In Major League Baseball (MLB), there is a premium placed on starting pitchers. Indeed, at the time of writing, three pitchers possess the three highest player salaries in MLB, and total annual expenditure on pitcher contracts exceeds US$1.6b (39). Accordingly, optimizing pitcher development is of primary interest to managers, pitching coaches, and organizations alike. Paradoxically, scholarly research has traditionally provided limited empirical insight into those factors that directly influence a pitcher's effectiveness during games. Instead, time-honored coaching anecdotes assert that the ability to generate speed and movement—from the same release point—is crucial to success (16,34,35). Furthermore, even if these assertions prove to be true, there are currently no scientifically informed thresholds to inform the objective appraisal of these performance metrics, relative to MLB benchmarks. Consequently, there exists scope to identify those factors that portend pitching success in MLB and equip stakeholders with an evidence base for enhancing pitcher performance.
Much of the scientific inquiry into pitching performance has focused on the biomechanics of the skill (13). With a view to preventing injury, this research has primarily examined mechanics as they relate to upper extremity joint loading (9,10,12). From a performance perspective, ball velocity (25,41) has traditionally been used a criterion, yet no empirical data have been presented to confirm that a pitcher's effectiveness is directly related to how fast he delivers his pitches. The potential impropriety of this assumption is highlighted by the fact that Fleisig et al. (11) reported that average fastball speed in a cohort of Minor League pitchers was 1.5 m·s−1 greater than that achieved by MLB pitchers. Similarly, the notions of movement (or “break”), release consistency, and accuracy—while prevalent in pitcher development and scouting (15,32,34)—have received meager research attention. Thus, it remains unclear how these factors contribute to success at the professional level. Interestingly, a recent study on NCAA Division I pitchers proposed that speed, movement, and release consistency were not related to in-season pitching success, although these metrics were garnered ex situ and correlated to pitching statistics during the season (43). On this basis, there is an apparent need to better understand those factors that characterize successful professional pitchers, such that pitcher development can be informed accordingly.
Further impeding progress in this space, researchers have had to navigate the accepted limitation of extrapolating laboratory-garnered data as a means to understand performance in situ. However, the advent and installation of ball-tracking technology in MLB provide an unparalleled solution to this ecological validity issue. Recent research has leveraged these in situ data to examine performance on return from surgery (18), elusive knuckleball trajectories (29), and umpire bias in adjudicating (33), providing unprecedented insight into professional competition. Consequently, there is scope to extend these analyses to examine pitcher performance, providing a complement to the above-mentioned biomechanical data.
Elucidating those factors that contribute to pitching success at the professional level would, most critically, allow practitioners to adopt an evidence-based approach to pitcher development. Likewise, this would provide a critical primer for future research in this domain, which has traditionally focused on velocity as a criterion performance metric. Finally, understanding what differentiates the most effective MLB pitchers also provides potential implications at the management level that could inform in-game and trade decisions. Correspondingly, the primary objective of this study was to examine how a pitcher's ball speed, ball movement, variation in speed and movement, and release location—as measured during games—related to his success in MLB. It was hypothesized that greater pitch speed, pitch movement, and release consistency would significantly predict pitcher effectiveness in MLB.
Experimental Approach to the Problem
There are limited in situ data that can be used to describe the performance of professional pitchers during competition. Consequently, those factors that relate to a pitcher's effectiveness remain undetermined. To address this, ball tracking data from 76,000 pitches thrown by a cohort of 190 starting pitchers during regular season MLB games were collated for analysis. Ball kinematics from 400 pitches of each pitcher were then related to his effectiveness (as measured by fielding independent pitching [FIP]) to determine those factors that predict a starting pitcher's success in MLB.
