-the-fact rationalizations that people always make for random occurrences studied in detail by social and cognitive psychologists. Now, if players were able to predict when they were going to go into a streak or slump before the fact and those predictions turned out to be accurate, then we would be able to trust them. Obviously I would love to see such evidence.

Jim Albert has been the leading figure in trying to make sense of this issue. Jim and Patricia Williamson (2001) described two different ways to try to find out. One way is to do what we did above; see if the pattern of, say, hits over a sequence of at bats does or does not resemble a random process. For example, one sees if the number of “runs” in the sequence is more or less than one would expect by chance. A run is a stretch of events with the same outcome. The first run above is HHH, the second TT, the third H, and so on. There are a total of 28 runs in that sequence of coin flips. More runs than expected by chance would indicate more streakiness than chance would allow, evidence that streaks are real. Fewer runs than expected by chance would indicate more consistency (“stability”) than chance would allow, which is also evidence that the data are non-random and that something “real” is going on. There is a statistical procedure called the runs test that allows us to compare a data set such as this with a “real” random process to see they have the same number of runs. It provides a z-score representing the comparison; if the z if statistically significant, then this sequence can be considered non-random (see Chapter 1 if a refresher on z-scores is needed). The sequence above resulted in a z of -.521, which is nowhere near the statistical significance level of +/-1.96.

The second way Albert and Williamson describe is to examine the conditional probabilities of the sequence (if you forgot what those are, see Chapter 2). If the process is random, then the long-term odds of one type of event following another should reflect the event’s overall probability. For a .300 hitter, the probability of a hit should be about .3 and of an out should be about .7 whether or not each follows a hit or an out. If, say, the probability of a hit following a hit for a .300 hitter is .5, that means that hits tend to come in bunches, evidence of streakiness. In our example, heads are followed by heads exactly half the time; tails by tails 55.2 percent of the time. The difference in proportions is, as with the number of runs, nowhere near statistical significance.

Later, Jim (2008a) described a third way to examine streakiness. One can group consecutive at bats into groups of, for example, 20. Using Jim’s example, during 2005 Carlos Guillen’s sequence of 20 at bat groupings produced 5, 5, 7, 10, 10, 10, 6, 9, 4, 4, 6, 7, 4, 2, and 6 hits (before finishing with 12 for 34). This looks streaky – starting relatively cold, Guillen seems to have heated up during the fourth through eighth of these sequences and then cooled off again. One can then test whether these ups and downs are or are not randomly organized. Jim developed a relevant statistical test (see Albert, 2013) and used it (Albert, 2014) to determine that there was more streaky behavior than one would expect from chance in home run hitting for batters with at least 200 ABs for seasons in the 1960 through 2012 interval.

Some of the work on streakiness has been demonstrations of statistical methods concentrating on the performance of individual players. For example, even before his work with Williamson, Jim (1998) compared the streakiness in Mike Schmidt’s home run hitting during his “competent” years (1974 through 1987), in which he averaged about seven homers every hundred at bats, with 2000 simulated Schmidts homering randomly at the same rate. Based on the pattern of number of games played between home runs, Schmidt’s record appeared to match the average of the simulated Schmidts, but based on expected home runs over two-week periods, the real Schmidt appeared streakier than expected by chance. In the 2001 Albert and Williamson (2001) paper, they reported an analogous study of Mark McGwire’s home runs from 1995 through 1999 and Javy Lopez’s hits in 1998 (a year for which he had been labeled in an Internet article as particularly streaky) using five-game periods and found both to resemble the average of the simulations. Scott Berry (1999a) examined whether the game-by-game home run performance of 11 prolific power hitters showed signs of streakiness during the historic 1998 season. In one analysis, he noted whether the number of at bats between home runs varied consistently with a random process. It did not for Sammy Sosa, who was streakier than chance would allow, and Andres Galarraga, who was more consistent than chance. In another, he adopted a Markov model with three states (normal, hot, and cold), in which the odds of a switch from normal to either hot or cold at any one at bat was 5 percent and a switch back to normal at any at bat was 10 percent. Again, Sammy Sosa appeared to have specific hot and cold streaks; this time, Ken Griffey Jr. seemed to have cold stretches. As Berry admitted, it is very difficult to distinguish whether Sosa’s streakiness was due to an actual “hot hand” or just a random outlier. Sommers (1999-2000) looked at the distribution of games in which Ruth (1927), Maris (1961), Sosa (1998), and McGwire (1998) had their historic home run years, and noted a random pattern. In his 1986 Baseball Abstract (pages 230-231), Bill James reported on a study he commissioned of seven Astros hitters by Steven Copley, who compared performance after “good games” (2 for 6 or better) or “bad games” (an oh-fer), and uncovered a slight improvement in the game after good games (.280) versus bad (.268). Bill felt that any evidence for across-game consistency was “very questionable.” James was right; the chi-square on that data are a minuscule .37.

As mentioned, these studies were intended more as demonstrations of statistical techniques rather than substantive pieces, as one player’s performance says almost nothing about whether streakiness is a real or random tendency. The analyst needs to examine the performance of a large number of players, which will undoubtedly result in some appearing to be particularly streaky and others seeming particular stable. The researcher then compares the distribution of performances among the players with the distribution that would be expected if streakiness was random (i.e., a normal distribution). If the distributions differ, than performance is not random, and the direction of the differences will indicate whether more players than chance allows are streaky or stable. If the distributions do not differ, then one has evidence that streakiness is random. However, again it is not definitive evidence, because results that look random could also be the result of a situation in which there are a very few players who really are by their nature streaky or stable, too few to appear as anything other than the sort of outliers that will always occur in a normal distribution. If instead the evidence points to non-randomness, then, for example, it makes sense to look for individual differences in streakiness (“Player C is more consistent than Player D”); if the “streaks are random” position is correct, then it does not.

The issue of randomness versus meaningfulness crops up across seasons. For example, the standard deviation for batting average in a 500 at bat season is about .020, which looks very low, but it means that there is a 66 percent chance that a .275 hitter will end up anywhere between .255 and .295 and a 95 percent chance somewhere between .235 and .315 due to chance. In a poorly conceived study, Gosnell, Keepler and Turner (1996) thought they were examining streaks and slumps lasting entire seasons and accounting for chance, but they failed. They looked at year-to-year batting averages for 100 randomly chosen players active between 1876 and 1987 with at least 300 career at bats and calculated that variation by chance alone can account for differences across seasons for 66 percent of the players and 90 percent of the seasons themselves. The problem with this sort of study is that it ignores the normal career trajectory, and so seasons not accountable by chance could well be those at the beginning and end of careers.

