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An Inferential and Descriptive Statistical Examination of the Relationship Between Cumulative Work Metrics and Injury in Major League Baseball Pitchers

Karakolis, Thomas; Bhan, Shivam; Crotin, Ryan L.

The Journal of Strength & Conditioning Research: August 2013 - Volume 27 - Issue 8 - p 2113–2118
doi: 10.1519/JSC.0b013e3182785059
Original Research

Karakolis, T, Bhan, S, and Crotin, RL. An inferential and descriptive statistical examination of the relationship between cumulative work metrics and injury in major league baseball pitchers. J Strength Cond Res 27(8): 2113–2118, 2013—In Major League Baseball (MLB), games pitched, total innings pitched, total pitches thrown, innings pitched per game, and pitches thrown per game are used to measure cumulative work. Often, pitchers are allocated limits, based on pitches thrown per game and total innings pitched in a season, in an attempt to prevent future injuries. To date, the efficacy in predicting injuries from these cumulative work metrics remains in question. It was hypothesized that the cumulative work metrics would be a significant predictor for future injury in MLB pitchers. Correlations between cumulative work for pitchers during 2002–07 and injury days in the following seasons were examined using regression analyses to test this hypothesis. Each metric was then “binned” into smaller cohorts to examine trends in the associated risk of injury for each cohort. During the study time period, 27% of pitchers were injured after a season in which they pitched. Although some interesting trends were noticed during the binning process, based on the regression analyses, it was found that no cumulative work metric was a significant predictor for future injury. It was concluded that management of a pitcher's playing schedule based on these cumulative work metrics alone could not be an effective means of preventing injury. These findings indicate that an integrated approach to injury prevention is required. This approach will likely involve advanced cumulative work metrics and biomechanical assessment.

1Department of Kinesiology, University of Waterloo, Waterloo, Ontario, Canada

2Department of Exercise Science, School of Public Health and Health Professions, State University of New York, University at Buffalo, Buffalo, New York

3Baltimore Orioles, Major League Baseball, Baltimore, Maryland

Address correspondence to Thomas Karakolis,

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Games pitched, innings pitched, and pitches thrown are examples of metrics used to quantify a pitcher's cumulative work. The aforementioned metrics have been used to set limits on the number of pitches a pitcher can throw per game and the number of innings a pitcher can pitch in a season (7), in an attempt to mitigate a potential negative effect of high cumulative work on performance and health. Recently, Bradbury and Forman (2) have shown that the maximum number of pitches thrown in a game has declined drastically over the past 30 years as a result of the pitch per game limit. Unfortunately, the limits selected for professional pitchers have been either decided arbitrarily or may be based on thorough analyses not published in the scientific literature. Pitch count limits currently exist in little league baseball. These limits are based on a small body of literature examining the association between youth pitchers' work and arm injury (5,11) or arm pain (9,10).

The purpose of this study was to examine the correlation between cumulative work metrics for a given season and injury during the following season in Major League Baseball (MLB) pitchers. The concept of using a given season's cumulative work to predict injury in the following season is predicated on a cumulative damage injury model. It is based on the idea that during a season, through continued high rate/magnitude loading of the tissues used during pitching, fatigue-related damage accumulates. It is also based on the assumption that the off-season does not provide sufficient time to completely recover from accumulated tissue damage. Although the scope of this study was limited to the available data (off-season work data were not available to us), this will be the first study to explore a cumulative damage injury model for professional baseball pitchers in a meaningful way.

Because associations have been reported between certain cumulative work metrics and injury/pain in youth baseball, it was hypothesized that the cumulative work metrics can be used to predict future injury for professional pitchers.

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Experimental Approach to the Problem

This study was designed to test the hypothesis that cumulative work metrics can be used to predict future injury for professional pitchers. Cumulative work metrics (explanatory variables) and injury days (dependent variable) were compiled using real-world data from outside a controlled laboratory setting. Statistical methods were used to determine if any of the cumulative work metrics were significant predictors of injuries.