Initial Delimitation of Population
This study protocol was granted approval by the institutional review board. An initial search identified a cohort of 371 pitchers who pitched at least 100 innings in MLB between the 2008 and 2014 seasons. Ball tracking data have only been comprehensively available in MLB since the competition-wide installation of the PITCHf/x system (Sportvision, Chicago, IL, USA) in 2008, thereby providing the rationale for only investigating data from 2008 onward. Each pitcher's unique Fangraphs identification and MLB identification number were then garnered manually from the respective websites. These identification numbers were used to scrape demographic, statistical, and pitch information for each pitcher according to the procedure that follows. The study conforms to the Code of Ethics of the World Medical Association (approved by the ethics advisory board of Swansea University) and required players to provide informed consent before participation.
Harvesting Pitcher Demographics, Fielding Independent Pitching, and Game Information
A custom MATLAB (Natick, MA, USA) script was written to harvest relevant data from three websites. First, the pitcher's date of birth, height, mass, and throwing hand were extracted from their Fangraphs player page and checked for consistency against their corresponding MLB player page. By parsing the player's game logs, the script then harvested game-by-game information (i.e., teams involved and date of game) for every regular season MLB game that the pitcher started during the 2008–2014 MLB seasons. These records were used to generate uniform resource locators (URLs) on the MLB Advanced Media (MLBAM) web pages that corresponded to each game and which contained the ball tracking data that were ultimately extracted for analysis. The game logs were also used to obtain the pitcher's FIP statistic—a criterion measure of his success—during the analyzed games.
Harvesting Ball Tracking (PITCHf/x) Data From Major League Baseball Advance Media
The PITCHf/x system uses two stadium-mounted cameras to record three-dimensional displacement, velocity, and acceleration data for every pitch thrown in MLB. At the end of each day, these data are then uploaded to a central database that is maintained by MLBAM. Having defined the URL that corresponded to each game, the MATLAB script extracted the above ball tracking information for every pitch that the pitcher threw during the defined period. Using these kinematic parameters, the trajectory of each pitch could be reconstructed to determine information about the pitch such as its release speed, deviation (or break), release location, pitch type and location that it crossed home plate.
As a first pass, a pitch count test was performed to determine whether the pitcher threw at least 100 of each of the following pitches: fastballs, changeups, curveballs, and sliders during the analyzed period. If he had not, he was removed from the cohort and the script immediately proceeded to the next pitcher. This initial screening procedure reduced the original population to 190 pitchers who comprised the experimental cohort for this study and who, collectively, provided 2,112,556 pitches for analysis. To permit meaningful analysis and interpretation, only the 4 most common pitch types in MLB—fastballs, changeups, curveballs, and sliders, which collectively accounted for 69.9% of all pitches in the 2014 MLB season—were analyzed in this study. Because grouping 4-seam and 2-seam fastballs would have provided a limitation, only 4-seam fastballs were analyzed in this study, as they are approximately 2.5 times more common in MLB. To (a) ensure that the sampled data were representative of the pitcher's true performance of a given pitch and (b) minimize the effect of system error (according the PITCHf/x manufacturer: <1.60 km·h−1 and <1.02 cm), 100 observations of each pitch type were obtained for analysis, for each pitcher.
Within the experimental cohort, most pitchers had thrown considerably more than 100 of each pitch type during the sampled period. Therefore, the 100 pitches of each pitch type (for a total of 400 pitches, per pitcher) that were selected for analysis in this study were randomly sampled from their population of pitches. The measures in this study were determined by reconstructing ball trajectories in each pitch, using the nine PITCHf/x parameters described above. First, the initial y-displacement was adjusted to a more realistic location of 16.764 m from home plate (8,24,40). A series of equations was then solved to calculate horizontal position of the ball at release, vertical position of the ball at release, release speed of the ball, and the magnitude of the ball's movement or break in both horizontal and vertical planes. Explicitly, movement was defined as the deviation (i.e., displacement) of the ball from its expected gravitational trajectory, at the time it crossed home plate, which has been illustrated previously by Nathan (30). The preferred drag-corrected method described by Nathan (30) was used to derive the most accurate reconstruction of the ball's trajectory. The movement and release location values were normalized such that all kinematic values presented in this study can be interpreted to pertain to a right-handed pitcher.