Evidence that Streakiness is Not “Real”

Most of the relevant work performed has found little evidence for the existence of non-random patterns, implying either that streakiness is a random occurrence or, if there is some actual non-random cause for it, that cause operates randomly (i.e., the occurrence of batters really seeing the ball well is unpredictable). I will organize this review in terms of studies using each of the three methods Jim Albert proposed.

Method 1 – Examining sequences of at bats

The Hirdts (Siwoff et al., 1989, page 164), noted a slight tendency (translating to a .015 BA improvement) for players to get a hit following an at bat with a hit versus an at bat producing an out within the same game. There was no corresponding tendency across games. As such, it is very likely that these results are due to facing the same pitcher in consecutive at bats. Based on 2013 Retrosheet data, Wolferberger and Yaspan (2015) basically replicated these findings; only the immediately preceding PA had any predictive value for a given PA’s outcome, and not more distant-in-the-past PAs.

Method 2 – conditional probabilities among at bats

The most important of the early studies of the issue was by S. Christian Albright (1993a), which was followed by responses by Jim Albert (1993) and Hal S. Stern and Carl R. Morris (1993), and a rejoinder by Albright (1993b). Albright studied the probability of getting on base using Project Scoresheet data from 1987 to 1990 and included the 501 500-at-bat seasons that occurred during that interim. He used three different types of analysis; a runs test, a test of conditional probabilities, and a logistic regression analysis in which he studied whether performance over the previous 1, 2, 3, 6, 10, and 20 at bats predicted whether or not the batter got on base during the next at bat. In each case, he noted the overall distribution of players to see if their performance appeared to reflect a random process or not. Both the runs and conditional probability analyses revealed very slight tendencies toward streakiness. The logistic regression analysis resulted in random findings for predictions based on one previous at bat and a slight tendency for stability (absence of streakiness) for predictions based on twenty previous at bats. Albright concluded that there was no conclusive evidence for either streakiness or stability. Both Albert, and Stern and Morris, proposed alternative statistical models and performed their own analyses, none of which resulted in evidence contradicting Albright’s conclusion. Stern and Morris also found that the logistic regression analysis is biased toward results favoring stability, which might account for Albright’s 20-game findings. Stern (1995) noted analogous findings in a subsequent reanalysis of part of Albright’s data set.

Method 3 – sequences of groups of at bats

In one of their better studies, the Elias folks (Siwoff et al., 1987, pages 97-99) were among the first to take on the issue of streakiness. The Hirdts first defined a streak as a five-game stretch hitting .400 or better and a slump at five games of .125 or worse, and then observed performance in the five games following a streak/slump as just defined. Between 1984 and 1986, 161 players who experienced both a streak and a slump in a given season hit better in the five games following a streak than in the five games following a slump, but 184 hit better for the next five games after a slump rather than a streak. This evidence against long hitting streaks was even more extreme when original streaks and slumps were defined as three games (107 versus 165) and ten games (154 versus 220).

My own work was another example of the third, grouping method, using week-to-week performance data over 11 seasons (1991-2001) and including players who had at least 10 at bats per week for ten consecutive weeks over four seasons (93 players qualified, with 549 seasons). In one study (Pavitt, 2002), performed a season at a time to protect against the impact of career performance trajectories, there was slight evidence for more inconsistency across weeks in BA and SA than chance would allow, probably due to the alternation of home and away games and any ballpark effects those would produce. In a second (Pavitt, 2003), including entire player careers corrected for career trajectories with a quadratic regression term, I noted non-random consistency across weeks for slugging average but not batting average, likely due to overall linear increases in power across careers that were not controlled by the curvilinear trajectory projection. Jim Albert (2007) looked at 284 batters during the 2005 season also using the groupings method (with 20 at bats) for hits, strikeouts, and home runs, and found that hit data led to about 20 batters displaying more streakiness than expected when 14 would be expected by chance; no analogous findings occurred for strikeouts and homers. Again, any home versus away effects could conceivably account for this discrepancy. In 2013, Jim used a method based on the distribution of the number of outs between hits for all 438 batters with at least 100 at bats in 2011. Although 70 players had distributions differing from pure chance, further analysis implied a random pattern. Jim replicated analogous findings for each season between 2000 and 2010. In contrast, an examination of the number of times batters made contact between strikeouts revealed significant streakiness for each of those seasons. Jim noted that striking out is more a function of skill and less of luck than getting a hit, and that difference may be crucial in explaining the contrast. Finally, using 2005 data, Lawrence Brown (2008) noted that batting average performance comparing the first and second halves of a season, and again month-by-month, resulted once again in an approximately normal distribution.

Tom Tango, Mitchel Lichtman and Andrew Dolphin (2006) in a sense replicated the first Elias study. Working with Retrosheet data from 2000 through 2003, they looked at sequences of five games with at least 20 at bats in which hitters performed in the upper and lower five percent (generally wOBAs of greater than .525 and less than .195) to see if those trends continued in subsequent games. Compared to the players’ average wOBA in the seasons immediately before, during, and immediately after the sequence, they uncovered wOBAs about 4 points higher for the streakers and 5 points lower for the slumpers, implying a continuation of the hot or cold stretches. However, the differences are slight, and TMA did not correct for strength of opponent or ballpark. As such, the findings are not definitive.

The Chinese Professional Baseball League on Taiwan has been the victim of a rash of game-fixing scandals, with one in 1996 and four between 2005 and 2009. As a consequence, eighty-two players were legally indicted, with at least 26 sentenced. Lin and Chan (2015) used data envelopment analysis to determine whether this method could indicate guilty players based on their week-to-week performance (SA for batters, total bases per inning for pitchers). The authors claimed accuracy rates ranging from 61% to 100% for indicating guilt through demonstrating stretches of anomalously poor performance. However, they never compared their findings to week-to-week patterns for non-indicted players to see if it differed, and in the end all they showed was that baseball players have performance slumps.