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This study was completed using only publicly available data on professional athletes from outside a laboratory setting, not gathered for the purposes of scientific research; therefore, institutional review board permission was not required. Professional pitcher statistics were obtained from a baseball statistics website (4) for the 2002–07 MLB seasons. Every pitcher who threw a pitch in MLB during the 6-year span was included. No exclusion criteria were used. Injury data were obtained from a website tracking all transactions involving the MLB disabled list (DL) for the 2003–08 seasons (6). To verify the authenticity of the data sources from each website, a random sample of 25 players were chosen and compared with records on the MLB website ( There was 100% agreement with the MLB website. In total, 3,760 pitcher-seasons were examined during the 2002–07 seasons.

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Each pitcher was treated independently across seasons, and therefore the term “pitcher-season” was used to describe cumulative work and injury data for a given pitcher during a single season. For example, cumulative work metrics and injury data for the same pitcher pitching in both the 2003 and 2004 seasons were treated as two separate pitcher-seasons. Days spent on the DL during multiple trips to the DL during a single season were summed for a total number of DL days.

Five cumulative work metrics were examined: (a) games pitched during a single season (appearances), (b) total innings pitched during a single season, (c) total pitches thrown during a single season, (d) average number of innings pitched per appearance during a full season, and (e) average number of pitches thrown per appearance during a full season.

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Statistical Analyses

Statistical analyses for this study were separated into two distinct types: inferential and descriptive.

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Inferential Statistics

Regression analyses were performed to determine if there was a correlation between cumulative work and injury, using the ordinary least-squares method, where the explanatory variable was the cumulative work metric (e.g., total innings pitched) and the dependent variable was number of days spent on the DL during the following season. A criteria of p < 0.05 was used to reject the null hypothesis.

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Descriptive Statistics

A descriptive statistical analysis beyond the inferential linear regression was performed to examine possible trends not detected in such a large cohort. Pitcher-seasons were “binned” with respect to each cumulative work metric. Bin sizes were five appearances for metric 1, 20 innings for metric 2, 300 pitches for metric 3, 1 inning per appearance for metric 4, and 10 pitches per appearance for metric 5. For each bin, the number of pitchers who were injured the following season was reported as a percentage of the total number of pitchers in the bin. Bin sizes were chosen to include a reasonable number of pitchers per bin and to parse out, as best possible, pitchers with different roles (e.g., starters, long relievers, setup, closer, etc.).

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During the span of this study, 1,031 pitchers spent time on the DL after a season in which they pitched. This translated into 27% of pitchers spent time on the DL the following season. For all pitchers, the average number of days spent on the DL per season was 21.45. When only injured pitchers were included, the average time spent on the DL during a single season was 78.22 days. For a typical MLB starting pitcher, this likely translated to approximately 10–15 missed starts.

The regression analysis showed an extremely weak positive correlation between all the cumulative work metrics and injury days the following season (Figure 1). Although the correlation was positive, it was not statistically significant and can be attributed to chance as likely as it can be attributed to any other underlying mechanisms.

Figure 1

Figure 1

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Total Appearances

Through the process of binning the appearances metric, it was found that the largest number of MLB pitchers made ≤5 appearances per season (Figure 2A, I). The number of pitchers who made 6–25 appearances steadily decreased until a second spike of pitchers was seen in the 31–35 appearances bin. This spike was likely attributed to the large number of starters who made a regular start every fifth day for an entire season. Pitchers who made >40 appearances per season were relief pitchers. A smaller spike was found in pitchers who made between 66 and 70 appearances in a single season. The 91–95 appearances bin only had one pitcher.

Figure 2

Figure 2

In terms of the number of pitchers who were injured the following season, there were no clear trends noticed (Figure 2A, II). Excluding the 91–95 appearances group, the highest percentage of pitchers injured the following season occurred in the 66–70 appearances bin (40%). Pitchers that made between 21 and 40 appearances were all found to have a comparable injury rate the following season (32–35%). Twenty-seven pitchers made between 81 and 85 appearances. This bin had the second lowest injury rate the following season (19%).

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Total Innings

The largest cohort of MLB pitchers pitched <20 innings in a single season (Figure 2B, I). The number of pitchers who pitched between 21 and 80 innings remained relatively constant for each 20-inning bin. There was a considerable drop off in number of pitchers who pitched >100 innings per season. A second markedly smaller peak was found in number of pitchers who pitched 201–220 innings. This small spike was likely attributed to the number of starters that made a regular 6- or 7-inning start for an entire season. The 261–280 innings bin only had 1 pitcher.

