Science and Baseball

Category: Biomechanics (Page 2 of 2)

Fatigue inferences on a 100 pitch limit

In the bottom right corner of your screen, you see the number of outs, you see the score of the game, the inning number, and right at the top of that ticker – the number of pitches that the pitcher has thrown (Figure 1).


Figure 1. Tickers from various broadcasts, illustrating a bunch of information to make you feel more informed.

Pitch counts have been used as a metric to measure workload in pitchers for some time now. Broadcasters constantly speculate on when a starter will be removed from a game as they approach that insidious 100 pitch limit – but is it just as simple as counting up the number of times that a ball has been thrown?

Zack Rymer found those pitchers who averaged 100 pitches per start were not more likely to get injured. Tom Karakolis and his crew pointed to the same findings – pitch counts or innings pitched may not be the best method of measuring workload.

Earlier this season, Ross Stripling was pulled from a no-hitter because he came up against the 100 pitch limit. This limit, while based on an article by Whiteside and colleagues (Whiteside et al., 1999), does ignore the fact that throwing 100 pitches over a complete game is probably going to be a lot less stressful than pounding through 100 pitches over 5 innings. Dieter Kurtenbach (@dkurtenbach) wrote a great article surrounding the mystique of the 100 pitch limit, and illustrated a few other workload measures (like the pitcher abuse points). The main point from this article, is that all pitches cannot be considered equal, and drawing a hard line in the sand at 100 is probably not going to save elbows, or preserve young pitchers.

Using the same fatigue model that was used to show Pitch Clocks are going to elevate muscle fatigue in pitchers, I wanted to show how the 100 pitch limit is probably not our best metric for evaluating stress in pitchers.

Fatigue Modeling

The fatigue model I used for this analysis is published in the Journal of Ergonomics (Sonne & Potvin, 2016), and has been used to estimate fatigue levels in baseball pitchers. This model is based off of motor unit physiology. From Wikipedia:

“A motor unit is made up of a motor neuron and the skeletal muscle fibers innervated by that motor neuron’s axonal terminals. Groups of motor units often work together to coordinate the contractions of a single muscle; all of the motor units within a muscle are considered a motor pool”.

When a motor unit fires, all of the muscle fibres it innervates contract, and this causes a force to be generated. Motor units can be quite small and generate small amounts of force, or quite large and generate lots of force. At the same time, the amount of force that a motor unit can generate is impacted by the fatigued state that it is in. If a motor unit is exhausted, it cannot generate any force, and it will rely on other motor units to pick up the slack on its behalf. The order in which motor units join the good fight of force production is best described by the size principle, originally hypothesized by Henneman et al., (1965). The size principle states that smaller, less forceful motor units will be recruited first, and larger, more forceful motor units will be recruited once they are required.

We could talk about motor unit physiology for days and days, but I kind of want to write about baseball now.

The fatigue model I’m using defines fatigue as “a loss of force generating capacity”. If your muscle is 10% fatigued, that means, it can now generate only 90% of it’s pre-fatigued force. When you’re exercising, failure can occur once you’ve reach a certain amount of fatigue. From an injury perspective, the muscles used to protect your joints during movement can become fatigued, and lose some of their protective capacity.

So, to drive the model, I used the muscle demands of the forearm seen during the throwing of fastballs (DiGiovine et al., 1992, Glousman et al., 1992, Hamilton et al., 1996 Sisto et al., 1986) (Figure 2).


Figure 2. Muscle Activation levels, broken down by phase of throw, and grouped by individual forearm muscles.

I then assumed an average amount of rest between pitches (as per FanGraphs – the value used was 22.6 seconds). I assumed 2:30 of rest between innings, and simulated the offensive half of an inning as being 17 pitches long, with 22.6 of rest between each pitch.

To examine the effect of the 100 pitch limit, I simulated starts ranging between 4 and 9 innings, throwing only fastballs, but having the appropriate average of pitches per inning to get to that limit (4 inning start – 25 pitches per inning, 5 inning start – 20 pitches per inning, etc (I rounded to the nearest whole pitch). While I have calculated fatigue for individual muscles, I’m just going to graph out the average fatigue for all forearm muscles (for ease of viewing – Figure 3).


Figure 3. Average forearm muscle fatigue during starts of 4 to 9 innings, all with the same pitch count (100 pitches).

The major take home from this figure should be how high each of those lines gets on the Y Axis – the greener the line, the more innings per start – and more importantly, less fatigue per start. Chances are, if your starter has gone through 100 pitches in their first four innings, they’re likely going to get the hook. For the sake of this exercise, let’s take a look at how fatigue would change with respect to those 4, 25 pitch innings.


Figure 4. Change in fatigue compared to 4 inning start with 100 pitches – positive values indicate the level of fatigue reduction (ie, 5% represents 5% less fatigue when compared to the 4 inning start – a higher value means there is a greater benefit for fatigue reduction when throwing fewer pitches per inning).  