Claimed Evidence that Streaks are “Real”

Some work by Trent McCotter (2008) led to quite a bit of debate. Trent’s method was as follows: Using Retrosheet data from 1957 through 2006, he recorded the number and length of all batting streaks starting with one game along with the total number of games with and without hits in them. He then compared the number of streaks of different lengths to what occurred in ten thousand random simulated permutations of the games with/without hits in them. There was a consistent and highly statistically significant pattern across all lengths starting at five for more real-life streaks than in the simulations. Trent concluded that hitting streaks are not random occurrences.

Although nobody challenged Trent’s method as such, there has been some criticism of other aspects of his work. He first proposed three alternative explanations for these patterns; batters facing long stretches of subpar pitching, batters playing in a good hitting ballpark, and streaks due to better weather conditions for hitting, i.e. warmer weather. He uncovered no evidence for the first, and claimed the second and third to be unlikely without empirically evaluating them. He instead opted for untestable speculations concerning a change in batter strategy toward single hitting and just the existence of a hot hand. I called him on these (2009); he responded (2009) with helpful analyses inconsistent with the second and third of the testable explanations and basically punted on the untestable ones. Jim Albert (2008b, summarized in 2010a) lauded the method and replicated it, but this time restricting the sample to five seasons of Retrosheet data studied separately (2004 through 2008). Again, real streaks occurred more often than in the random permutations, but only three out of twenty comparisons were significant at .05 and a fourth at .10. This initiated a debate in the Baseball Research Journal Volume 39 Number 2, in which Jim questioned the practical significance of Trent’s findings giving the huge sample size Trent used, Trent defended the huge sample size as necessary to tease out streaks buried in noisy data, and Jim challenged and Trent (McCotter, 2010a) upheld Trent’s use of the normal distribution as the basis for comparison. A subsequent publication (McCotter, 2010) added nothing substantive to the debate.

Another reported demonstration that received a good bit of publicity was an unpublished study by Green and Zwiebel, based on Retrosheet data from 2000 through 2011. In essence using the second, conditional probability method, Green and Zwiebel wanted to see if the outcome of a particular plate appearance for both batters and pitchers could be predicted more accurately using the outcomes of the previous 25 at bats than overall performance for the given season, minus a 50 at bat window around the plate appearance under question. They provided various operational definitions for hot and cold streaks. Some of these definitions seem to bias the study in favor of finding streakiness; these established criteria based on the assumption that the average player is hot five percent and cold five percent of the time, which strikes me as out of bounds given that it presumes streakiness exists. A more defensible definition required the batter to be hot or cold if in the upper or lower five percent of a distribution based on his own performance. Their equations also controlled for handedness and strength of opposing pitchers and ballpark effects, but not, as Mitchel Lichtman (2016) pointed out, for umpire and weather. Unfortunately, the ballpark effect was poorly conceived, as it was based solely on raw performance figures and did not control for relative strength of the home team (i.e., a really good/bad hitting home team as indicated by performance in away games would lead to the measure indicating a better/worse hitting environment than the ballpark is in truth). The authors’ results indicated the existence of hot/cold streaks for all examined measures: hits, walks, home runs, strikeouts, and times on base for both batters and pitchers. Interestingly, after noting improved performance after the plate appearance under question than before, the authors attributed half of the reported increase in that PA to a “learning effect,” in essence true improvement in hitting. As Mitchel Lichtman (2016) pointed out, if so, then it should not be considered evidence for the existence of streakiness. I would guess that this result is due to facing the same pitcher multiple times.

Green and Zwiebel’s work elicited a lot of critical comment. Along with the ballpark problem, which Zwiebel acknowledged in email correspondence with Mitchel Lichtman, one criticism was that subtracting the 50 at bat window biased the study in favor of finding streaks. Here’s an example showing why: let us assume that a player is a .270 hitter. If a player happens to be hitting .300 or .240 during that window, then the rest of the season he must be hitting say .260 or .280 to end up at that .270. In this case, the .300 and .240 are being compared to averages unusually low and high rather than the player’s norm. But it strikes me that this would only be a problem if hot and cold streaks actually existed – if not, it would be .270 all the way. It is the case that subtracting the 50 at bat window lowers the sample size of comparison at bats, increasing random fluctuation and again adding a bias in favor of finding streakiness. Whether this loss of 50 at bats is catastrophic during a 500 at bat season for a regular player is a matter for debate. In any case, Mitchel Lichtman (2016) performed his own study using 2000-2014 Retrosheet data, but in this case used the sixth PA after the 25 window in order to insure that it usually occurred in a different game. He also used a standard projection method (i.e. three years of past performance with the more recent weighted over the less) rather than a within-season window. The results were a small hot and slightly larger cold hand effects for BB/PA, OBA, wOBA, and HR/PA, and almost none for BA. Mitchel speculated that changes in both batting (such as swinging for homers after hitting a few) and pitching (such as pitching more carefully to the hot batter and less so to the cold) strategies might be at least partly responsible, along with cold batters playing with an injury. Neither of the first two proposals are realistically testable.

Green and Zwiebel were eventually able to publish their paper in 2018, basically unchanged but with an additional analysis claiming that the opposition notices hot streaks and responds by walking the batter in question more often than the batter’s norm. They also criticizes the TMA method on two counts, both basically implying that TMA’s use of a three-year average wOBA as the baseline for comparison to hot streaks is wrong. The implications for them is that the data representing the possible hot streak data are also included in the comparison data, which is statistically invalid, and that the TMA method does not take regression to the mean for players performing over and under their heads during the three year period. The problem in Green and Zwiebel’s claim for me is the same as it was before; it presumes that hot and cold streaks exist rather than demonstrating that they do.

In conclusion, it is possible that streaks and particularly slumps have some “reality,” but the bulk of performance variation across time is undoubtedly random fluctuation.

And…

A good example of regression to the mean is the supposed “Home Run Derby curse.” Players are chosen for this All-Star-Game-related event due to their HRs during the previous three months of the season, and it is not unusual that quite a few contestants have been productive well beyond their performance in past seasons. Consistently with the curse, Joseph McCollum and Marcus Jaiclin (2010) noted that contestants had significantly lower HR/AB and OPS after participating than before, and that no analogous differences occurred for the same players when not taking part. However, they also discovered that both the first and second half performance of contestants were on average about equally superior to their normal performance. The point is that contestants tend to be chosen after unusually good starts while enjoying their best seasons. O’Leary (2013) examined relevant 1999-2013 data and basically replicated this result, but also noted that this decrease only occurred for losers and not winners.