Variables of Interest
Demographic information included age (at the median date of the pitcher's sampled period), height, mass, and throwing hand. Pitch selection was the only variable calculated using the pitcher's entire population of pitches and was defined as the ratios of each pitch type that a pitcher threw, relative to his total number of pitches. Pitch speed was the mean exit speed of the ball from the hand. To permit meaningful comparisons, vertical and horizontal release locations were normalized to the pitcher's height with positive x pointing to the pitcher's right and positive z pointing up. Horizontal and vertical ball movements were expressed in the same frame. To gauge the degree to which the pitcher varied his pitches, the SDs of pitch speed and movement were also calculated across (a) each individual pitch type, using n = 100 pitches and (b) across the grouped pitch types, using n = 400 pitches. Likewise, 95% confidence covariance regions of the release location were computed (a) within each pitch type and (b) across the grouped pitch types. The area of the ellipsoid quantified the 2-dimensional (i.e., approximate batter's perspective) spatial variability of the pitcher's release location. Because measures of variability are dependent on the number of observations, this provided the rationale for analyzing precisely the same number of pitches for every pitcher (as opposed to their entire sample of pitches).
Fielding independent pitching was selected as the criterion measure of pitching performance as it controls for competition-wide differences in fielding ability (which are beyond the pitcher's control). Consequently, this metric isolates performance outcomes that are exclusively within the pitcher's control, thereby providing the most representative measure of his effectiveness (43). The specific calculation for FIP in this study was akin to the defense-independent component-earned run average (ERA) statistic originally developed by Clay Dreslough (5):where HR was the number of home runs conceded, BB the number of (nonintentional) walks, HBP the number of pitches that hit the batter, K the number of strikeouts, IP the number of innings pitched, and c was constant used to transform FIP onto an ERA scale (and fluctuates marginally each season). A lower FIP is indicative of better performance, and Table 1 provides a scale for interpreting FIP, as developed by seminal baseball statistics' website Fangraphs.com (7).
Strong correlations between independent variables can distort regression models, precluding the insertion of variables from each of the 4 pitch types (which were highly correlated). Instead, variables from the 4 pitch types (i.e., 400 pitches) were grouped and then used to construct a correlation matrix to detect collinearity. None of the grouped variables displayed a Pearson's product moment coefficient |r| greater than a conservative threshold of 0.5, permitting their independent inclusion in the regression model calculation. A multiple linear regression model was then used to identify which of those variables significantly predicted FIP. From the regression analysis, standardized beta coefficients (β) were used to interpret each predictor variable's contribution to the model. After the significant predictor variables had been identified, post hoc bivariate correlations subsequently evaluated how that variable related to FIP at the pitch type (i.e., fastball, changeup, slider, and curveball) level. Furthermore, post hoc bivariate Pearson correlations were conducted to examine the relation between the measured demographics and significant predictor variables. The strength of the relation was considered negligible ( < 0.01); weak (0.1 ≤ 0.3); moderate (0.3 ≤ < 0.5); strong (0.5 ≤ < 0.7); very strong (0.7 ≤ < 0.9), or nearly perfect (0.9 ≤ < 1.0) (1). Significance was set at p ≤ 0.05. Statistical procedures were performed in SPSS Statistics 21 (IBM, Armonk, NY, USA).
The 190 pitchers in this study were 28.1 ± 3.9 years at the median date during their sampled period; their height was 189.7 ± 5.4 cm; their mass was 97.6 ± 9.3 kg; and 139 were right-handed. During the sampled period, the mean number of games started, per pitcher, was 91 ± 61; innings pitched was 548 ± 389; and FIP was 4.22 ± 0.67 (range: 2.33–6.25).