Excluding the 261–280 bin, the bin with the largest percentage of pitchers being injured the following season (Figure 2B, II) was 141–160 innings (42%), followed by the 201–220 innings bin (41%). The 161–180 and 181–200 innings bins did not have drastically lower injury rates (37% and 39%, respectively) than the 201–220 innings bin. The 221–240 innings bin had the second lowest injury rate (26%).

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Total Pitches Thrown

A considerable number of pitchers threw ≤300 pitches in the major leagues during a single season (Figure 2C, I). The number of pitchers that pitched between 301 and 600, 601 and 900, and 901 and 1,200 pitches was relatively even (546, 530, and 540, respectively). Relatively few pitchers pitched between 1,501 and 2,700 pitches in a single season. There was a small spike in the number of pitchers that pitched between 3,001 and 3,300 pitches a season.

Pitchers who pitched either between 1,801 and 2,400 or 2,701 and 3,300 pitches had a similar rate of injury (40–43%) the following season (Figure 2C, II). There was a drop off in injury rate for pitchers who threw more than 3,300 pitches in a season (31%).

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Innings Pitched Per Appearance

The two peaks in the innings pitched per appearance histogram (Figure 2D, I) was a clear representation of the current manner in which pitchers are used in MLB. A number of pitchers are used as starting pitchers, and those pitchers were seen in the peak centered at approximately 6 innings per appearance. A larger peak was centered at approximately 1 inning per appearance, and this was representative of relief pitchers.

In terms of injury (Figure 2D, II), the peak rate occurred in pitchers that pitched between 6 and 7 innings per appearance (39%). Although only 29 pitchers averaged between 7 and 8 innings per appearance, it must be noted that the injury rate did not increase for this group when compared with the adjacent group (7–8 innings = 38%; 6–7 innings = 39%). No pitcher averaged >8 innings per appearance. The lowest injury rate occurred in pitchers that averaged between 2 and 3 innings per appearance (21%).

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Pitches Per Appearance

Two peaks, similar to that of innings pitched per appearance, were found (Figure 2E, I). A large number of pitchers pitched between 11 and 30 pitches per appearance or between 81 and 110 pitches per appearance. These modes likely correspond to the distribution of relief and starting pitchers in MLB. Very few pitchers (only 9) averaged over 110 pitches per appearance.

The corresponding injury rate data showed a steadily increasing trend in injury rate, starting from the 41 to 50 pitches bin all the way to the 91 to 100 pitches bin (Figure 2E, II). The 101–110 pitches bin indicated that pitchers who averaged over 100 pitches per appearance had a similar injury rate the following season when compared with the 91–100 pitches bin (38% and 39%, respectively). Pitchers who threw between 11 and 20 pitches per game had a noticeably higher injury rate than either of the adjacent bins.

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Because the ordinary least-squares regression analyses did not find a single cumulative work metric to be a significant predictor of injury, this can be taken as a first piece of evidence that the currently used pitch count and inning limits are not able to prevent future injury. The further descriptive statistical analyses (histograms) of each of the cumulative work metrics showed some interesting trends that merit further discussion.

To allow for perspective in a discussion of the appearances metric, it must be stated that if a pitcher were to pitch in every fifth game his team played, that pitcher would pitch in either 32 or 33 games. The injury rate for the pitchers in the 21–40 appearances bins (Figure 2A, II) showed that it was not likely that pitching every fifth game was more detrimental to the pitchers' health than pitching slightly more often. Although this metric alone had some crucial limitations, for example, the group likely contained a combination of starters and relievers, pitching more often than once every fifth game may not correlate to a higher injury rate. With that being said, the peak injury rate occurred in pitchers with 66–70 appearances (corresponding to approximately 1 appearance every 2–2.5 games), and thus pitching too often may be detrimental to a pitchers health.

The total innings pitched metric is of particular interest because of the perceived importance of monitoring and, even in some cases restricting, innings pitched per season in young pitchers (12). Although this study did not specifically look at a subgroup of young pitchers, based on the injury rates reported, there does not appear to be a considerable increase in injury risk associated with total number of innings pitched in a single season. In fact, it appears as though a negative correlation may exist between pitching >220 innings and injury rate. Based on these descriptive statistics, this correlation cannot be stated with any certainty.