Team Interdependence

Along with protection, another platitude one often hears from baseball “insiders” is that hitting is contagious, such that good performance from one hitter begets good performance from the others such that everyone reinforces one another’s success, and analogously for bad performance. Although not directly studying that specific issue, which would require looking at performance at the level of the game, there is evidence of interdependence in the sense that playing on a good team tends to improve counting indices. Bill James not surprisingly got the ball rolling in the 1985 Abstract (pages 175-177), with an informal study in which he matched 68 players into pairs with similar performance in a given season, with one member of the pair on a very good offensive team (a mean of 834 runs scored over the season) and the other one a very poor one (mean of 568). The players on good hitting teams averaged 13% more runs scored and 15% more RBI than those on bad hitting teams. Bill proposed the idea that this could be partly due to those of good hitting teams having more at bats, which makes sense in general but not here as ABs were part of Bill’s matching, and also the fact that on good hitting teams one gets up with more runners on base (thus more RBI) and gets on base with better hitters following (thus more runs scored).

David Kaplan (2006) performed a far more rigorous analysis, including two seasons (2000 and 2003) with players totaling at least 200 plate appearances. David found evidence in support of interdependence for a wide array of cumulative indices –hits, walks, total bases, runs scored, runs batted in, runs created – but not for a set of related average measures – on-base and slugging averages, isolated power, on base plus slugging. As cumulative measures are affected by individual opportunity to play whereas average measures are not, what seems to be implied is that, with a season, there are teams who tend to allot most of the playing time to a few regulars, increasing their cumulative indices as a set, and others, either by design or happenstance (injury, personnel changes) that divide opportunity among more players, limiting their individual ability to accumulate counting statistics.

A different type of interdependence among players is the performance of hitters with and without baserunners. Here, there is evidence consistent with the platitude that baserunners disrupt the defense and improve the fortunes of hitters. Based on 1999-2002 Retrosheet data, the TMA group (2006) determined that mean wOBA, .358 overall, was .372 with runners on first and fewer than two outs. Again not surprisingly, that broke down to .378 for lefthanded hitters and .368 for righties.

Transactions

Contract Status

Is it true that players shirk after signing long term contracts and perform better the year before entering free agency? There have been quite a few studies of this issue, but unfortunately many of them have been seriously flawed. In the majority of cases, free agency arrives after players have past their peak, and distinguishing shirking from general skill erosion requires more than just comparing what happens before signing a long term contract with what happens afterward. Comparisons between free agents and non-free agents can help determine whether performance differences are indeed a function of free agency or a function of overall changes in player skill level across years.

The issue itself is of more than passing interest to both organizational psychologists and economists, as it is relevant to significant theoretical issues within their domains. For example, organizational psychologists have approached the issue of contract status through pitting two theories with opposing implications, equity theory and expectancy theory, against one another. Advocates of expectancy theory, which basically implies that the opportunity to improve one’s salary would lead to harder work, would argue that players would be motivated to perform better the last year of their contract in order to try to gain attractive offers the following year, and that they would be less motivated during other years and underperform (Krautmann & Solow, 2009). On the other hand, equity theory predicts that people who feel that they have not gotten the rewards they deserve for their effort become angry whereas those who feel they do more than they deserve become guilty. This could imply that players in their last year may suffer feelings of inequity in pay given salary increases others have received for comparable performance during the length of their contract, and respond by underperforming during the final year of their contract as “payback” for their lower pay. They would then bounce back to normal performance with what they consider a more equitable new contract the next season (Lord & Hohenfeld, 1979).

A majority of the early evidence favored the equity theory prediction. Specific hypotheses and relevant evidence both for and against included the following:

Hypothesis 1: As stated above, the most basic hypothesis is that the year before free agency, players will perform worse than before and then bounce back after signing. During the early years of free agency, players who wanted to test the waters had to wait one additional season with their team (the option year). Lord and Hohenfeld (1979) supported the implied hypothesis of poorer performance for 13 relevant players in 1976 in the cases of home runs, runs scored, and runs batted in, but not batting average, as compared to the three previous years and the one following. However, Duchon and Jago (1981) extended the analysis to 30 position players with option years from 1976 to 1978 and found no difference across years, suggesting that the Lord/Hohenfeld findings had been a small-sample fluke. Harder (1991), considering 106 position players in the 1977 through 1980 stretch, noted a decrease in batting average but no discernible change in home runs per at bat. In another analysis, based on the contracts achieved by the very first (1976) cohort of free agents, he observed that home runs per at bat but not batting average were related to salary; note the inconsistency across the two findings.

Hypothesis 2: “Winners” will feel guilt and improve their performance to assuage it, whereas “losers” will feel robbed and perform worse. In the case of salary arbitration, the extent to which the player’s arbitration offer differs from the team’s will predict the extent of that over- or underperformance. Hauenstein and Lord (1989) noted some support for this hypothesis for 81 players who went through arbitration between 1978 and 1984. Looking at all position players with new contracts in the years 1976, 1977, 1987, and 1988 with new contracts in those years, Harder (1992) claimed some evidence that players paid better than predicted by the before-contract performance/salary relationship had a higher runs created figure, and in some years a higher total average, than would be expected in the year after the contract signing. However, for players who were “underrewarded,” there was only a slight decrease in total average the next year and no impact on runs created. Bretz and Thomas (1992) examined performance before and after arbitration cases for 116 position players between 1974 and 1987. Their performance index was a very strange amalgam of several disparate measures purposely biased toward power, which they felt has a disproportionate impact on salary. Arbitration winners’ performance afterward was markedly better than it had been both two years before arbitration and across their entire career, whereas arbitration losers’ performance was not better a year and worse two years afterward.

Complicating the picture is work by Weiner and Mero (1999), in a study based on 205 position players with at least two years of experience who were in the major leagues in 1991 and 1992. After controlling for a few performance indices (with experience, at bats, and career runs created per at bat significant covariates), they uncovered evidence that players who are paid more than average in 1992 relative to others at the same position tended to increase their runs created per at bat and their total player rating between 1991 and 1992 whereas those below average tended to decrease theirs. These findings are consistent with equity notions, but there was no control for whether or not the players changed teams, and one would suspect that only a minority did. The implication is that changing teams may not be as significant as relative pay alone.