Descriptive statistics for the 4 pitch types are presented in Table 2. The stepwise multiple regression revealed a significant prediction equation (F4,185 = 14.318, p < 0.001) that explained 23.6% of the variance in FIP and contained four significant predictor variables (Table 3). Specifically, grouped pitch speed was negatively correlated with FIP, denoting a moderate inverse relation between pitch speed and FIP. Release location variability across the grouped pitch types exhibited a weak positive correlation with FIP, suggesting that pitchers with a more variable release location possessed a higher FIP (i.e., were less successful). Variability in pitch speed across the grouped pitch types displayed a negligible negative correlation with FIP. Finally, the lateral release location of the grouped pitch types exhibited a negligible negative correlation with FIP. Collectively, these variables produced the following prediction equation:where a was the pitcher's mean pitch speed across the four pitch types; b was the area of the 95% covariance ellipse that defined his release locations; c was the SD of his pitch speed; and d was his mean horizontal release location, normalized to standing height.
Within the significant predictor, pitch speed, the fastball, changeup, and slider were all significantly correlated to FIP, although curveball speed was not (Table 4). The release location variability of each pitch type exhibited a significant positive correlation to FIP. Despite significance at the grouped pitch level, variation in pitch speed and horizontal release location was not significantly correlated to FIP in any of the individual pitch types.
With respect to demographics, height (r = 0.184; p = 0.011), handedness (r = 0.286; p < 0.001), and age (r = −0.385; p < 0.001) were all significantly correlated to pitch speed. Height also shared a positive correlation to release location variability (r = 0.279; p < 0.001). Both height (r = −0.239; p = 0.001) and mass (r = −0.229; p = 0.001) were weakly negatively correlated to horizontal release location.
This study endeavored to identify pitching metrics that predict a pitcher's success in MLB. A regression model revealed that—of variance explained—pitch speed, release location consistency, variation in pitch speed, and horizontal release location were significant predictors of FIP. Therefore, among the variables analyzed in this study, these four metrics provide the most logical focal points for MLB pitchers who desire to improve their effectiveness. However, 76% of the variance in FIP was not explained in our model and underlines the shortcomings of evaluating and/or forecasting pitcher ability based only on standard pitching metrics.
To our knowledge, the mean fastball pitch speeds recorded in this study were the fastest speeds ever reported in a population of pitchers. Collectively, the individual pitch speeds corresponded to previous descriptions of MLB pitchers who have used on this technology (18,23) and were 2.7–6.5 m·s−1 faster than those previously reported in Minor League (11) and collegiate (19,28,43) cohorts. At a descriptive level, this confirms that these MLB pitchers generated greater ball speeds than pitchers at lower levels of competition. If obtaining a place on a MLB roster is a sufficient criterion, this finding provides initial support to the assertion that speed generation is crucial to achieving success as a pitcher (20,37). Unfortunately, the authors are not aware of any research that has quantified release location or ball movement in any populations, although the values in Table 2 provide benchmarks against which future cohorts may be evaluated.
As hypothesized, the regression model identified pitch speed as a significant predictor of the pitcher's effectiveness, explaining 10.4% of the variance in FIP. According to the regression model, a 1-m·s−1 increase in ball speed reduces a pitcher's FIP by 0.258 (assuming the three other predictor variables remain constant). This makes logical sense considering that faster pitches afford batters less time to detect the ball, forecast its trajectory, and execute their swing. When considered alongside the descriptive evidence above, this finding supports the notion that the ability to generate ball velocity is a critical prerequisite to achieving success at the MLB level. Likewise, these data justify the emphasis on velocity that is customary when scouting pitchers (15,34,35). At the pitch type level, the changeup and fastball displayed moderate negative correlations to FIP and present the most logical foci for speed development, although any increase in a pitcher's ball speed would logically translate to all of his pitches.