Total pitches thrown in a given season is the simplest cumulative work metric to comprehend. Given the cumulative damage injury model proposed, it was expected that this metric would have had the strongest positive correlation with injury days and injury rate. This was not the case. In fact, after a certain threshold (3,300 pitches), injury rate appeared to decrease. A hypothesis which may explain this curious finding is a pitcher who is able throw 3,300 pitches must have tissue tolerances, or pitching mechanics, or a combination of both, which allow them to throw this number of pitches in a single season without injury. Continuing with that assumption, it is reasonable to hypothesize that a pitcher's tissue tolerances/pitching mechanics do not drastically change between seasons, and therefore, a pitcher is likely able to withstand a similar cumulative work the following season, again without being injured.

Based upon the injury rate data for innings pitched per appearance, there is an indication that starting pitchers who averaged 6–7 innings per game may be more likely to get injured the following season than relief pitchers who averaged between 0 and 3 innings per game. This is noteworthy because, from a strict injury perspective, these data support the idea of changing the pitching paradigm in MLB from the traditional starter/relief pitcher model currently used to a model consisting of pitchers working in teams, pitching 3 innings each per game. It must be reinforced that the previous statement was strictly from an injury perspective and does not account for obvious performance concerns that would undoubtedly arise from the proposed pitcher paradigm shift.

Although only descriptive, the trend of increasing injury rate associated with increasing pitches per appearance, found during the binning process, is an example of a promising metric. Combined with supporting biomechanics literature showing changes in throwing mechanics in college pitchers throwing >70 pitches in a single appearance (8), a better strategy for preventing pitcher injury can be developed.

The exciting possibility of combining the cumulative work metrics described, with the development of novel advanced work metrics that incorporate intensity and rest, can be a small first step. Integration of previously described biomechanical approaches at predicting injury-based off kinetics (1,3) and newly developed kinematic approaches is also a future possibility to help further understand injury.

A technical limitation of this study was the assumption that if a pitcher did not appear on the DL the following season, that pitcher was healthy and pitching. The possibilities that a pitcher was either retired or was injured but not on a major league roster/DL the following season was not accounted for because of a lack of required data. As a result, reported injury rates are likely slight underestimates. Additionally, the underestimation is likely not a random error. The error is systematic because it likely underestimates pitchers with lower cumulative work metrics because they are also the pitchers more likely not to be on a major league roster the following season. Another limitation of this study is a lack of data on any of the cumulative work metrics for the minor leagues or winter ball. Some pitchers could have pitched more than their MLB statistics indicated.

More generally speaking, a limitation of using cumulative work metrics is, none of the metrics account for intensity of the pitching or rest/recovery between appearances. Perhaps, a metric including pitch velocity or pitch type may provide further insight. The amount of time between appearances (i.e., rest) will also undoubtedly provide even further insight.

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Practical Applications

The findings of this study provide strong evidence that the current methods of limiting cumulative work (specifically inning limits) cannot be effective tools to prevent future injury. Cumulative work for major league pitchers during the season can be broken down into two separate categories: (a) in-game cumulative work (e.g., pitch count, inning count, etc.), and (b) between-game cumulative work (e.g., pitches thrown during an off-day bullpen, strength training, etc.). This study only examines in-game cumulative work. From our results, there is no clear relationship between in-game cumulative work metrics and future injury. Consequently, more research needs to be done combining between-game and in-game cumulative work, to potentially form an association with injury. Strength and conditioning coaches, sports medicine specialists, and team trainers should work toward better monitoring between-game cumulative work, with the goal of accurately assessing the relationship between combined cumulative work (in-game/between-game) and future injury. For example, perhaps through quantifying between-game work, strength and conditioning coaches may find a relationship between training-volume (sets × reps × weight), pitches thrown during games and injury. Furthermore, perhaps between-game training and recovery techniques hold valuable insights into why some pitchers can withstand extremely high levels of in-game cumulative work and other pitchers breakdown at relatively low levels of cumulative work. This study provides evidence that a true determination of cumulative work exposures of MLB pitchers may require a greater understanding of what these athletes do off the field.

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fatigue; cumulative damage; innings; prediction; prevention

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