Hypothesis 3: Guilt from leaving their old team would result in performance decrements against it. Kopelman and Schneller (1987) examined 54 players who switched teams during the first nine years of free agency (between 1976 and 1985), but noted only negligible differences in batting average.

As for expectancy theory, the basic hypothesis is the opposite of equity theory’s; better performance the year before returning to normal afterward. Examining 110 position players who between 1976 and 1983 signed a contract lasting at least 5 years, Krautmann (1990) first noted that the number of players performing above (68 versus 71) and below (42 versus 39) their career means in slugging average did not differ between the year before and year after the signing. Second, he observed that only 5 of the 110 in the sample performed above their expected range of random variation in slugging average, as calculated across seasons for each player, the year before, and only 2 produced below that range. The implication is that performance differences between the two seasons were random. Scoggins (1993) responded by claiming that any shirking after the signing would be reflected in time spent on the disabled list, arguing that total bases is a better measure than slugging average because it includes both hitting prowess and endurance as causal factors. Using the same sample, he demonstrated that, combined across players, total bases decreased from the year before to the year after the signing. In reply, Krautmann (1993) contended that it is wrong to combine player data, and uncovered only 6 out of the 110 in the sample who had fewer total bases the year after than the range of their expected random variation.

Krautmann and Donley returned to this issue again (2009), based on position player signings for the 2005 and 2006 seasons, noting no performance decrement the year after signing as measured by OPS but some as measured by a player’s estimated monetary value. Turning to other analysts, Ahlstrom, Si, and Kennelly (1999) specifically pitted the two theories against one another. They uncovered no change between the free agency year (mean BA = .261, mean SA = .391) and the previous season (mean BA = .258, mean SA = .392) for 172 free agent hitters changing teams from 1976 through 1992, but a significant decrease going into the season after (mean BA = .247, mean SA = .367), leading them to support expectancy theory. Sturman and Thibodeau (2001) examined a paltry 33 players who gained a 30 or more percent increase in salary in a multi-year contract averaging at least one million dollars per year that was signed between the 1991-1992 and 1997-1998 off seasons. Batting average, home runs, and stolen bases decreased in the first year after signing from the previous two years but bounced back the second year after signing. Martin, Eggleston, Seymour, and Lecrom (2011) examined 293 free agents between 1996 and 2008 and noted that batting average, on-base average, slugging average, runs created per game, and adjusted batting wins were all greater in the walk year than the seasons before and after. Finally, White and Sheldon (2014) looked at players on their first multiyear contract for 66 players between 2006 and 2011. There was only a slight increase in performance as measured by BA, SA, OBA, HRs, and RBIs for the last year of the old contract as compared to the previous season, but a significant decrease between year of and year after.

In summary, given evidence for and against both theories, we cannot reach a conclusion one way or another based on this research. All of it, however, is fundamentally flawed. As mentioned earlier, you cannot just examine performance relative to free agency; you have to place it in the context of the general trajectory of performance over a career, and you should compare your sample with a matched set of non-free agents. Even non-academic baseball researchers who should know better have made this error. Dayn Perry (2006a) of the Prospectus group demonstrated that 212 free agents between 1976 and 2000 had a Wins above Replacement Player 0.48 greater than both the year previous and the year after, while noting their average age (31) but without correcting for it, or at least compensating for differences in ages among them. In addition, WARP, as a counting index rather than an average, is strongly affected by number of games played, and the sample did indeed play more games the free agency year than those around it. Perry claimed that this only makes up part of the free agent performance increment but does not provide relevant data.

A couple of researchers did slightly better. Woolway (1997) calculated a “production function” relating team winning average to batter OBA, SA, and SBs, pitcher ERA, and unearned runs (representing team defense), and then used that function to estimate the number of wins the team would have both with and without 40 players who signed multi-year contracts between 1992 and 1993. He concluded that these 40 players were worth an average of 1.191 fewer wins to their teams in 1993 than in 1992, and to his credit found no difference in this decrement between players in their primes (26-30 years of age) and past it (older than 30). But he failed to compare these 40 to other players, and to other seasons in these players’ careers, so for all we know many of these players had career years in 1992 that made them particularly attractive for multi-year deals. Finally, Paulsen (2019) examined 535 position players with 3 or more years of service between 2010 and 2017, with a total of 1068 contracts, and concluded that the more seasons left on a contract, the worse the performance, to the tune of a tiny .07 rWAR per year. This tendency was not impacted by whether players changed teams. Happily, he controlled for past rWAR (because higher rWAR means longer contracts) and experience (not surprisingly negatively related with rWAR). The results were substantially the same when limited to players with 6 or more years of service, i.e. free agent years.

Some research by economists has attempted to compensate for the problems stated above through computing expected career performance trajectories for players and then seeing if the expected performance differed reliably from actual performance for hitters before and after the signing of a new contract. Maxcy (1997) examined slugging average for more than 2200 player-seasons for an unknown number of players between 1986 and 1993 (and some seasons back to 1983 for long-term contracted players) and uncovered no decrease in performance independently of the effects of aging. Analogously, Maxcy, Fort, and Krautmann (2002) used slugging average for 1160 seasons for 213 position players from unnamed seasons and observed no impact for contract status; they did note that players spend less time on the disabled list and play more than expected during the last year of a contract. Marburger (2003) compared before-and-after performance, as measured through bases gained through hitting and base stealing, by 279 free agent position players in the 1990 through 1993 interim with that for a matched set of players from before the free agency period, and discerned no differences between the groups. In a sample of 527 free-agent position players between 1997 and 2007, Krautmann and Solow (2009) noted OPS adjusted for home-field and league effects was a scant 3 points greater in the year before free agency than career trajectories would imply, and a still-small 10 points less in the first of five-year contracts (which was a rare length; 80 percent were for either one or two years and only 5 percent for five years or greater).