Evidence suggests that increases in pitch speed can be achieved through mechanical (13,37,38) and physical (6,21,31) interventions. However, this notion presents an acute challenge for MLB stakeholders as greater pitch speeds have been associated with greater upper extremity joint loads (3,38) and implicated in catastrophic ulnar collateral ligament injury (42). Accordingly, increases in pitch speed may yield diminishing returns beyond a threshold, which future research should seek to quantify. In this sense, it is imperative that practitioners consider a pitcher's injury history/risk before administering speed development programs. Equally, strength training may be a valuable precursor to these programs as rotator cuff strength has been shown to inversely relate to injury risk (4). Where injury risk controverts enhancing pitch speed, or training loads are restricted, the other significant predictors of FIP in this study serve as alternative foci for coaching and conditioning staff.
Variability of the release location was the second critical predictor of a pitcher's effectiveness, with the relation suggesting that FIP is superior (i.e., lower) in pitchers who possess more consistent release locations. This does not conform to what has been noted in US collegiate pitchers, where release location and FIP have been reported as independent (43) (albeit using an admittedly limited cohort and volume of ex situ pitches and a more rudimentary statistical approach). However, this finding does support the premise that release consistency is a hallmark of elite pitching (43) and vindicates the attention coaches (22,26) and scouts (15,34) afford to this performance factor.
Interestingly, release location variability in each of the four pitch types was significantly correlated to FIP and implies that the ability to release the ball from the same location should transcend the pitcher's entire repertoire. The most likely explanation for this association is that a consistent release location removes perceptual cues for the batter, thereby impeding their anticipatory proficiency (36). Taken with the ball speed findings, these data indicate that aspiring MLB pitchers should refine their ability to not only release the ball with high velocity but also to do so from a consistent spatial location. Evidence from the motor control domain indicates that stable endpoint conditions manifest as a result of practice (27). Therefore, although speed improvements may be more dependent on conditioning, bullpen sessions seem more beneficial in this case. Striking this balance between gym and throwing practice without overburdening the pitcher necessitates that training prescription emerges from dialogue between the conditioning and coaching staff.
Based on the mean values in this study, the regression model indicated that a 1% increase in pitch speed produced a 2.3% improvement in FIP, whereas a 1% increase in release consistency only yielded a 0.1% improvement in FIP. Ostensibly, these results encourage coaches to prioritize improvements in speed, although the between-pitcher variations noted in this study underline how it would be most prudent to appraise pitchers at the individual level. As an example, it seems most sensible for a pitcher in sector B of Figure 1—who possesses above average pitch speed but below average release consistency—to improve FIP by refining his release location. An illustration of this scenario exists in Figure 2, where there is considerable scope for less successful pitcher to refine a more consistent endpoint. In contrast, a pitcher with above average release consistency in sector C would seemingly benefit more from a targeted intervention to enhance his below-average pitch speed.
The final 2 significant predictors of FIP in our regression model were variation in pitch speed and horizontal release location, with the former explaining 2.5 times more variance in FIP than the latter. Evidently, pitchers who used a larger bandwidth of pitch speeds were more effective. This is consistent with preliminary reports that varying pitch speed can “fool” batters (16). Indeed, a predictable ball speed would, in theory, allow the batter to program the temporal component of their swing a priori, thereby reducing the complexity of the task. It is also important to note that variation in pitch speed did not significantly correlate with FIP in any of the four individual pitch types, suggesting that the aggregated variation in pitch speeds across the pitcher's entire repertoire is most critical. To align their development programs with these data, coaches could cultivate several different pitch types and instruct their pitchers to vary their delivery while on the mound. Instructive to this process, the range of speeds used by the average pitcher in this study was 10.85 m·s−1.
Although the results indicated that a more pronounced lateral release location (i.e., further out to the side) was associated with enhanced effectiveness, the factor underlying this relation was not readily apparent. Sidearm pitchers—who possess exaggerated lateral release locations—are known to generate lower ball speeds than traditional overhand pitchers (2), eliminating speed as the motivator. However, sidearm pitchers are notoriously rare at all levels of baseball and, thus, are more unfamiliar to batters. Relatedly, it is common for sidearm pitchers to testify that their unique style is more deceiving for the batter (14). This might help explain why a more pronounced lateral release location would yield a lower FIP, although this explanation should remain speculative, pending scientific confirmation. In a practical sense, the beta coefficients and Pearson correlations in Table 3 denote that increases in ball speed variability or horizontal release location only elicit incremental improvements in FIP. Consequently, in most scenarios, it would not make sense to prioritize these performance factors ahead of ball speed or release consistency, both of which would be expected to yield comparatively greater performance returns.
This study was delimited to the 4 preeminent pitch types in MLB, although there did not seem to be an optimal usage pattern of these pitch types that differentiated successful pitchers. Contrary to expectations, the magnitudes and variation of horizontal and vertical pitch movements were not significantly correlated to FIP. Without discounting the importance of these elements, the current findings suggest that these performance factors are less critical to pitching success than those expressed in the regression model.
The bivariate correlations suggested that pitch speed decreased with age, which is most relevant to pitcher recruitment and trade decisions in MLB. From a recruiting/scouting perspective, significant weak correlations denoted that taller and right-handed pitchers produced faster ball speeds. None of the demographics—age, height, mass, or handedness—were significantly correlated to release location variability or pitch speed variation.
It is critically important to note that despite identifying some key predictors of pitching effectiveness, and their relations thereto, the regression model derived in this study ultimately accounted for only 24% of a pitcher's FIP. Therefore, although the predictor variables in this study provide focal points for practitioners, they should not be considered the lone determinants of pitching success in MLB. Rather—and directly supporting what has been noted in US collegiate pitchers (43)—these data imply that a considerable portion of a pitcher's success in MLB is determined by factors other than the standard metrics that describe his delivery. For this reason, it would appear as though a comprehensive pitching development program should be multidisciplinary and not simply reduced to mechanics and conditioning. To that end, future scientific inquiry should endeavor to ascertain the other contributors to success, with psychological, strategic, and physiological factors providing logical avenues for investigation.
This study only examined a confined cohort of established MLB pitchers, and it is, therefore, difficult to generalize these findings to other pitching populations and/or competitions. Likewise, this study confirmed that factors beyond the variables of interest in this study determine a pitcher's effectiveness—which future work should aim to elucidate. We also did not have access to these athletes' practice and/or conditioning regimes, which would almost certainly enhance how these data are construed and should, therefore, be sought in extensions of this work. Finally, from a practical perspective, the beta coefficients in the model denote how each predictor variable would contribute to FIP if the other three remained constant. However, the current data cannot speak to the propriety of such an assumption, and prospective research should investigate remedial programs that target the predictor variables identified in this study.
These data support the premise that superior pitch speed and consistency in the release location herald greater success at the professional level. Likewise, pitch speed variability was also a significant predictor of pitchers' effectiveness during MLB competition. From a strict performance optimization perspective, the current findings suggest that practitioners' pitching development programs should place a primary focus on maximizing ball speed and improving spatial consistency in the release location. However, performance variations between pitchers and the reported link between ball speed and injury necessitate that these programs be tailored at the individual level. Tactically, the data suggested that pitchers should be encouraged to use a variety of pitch speeds. Despite being identified as significant predictors of a pitcher's FIP, pitch speed, release location, and pitch speed variation should not be considered the exclusive indicators of pitching success as they, collectively, only explained 22% of the variance in pitching effectiveness. Finally, pitching coaches and conditioning staff may use the empirical data presented in this study for benchmarking purposes when scouting and developing pitchers for MLB competition.
This study was funded by the University of Michigan.
1. Adams M. BTEC National Sport and Exercise Sciences: Heinemann, 2007. pp. 215.
2. Aguinaldo AL, Chambers H. Correlation of throwing mechanics with elbow valgus load in adult baseball pitchers. Am J Sports Med 37: 2043–2048, 2009.
3. Bushnell BD, Anz AW, Noonan TJ, Torry MR, Hawkins RJ. Association of maximum pitch velocity and elbow injury in professional baseball pitchers. Am J Sports Med 38: 728–732, 2010.