O’Neill was involved in two studies that were substantially the same as Krautmann and Solow’s, including predictors for age and age squared along with a dummy variable indicating whether the player’s career ended at the conclusion of his contract. The first (Hummel & O’Neill, 2011) included 227 position players reaching free agency between 2004 and 2008, the second (O’Neill, 2013, 2014) consisted of 546 instances for 256 position players between 2006 and 2011. The first indicated a substantial 4.2 to 5.5 percent increase in OPS during the contract year; the second a smaller 1.1 to 1.8 percent improvement. However, Phil Birnbaum (2015) described a problem with O’Neill’s work; let me describe it in my own terms. As noted above, older players are often unable to get another contract after a particularly poor year. For the best of these players, that year may be randomly bad and not representative of their true remaining talent level. A randomly good year would of course lead to another contract. So, careers are likely to end with randomly bad seasons. This results in projections that are unrealistically pessimistic for the last years of good but aging players (Phil used Moises Alou as an example). For this reason, Phil was for good reason convinced that O’Neill’s projections could not be trusted. Earlier, Phil (2007), using runs created per 27 outs as his offensive index for 399 free agents between 1977 and 2001 with at least 300 batting outs that year, corrected for random variation in performance by weighing RC/27 for the free agent year for regression toward the seasons around it, and then compared them to 3692 non-free agents. The free-agents were 1.2 runs per year better, which Phil likened to turning one out into a triple; in short, very little.

O’Neill’s latest work (O’Neill & Deacle, in press as I write this) took care of that problem, but is further plagued with another; the failure to control for player age. The sample consisted of players eligible for free agency (6+ years) who played for at least two seasons between 2007 and 2011; a total of 225 players and 822 player-seasons. Without going into too much detail, here are her estimates for differences between predicted and obtained OPS+ for position players overall, for those in the top quartile, and for those in the bottom quartile, for their contract year and the subsequent season depending on the length of their new contract:

Contract |Contract year |One year contract |Two year contract |Three year contract |Four year contract |Five year contract |Six year contract | |Overall |+6 |+12 |+3 |0 |-3 |-6 |-8 | |Top quartile |+7 |+15 |+6 |+5 |+3 |+1 |-1 | |Bottom quartile |+2 |+1 |-7 |-14 |-20 |-27 |-34 | |

The overall effect remains as tiny as in previous work, and additionally looks like players, during the first year of a new contract, shirk a bit more the longer that contract lasts. But check out the distinction between quartiles. It looks as if the strongest hitters are inspired by their new contract whereas the weaker ones shirk significantly that first year after signing contracts of any considerable length.

O’Neill’s interprets these data along the extra effort/shirking lines. That could well be correct, but I am not at all convinced, and the quartile distinction reveals why. As I noted, O’Neill failed to sufficiently control for player career trajectories. As described in the Age section above, stronger players on average enter the majors a couple of years earlier than weaker ones. Putting the two together, I hypothesize the following alternative:

1 - The top quartile players hit their contract year a couple of years earlier than the bottom quartile players. Therefore, the former are coming into their peak whereas the latter are at theirs. This is why the data are higher for the top quartile than the bottom.

2 – The more that a player randomly happens to overproduce above expectation given their career trajectory during the contract season, aka has well-timed “career year,” the longer a contract they are able to sign. After that signing, they return to normal. The greater the overproduction, the greater the fall to normal. That is why productivity is lower the longer the contract.

The relevant data are available for both of these hypotheses to be tested on their own. In any case, O’Neill has one more study to do, this time including age and age squared as controls.

Arbitration has remained a fertile area to study. Dumble (1997) performed an analogous but simpler study including player eligible for arbitration from 1986 through 1992. In this case, winners did better the year before arbitration than the year after, losers a bit better the year after than the year before, and eligible players who did not experience the arbitration process had no change in performance, as measured by Palmer’s Batting Runs. The author noted the obvious explanation: those playing over the heads the year before won their cases and then reverted to normal, those playing below their heads the year before lost and then reverted to normal. Dumble ought to have included previous and subsequent seasons to the analysis to be sure.

Marr and Thau (2014) hypothesized that what they called “status loss” has a more negative impact on performance for those with previous high status when compared to those with previous low status, and used MLB final-offer arbitration as one of their tests. Their sample was 186 players who experienced arbitration once only between 1974 and 2011. They concocted a status scale by summing the number of All-Star Game appearances, MVP, Rookie of the Year, Silver Slugger, and Gold Glove awards. Status itself was totally unrelated with odds of the player winning or losing arbitration. Anyway, those toward the higher end of the status scale tended toward lower OPS the season after an arbitration loss as compared with the season before, whereas those toward the lower end of the status scale had no such tendency. Importantly, player age was included as a control in their models, which is critical because older players would tend to have high status and have decreasing performance, biasing the results. Phil Birnbaum (2007) used the same sort of method for arbitration as that just described in his work on free agency, and learned that those who lost actually slightly outperformed the winners, and both of those groups were outdone by those not undergoing arbitration.

Finally, and in contrast with both equity and expectancy theories, the very experience of arbitration may hurt performance. Based on 1424 filings between 1988 and 2011, Budd, Sojourner, and Jung (2017) proposed that the 1182 that ended with agreement before the case resulted in better subsequent performance by those players than the 98 who won and 144 who lost their case due to greater trust in and more positive feelings about the team. The evidence did not support that hypothesis, as there were no consistent differences in batter BA, OBA, and runs created, pitcher ERA (both regular and fielding-independent), and overall WARP. They did, however, note a tendency for players who went before the arbitrator to be released or traded before the end of the next season, and likewise before the next season started, particularly if the player won the case. Interestingly, the greater the difference between the team’s and the player’s offers, the worse the performance the next year (do relatively lousy players unrealistically inflate salary expectations?).

In conclusion, the best research suggests results consistent with expectancy theory and the general idea of shirking, but if there is an effect, it is tiny.

Switching Teams

The impact of switching teams on subsequent performance has received a bit of attention from academics, who noted immediate improvement right after the transaction. Bateman, Karwan, and Kazee (1983), with a sample of 97 batters between 1976 and 1980, noted increased BA, HR, and RBI if the transaction occurred midseason but not between seasons. Jackson, Buglione, and Glenwick (1988) looked at 59 batters switching teams within season and observed BA and SA to be lower in the months during that season before the transaction than in previous years and higher in the subsequent months that season than in the next year. Explanations for the effect include one similar to expectancy theory (Bateman et al., job transfers lead to increased motivation to do well, with the absence of improvement across seasons explained away as motivation dissipating over the winter) and psychological drive theory (Jackson et al., fear of a trade beforehand leads to over-arousal and poor performance whereas pleasure at being somewhere they are wanted leads to extremely good performance afterward). A much better explanation, analogous to Bill James’s for team performance under new managers, is that these findings are an artifact of the probability that players are more likely to be discarded when they are randomly performing below form and thus disappointing their team, and then bouncing back to normalcy after the move. Muddying the waters, the Hirdts (Siwoff et al., 1991, pages 4-5) examined the records of 49 batters who were traded to a different team in the other major league a year after hitting at least 20 home runs, and uncovered a strong tendency for their home run totals to decrease with the new team; 40 of the 49 for raw homer numbers and 37 of the 49 for HR per AB. However, Pete Palmer implied in a personal communication, much of this decrease could be regression to the mean, and the Hirdts did not examine batters who were not traded as a comparison.

Reasoning that as a consequence of anger and/or the desire to protect self-esteem, Kopelman and Pantaleno (1977) hypothesized that performance the year after being traded or sold would be better against the player’s former team than other teams. Note that this thinking is the opposite of the equity-based prediction for free agency movement above. The authors, based on 47 players traded or sold in 1968 or 1969, obtained marginally significant findings supporting this conjecture for batting average, particularly for players who had never been traded before, players with the former team at least three seasons, younger players, and players in the upper half of the sample in batting average, all of whom would hypothetically be more upset by the transaction. In addition, these effects faded away during the second and third year after the move, supposedly because the anger would have faded away.

As with the shirking issue, this work means little due to the absence of comparisons with players remaining with their teams. As a consequence the best work is by Rogers, Vardaman. Allen, Muslin, and Baskin (2017), although it is still compromised due to insufficient thinking about the relevant issue. They compared position players who, after two seasons with at least 100 PAs for one team during the 2004 through 2015 stretch, switched to another team after declining (422 cases) versus stable or improving (290 cases) performance across those two seasons. Performance indices included BA, OPS, weighted runs created plus, and fielding average, with a set of controls including among others career batting average and age “to account for the effects of a player’s declining ability” (page 552); I think it would have been better if the authors had computed a career trajectory and then used the relevant season’s estimate from that trajectory as a stand-in. There were also comparisons to players with declines (922 cases) versus stable or improving performance who did not change teams. The findings: On average, those who declined across years 1 and 2 improved in year 3 on all three batting indices, a simple case of regression to the mean. Those who switched teams declined more than those that stayed, which I hypothesize indicates that those who declined more were more likely to switch teams than those who stayed; the authors do not seem to have performed this easy test. On average, those who were stable or improved across years 1 and 2 declined in year 3 on all three batting indices, again more so if they changed teams than if they did not, with the same implications as beforehand. Reason for movement, i.e. trade versus free agency did not matter in either case. These regressions to the mean remained stable for year 4 for those remaining with the year 3 team. Fielding average changed in unison with the batting indices, but was never significant. Rogers and associates realized that the issue here was the absence of variance in fielding average; obviously, they should have used one of the range factor-type measures instead.

In summary, there is no reason to believe that performance is affected by switching teams.

True Ability

A player’s batting performance in a given year is partly due to skill and partly due to luck (some years all the grounders find holes, other years all the line drives are caught). Assuming random processes at work, in a 600 at bat season, the expected standard deviation for batting average is 17 points (Heeren & Palmer, 2011, page 31). This means that, through luck alone, the odds are about two-thirds that someone who is “really” a .275 hitter will end up between .258 and .292 and 95 percent that he will finish between .241 and .309 in a given year. If 200 regular players get 600 at bats, then about five would be expected to end up 34 or more points higher and another five 34 points lower than their “true” ability. Pete Palmer also noted that the 600-AB s.d. for slugging average is 35 points. Given the non-independence of slugging average and one-base average (hits are included in both), figuring out the s.d. for OPS is complicated; through simulation, Pete came up with an s.d. of 51 points.

In the chapter on offensive evaluation, I described Jim Albert’s (2005, 2006b, 2007) work on consistency in performance, which he wisely interpreted as relevant to the question of distinguishing how much of performance reflects true ability rather than luck. Although not originally interpreted as such, the first relevant work in this area was by Carl Morris (1983, 1998), who proposed a method for estimating what batting averages “should” have been without normal random variation. He determined that Ty Cobb was 88 percent likely to be, in his words, a “true” .400 hitter at some point in his career; the only other player with a reasonable chance was Rogers Hornsby. Earlier, Jim Albert (1992) demonstrated a method for estimating a batter’s “true” peak and career home run performance that discounts unusually good and poor seasons and accentuates the general trajectory of a player’s performance during his career. In truth, the “true” career totals of 12 hitters Albert used in his demonstration did not differ much from their actual totals. Casella and Berger (1994) demonstrated a method with the same goal for situations in which the data used for estimation are known to be biased; using their example, for when an announcer has mentioned that Dave Winfield has 8 hits in his last 17 at bats and you know that exact number of at bats was chosen rather than others because it best accentuates his recent hitting success.

Frey (2007) provided a model for estimating a batter’s “true” ability based only on his batting average. The point of the model is that a batting average of, to use his example, .833 is achievable with only 6 at bats (5 hits), and as such provides far less information about the player’s true ability than an average of .338, which requires at least 65 at bats (with 22 hits) to achieve. To be honest, the method may be of interest to pure statisticians but does not offer as much to the baseball analyst as those attempts that explicitly include number of at bats in the model. As part of his work, Frey also noted that mean batting average in a season increases with number of at bats, particularly for those with fewer than 200 at bats. This finding is the result of the fact that players with lower batting averages are more likely to be benched or dropped from a team before amassing a large number of at bats than players with higher batting averages. Null (2009) attempted to project future performance through distinguishing among fourteen different “abilities” (for example, tripling through fly ball versus doubling through fly ball versus tripling ground ball) plus considering age effects.

Finally, based on implications of the binomial distribution (his method is described in more detail in the Team Evaluation chapter), Pete Palmer (2017) estimated that variation in batting average among major leaguers is about half skill and half luck; as we know, whether a batted ball leads to a hit or an out has a fair element of randomness. Variation in normalized OPS among major leaguers is more in the order of 60 percent skill and 40 percent luck, given that getting walks and hitting for power have a smaller randomness element than getting hits.