4. Byram IR, Bushnell BD, Dugger K, Charron K, Harrell FE, Noonan TJ. Preseason shoulder strength measurements in professional baseball pitchers identifying players at risk for injury. Am J Sports Med 38: 1375–1382, 2010.
5. Dreslough C. DICE: A new pitching stat. Available at: http://www.sportsmogul.com/content/dice.htm
. Accessed May 20, 2015.
6. Escamilla RF, Ionno M, deMahy MS, Fleisig GS, Wilk KE, Yamashiro K, et al. Comparison of three baseball-specific 6-week training programs on throwing velocity in high school baseball players. J Strength Cond Res 26: 1767–1781, 2012.
7. Fangraphs.com. Baseball statistics and analysis fangraphs. Available at: http://www.fangraphs.com/
. Accessed May 20, 2015.
8. Fast M. What the heck is PITCHf/x. Hardball Times Annual 6: 153–158, 2010.
9. Fleisig GS, Andrews JR, Dillman CJ, Escamilla RF. Kinetics of baseball pitching with implications about injury mechanisms. Am J Sports Med 23: 233–239, 1995.
10. Fleisig GS, Barrentine SW, Zheng N, Escamilla RF, Andrews JR. Kinematic and kinetic comparison of baseball pitching among various levels of development. J Biomech 32: 1371–1375, 1999.
11. Fleisig GS, Chu Y, Weber A, Andrews JR. Variability in baseball pitching biomechanics among various levels of competition. Sports Biomech 8: 10–21, 2009.
12. Fleisig GS, Kingsley DS, Loftice JW, Dinnen KP, Ranganathan R, Dun S, et al. Kinetic comparison among the fastball, curveball, change-up, and slider in collegiate baseball pitchers. Am J Sports Med 34: 423–430, 2006.
13. Fortenbaugh D, Fleisig GS, Andrews JR. Baseball pitching biomechanics in relation to injury risk and performance. Sports Health 1: 314–320, 2009.
14. Freeborn G. Interviews. Available at: http://www.sidearmnation.com/interviews/
. Accessed May 20, 2015.
15. Goldis A, Wolff J. The fundamental ingredients of a Major League ballplayer. In: How to Make Pro Baseball Scouts Notice You: An Insider's Guide to Big League Scouting. New York, NY: Skyhorse, 2009. Chapter 5.
16. Gray R. “Markov at the bat”: A model of cognitive processing in baseball batters. Psychol Sci 13: 542–547, 2002.
17. Hample Z. The basics. In: Watching Baseball Smarter: A Professional Fan's Guide for Beginners, Semi-experts, and Deeply Serious Geeks. New York, NY: Vintage Books, 2007. pp. 5–6.
18. Jiang JJ, Leland JM. Analysis of pitching velocity in major league baseball players before and after ulnar collateral ligament reconstruction. Am J Sports Med 2014. Published before print.
19. Jinji T, Sakurai S. Baseball: Direction of spin axis and spin rate of the pitched baseball. Sports Biomech 5: 197–214, 2006.
20. Lachowetz T, Evon J, Pastiglione J. The effect of an upper body strength program on Intercollegiate baseball throwing velocity. J Strength Cond Res 12: 116–119, 1998.
21. Lehman G, Drinkwater EJ, Behm DG. Correlation of throwing velocity to the results of lower-body field tests in male college baseball players. J Strength Cond Res 27: 902–908, 2013.
22. Maher C. Self-motivating: Setting and pursuing goals. In: The Complete Mental Game of Baseball: Taking Charge of the Process on and off the Field. Bloomington, IN: AuthorHouse, 2011. pp. 87–105.
23. Makhni EC, Lee RW, Morrow ZS, Gualtieri AP, Gorroochurn P, Ahmad CS. Performance, return to competition, and reinjury after Tommy John surgery in major league baseball pitchers: A review of 147 cases. Am J Sports Med 42: 1323–1332, 2014.