Walks

No, a walk is not as good as a hit; it is about two-thirds as good according to the bottom-up regression methods cataloged last chapter, making it a significant offensive weapon. Further, whereas the variation among batters in BA is about 1¾ (from a high of say .350 to a low of .200), the variation among batters in the proportion of walks per plate appearance is about 5, from the high teens (Bryce Harper was at 18.7% in 2018) to less than 5 percent (the same season, Salvatore Perez was at 3.3%). Obviously, disparities such as this would not be allowed to exist for hits per plate appearance, as someone with a batting average one-fifth of the league leader would not last in the major leagues very long.

One way to think about walks is in relation to strikeouts. Long-time SABR stalwart Cappy Gagnon (1988) proposed what he called the Batting Eye Index, a simple measure of walks minus strikeouts divided by games played (at that time, Ted Williams was the career leader at .572). Jonathan Katz (1990) argued for the advantages of dividing by plate appearances or, even better, walks plus strikeouts (as the latter is by definition bounded by +1 and -1 and so easier to interpret). Given that the three indices intercorrelated around .9 in his data, none has a real statistical advantage over the other. What is surprising is that neither Gagnon’s or Katz’s versions had any correlation whatsoever with lifetime batting or slugging average or career length. This implies that batting eye seems to be a skill independent of, and thus not predictive of, the skills involved in hitting the ball.

This work was actually predated by a monumental examination of the walk by then Texas Ranger employee Craig Wright (1984a, 1984b, 1985). In the two 1984 pieces, Wright analogously with Katz found few discernible differences in overall offensive performance between high (mean of 11.4 walks per 100 plate appearances in 1983; I assume similar for 1982), average (mean of 8.1 walks), and low (mean of 5.2) walks among American League players with at least 400 PA in 1982 and 1983; the best tended to have a couple of more home runs and slightly fewer triples, but nothing really glaring. It did turn out that the best walkers were slightly older (average 29.9 years as opposed to 29.3 for average and 28.4 for low), which was consistent with the evidence described in the Age section of this chapter. There was also evidence here that rising walk rates might be correlated with better offensive performance during the latter stages of a career, prolonging both the player’s peak and slowing his inevitable decline. There was, however, evidence that high walkers were more successful than average or low in situations meeting Elias’s clutch definition (late inning pressure), with a only slightly higher batting average but a good 50 percent more home runs, which Wright hypothesized might be an indication of the high walkers being more adaptable in batting style than the others. The 1985 article is a historical study on this last theme; implying that walking is a learnable skill that at least some players are able to take advantage of (whereas others are too stubborn), and that some managers have recognized that, in so doing improving their teams.

Due to the availability of PITCHf/x plus data from organizations such as Baseball Info Solutions, we are now able to make extremely detailed studies of plate discipline. New indices measuring the percentage of swings at pitches outside (O-Swing%) and inside (Z-Swing%) the strike zone and contact rates on these swings (O-Contact% and Z-Contact%; see “Plate Discipline”, n.d. for a list of indices and the following data) allow ratings of batter discipline along with pitcher effectiveness. For the record, reported mean figures are 30% for O-Swing%, 65% for Z-Swing%, 66% for O-Contact, and 87% for Z-Contact% for 2002 through (I think) 2017. Using these data, Ryan Pollack (2017) defined an Aggression Factor based on a box representing the median deviation along horizontal and vertical axes of pitches swung at, normalized for different numbers of plate appearances, with lower numbers representing only swinging at pitches in a relatively tighter area. Aggression Factor ranged from about 4 (extreme discipline) through about 20 (the opposite). The correlation between AF and wRC+ was negative .35, implying an average gain of almost three wRC+ points for each square inch in which the box narrowed, based on (I believe) 2015-2017 data. Jim Albert (2017, Chapter 7) presented data relevant to overall batter swing and contact rates for the 2016 season. That year, batter swing rates varied from 35 percent to 60 percent; contact rates went from 70 percent to 90 percent. Higher swing rates were associated with lower contact rates for pitches both in and out of the “real” strike zone, more strikeouts, and fewer walks. Vock and Vock (2018) constructed a method for computing what a player’s BA, SA, and OBA would be with differing amounts of plate discipline, based on his actual performance as influenced by his odds of swinging against different types of pitches of different speeds/movements/locations. Using PITCHf/x data for 2012 and 2014, they estimated what Starlin Castro would have done if he had Andrew McCutcheon’s discipline.

As for the opposite of plate discipline; in a study receiving plenty of publicity in the popular press, Kutscher, Song, Wang, Upender, and Malow (2013) noted a linear relationship in batters swinging at pitches out of the strike zone across the months of the season, from 29.2 percent in April 2012 to 31.4 percent in September 2012, demonstrating what they interpreted as a fatigue effect. Importantly, they added that the same tendency existed for the years 2005 through 2011 in previously reported data.

And…

Winter, Potenziano, Zhang, and Hammond (2011) were able to convince 16 major league players to fill out the Morningness Eveningness Questionnaire, which based on self-report answers can type people according to the time of day during which they perform best (I did an on-line version and it absolutely nailed what I thought is my best bedtime). Based on their 2009-2010 BA performance with game start time adjusted for travel between time zones, the nine counting as “morning type players” averaged .267 in games starting before 2 p.m. versus .259 for games starting at 8 p.m. or later; the corresponding numbers for the seven “evening type players” were .252 versus .306. A small sample size, but suggestive nonetheless.

Does playing every day result in performance decrements? Harold Brooks (1992) used Cal Ripken as an example, showing that his September/October performance between 1984 and 1991 was somewhat poorer than his April-to-August production (incidentally, I did a little study [1994] showing that when the Orioles had a long stretch of games without an off-day between 1984 and 1989, Ripken’s hitting suffered during the last few days [starting day 17]). Harold went on to show evidence that this seems to be true across the board. While there is normally a decline in September, he showed that the more games played, the greater the late-season drop-off for “throwing infielders” (2B, SS, 3B) relative to league average for those starting 153-157 and particularly 158-162 games at those positions. Outfielders did not suffer the same decline.

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