24. Marchi M, Albert J. Analyzing Baseball Data with R. Boca Raton, FL: CRC Press, 2013. pp. 311–325.
25. Matsuo T, Escamilla RF, Fleisig GS, Barrentine SW, Andrews JR. Comparison of kinematic and temporal parameters between different pitch velocity groups. J Appl Biomech 17: 1–13, 2001.
26. McFarland J. Creating a winning mental approach. In: Coaching Pitchers. Champaign, IL: Human Kinetics, 2003. pp. 115–132.
27. Müller H, Sternad D. Decomposition of variability in the execution of goal-oriented tasks: Three components of skill improvement. J Exp Psychol Hum Percept Perform 30: 212, 2004.
28. Nagami T, Morohoshi J, Higuchi T, Nakata H, Naito S, Kanosue K. The spin on fastballs thrown by elite baseball pitchers. Med Sci Sports Exerc 43: 2321–2327, 2011.
29. Nathan AM. Analysis of knuckleball trajectories. Proced Eng 34: 116–121, 2012.
30. Nathan AM. Determining pitch movement from PITCHf/x data. Available at: http://baseball.physics.illinois.edu/Movement.pdf
. Accessed May 20, 2015.
31. Newton RU, McEvoy KI. Baseball throwing velocity: A comparison of medicine ball training and weight training. J Strength Cond Res 8: 198–203, 1994.
32. Parks J. How are players scouted, acquired and developed? In: Baseball Prospectus: Extra Innings More Baseball between the Numbers from the Team at Baseball Prospectus. Goldman S., ed. New York, NY: Basic Books, 2012. Part II.
33. Parsons CA, Sulaeman J, Yates MC, Hamermesh DS. Strike three: Discrimination, incentives, and evaluation. Am Econ Rev 101: 1410–1435, 2011.
34. Perkin D. The basics of scouting. In: Five-Plus Tools: The Past, Present and Future of Baseball through the Eyes of a Scout. New York, NY: Sports Publishing, 2014. Section One, chapter 2.
35. Sandoval J. The good face. In: Can He Play? A Look at Baseball Scouts and Their Profession. Sandoval J., Nowlin B., eds. Phoenix, AZ: Society of American Baseball Research, 2011. pp. 51–80.
36. Shank MD, Haywood KM. Eye movements while viewing a baseball pitch. Percept Mot Skill 64: 1191–1197, 1987.
37. Stodden DF, Fleisig GS, McLean SP, Andrews JR. Relationship of biomechanical factors to baseball pitching velocity: Within pitcher variation. J Appl Biomech 21: 44–56, 2005.
38. Urbin M, Fleisig GS, Abebe A, Andrews JR. Associations between timing in the baseball pitch and shoulder kinetics, elbow kinetics, and ball speed. Am J Sports Med 41: 336–342, 2012.
39. MLB salaries. Available at: http://www.usatoday.com/sports/mlb/salaries/
. Accessed May 20, 2015.
40. Weinstein-Gould J. Keeping the hitter off balance: Mixed strategies in baseball. J Quant Anal Sports 5: 1–20, 2009.
41. Werner SL, Suri M, Guido JA, Meister K, Jones DG. Relationships between ball velocity and throwing mechanics in collegiate baseball pitchers. J Shoulder Elb Surg 17: 905–908, 2008.
42. Whiteside D, Martini DN, Lepley AS, Zernicke RF, Goulet GC. Predictors of ulnar collateral ligament reconstruction in Major League Baseball pitchers: Fewer days between games, smaller pitch repertoires, wider release locations, taller stature, greater ball speeds, and higher pitch counts. Am J Sports Med. In review.
43. Whiteside D, McGinnis RS, Deneweth JM, Zernicke RF, Goulet GC. Ball flight kinematics
, release variability and in‐season performance in elite baseball pitching. Scand J Med Sci Sports 2015. Early view.