A quality start is defined as 6 innings pitched, allowing 3 ER or less. If a pitcher throws 100 pitches in those 6 innings, they’ll see nearly 10% less fatigue in their forearm muscles when compared to a 4 inning start. Looking at a 100 pitch, complete game start, there is a benefit of nearly 20% compared to that 4 inning start. To see the benefits in individual forearm muscles, check out table 1.

Table 1. Fatigue levels in individual forearm muscles, and the improvement in fatigue compared to a 4 inning, 25 pitch start.

fatigue reduction

So, what does this all mean? A 100 pitch limit is rooted in science, but looking at pitch counts alone in the start do tend to miss the bigger picture – the amount of work done in an individual inning appears to induce more fatigue than looking at the total pitches performed in a start alone. Working deep into games and limiting the pitches in each inning is the most effective way of keeping muscle fatigue levels low.

Effective tools for fatigue monitoring are essential to pitcher health. If you’re looking for more insight into the topic, I highly recommend following guys like Ryan Faer and Kyle Boddy on Twitter. If you’re a coach and want to look at tools to measure workload in pitchers, a great place to start is this guide from the Baseball Performance Group.

If you want to learn more about the fatigue modeling process – check out the paper I wrote for the Journal of Sports Sciences here. I’m not saying use sci-hub to download it… but I’m also not saying not to.


DiGiovine, N. M., Jobe, F. W., Pink, M., & Perry, J. (1992). An electromyographic analysis of the upper extremity in pitching. Journal of Shoulder and Elbow Surgery, 1(1), 15-25.

Glousman, R. E., Barron, J., Jobe, F. W., Perry, J., & Pink, M. (1992). An electromyographic analysis of the elbow in normal and injured pitchers with medial collateral ligament insufficiency. The American Journal of Sports Medicine, 20(3), 311-317.

Hamilton, C. D., Glousman, R. E., Jobe, F. W., Brault, J., Pink, M., & Perry, J. (1996). Dynamic stability of the elbow: electromyographic analysis of the flexor pronator group and the extensor group in pitchers with valgus instability. Journal of Shoulder and Elbow Surgery, 5(5), 347-354.

Henneman, E., Somjen, G., & Carpenter, D. O. (1965). Functional significance of cell size in spinal motoneurons. Journal of neurophysiology,28(3), 560-580.

Sisto, D. J., Jobe, F. W., Moynes, D. R., & Antonelli, D. J. (1987). An electromyographic analysis of the elbow in pitching. The American journal of sports medicine, 15(3), 260-263.

Sonne, M. W., & Keir, P. J. (2016). Major League Baseball pace-of-play rules and their influence on predicted muscle fatigue during simulated baseball games. Journal of sports sciences, 1-9.

Sonne, M. W., & Potvin, J. R. (2016). A modified version of the three-compartment model to predict fatigue during submaximal tasks with complex force-time histories. Ergonomics, 59(1), 85-98.

Can PitchFX data be used to identify muscle fatigue in starting pitchers?

Acknowledgements – Thanks to Daanish Mulla for his help with data processing, and Patsy Sonne for her helping hand.


Muscle fatigue is a process that results in decreased force generating capacity, and impaired performance [1]. Reduced force due to muscle fatigue may result in less stable joints, which can increase the risk of injury [2].  Furthermore, muscle fatigue is known to reduce joint proprioception  [3]–[6], which can result in further compromised joint stability and increased injury risk. Baseball pitchers have been shown to alter their kinematics (joint angles) when fatigued, which may strain different tissues when compared to pitching without fatigue [7].  Repetitive strain on these tissues can result in injury, and in baseball pitchers, injuries such as Ulnar Collateral Ligament tear.

Fatigue has been named the number one cause of injuries in baseball pitchers, leading to a 500% increase in injury likelihood [8]. Handgrip strength has decreased by up to 5% after simulated baseball games [9], and pitch velocity decreases over the the course of a game [10]. Pitcher kinematics also change with fatigue, with the elbow dropping lower, and the stride getting shorter.

The PITCHf/x system was created by Sportvision, and installed in every MLB stadium since 2006. The system allows for tracking of pitch movement, velocity and release point for every pitch thrown at the major league level. Two cameras are mounted in each stadium, and are used to track each pitch and display data during live broadcasts and websites. With the use of free software, like the programming package R, and database software MySQL, anyone can download gigabytes of data within hours, allowing for detailed analyses of pitching and hitting. With this detailed data, it would theoretically be possible to track changes associated with muscle fatigue. The purpose of this study was to examine how pitch velocity and release point changed in starting pitchers during the 2015 season.


Data Acquisition

I queried the pitchFX data from the 2015 season, grouping pitches by pitch type, pitcher, and inning. A pitch had to be thrown 20 times in an inning to be included for further analysis. The pitchers included in this analysis were those who pitched a minimum of 100 innings as a starting pitcher. The main focus of this analysis was to examine peak velocity changes, so only fastball type pitches were included in the analysis (four-seam, two-seam, split finger, sinking, cut, and general fastball).

I calculated the average velocity for each pitcher during their first inning of pitching. I then calculated the minimum average velocity for these pitches during either the 5th, or 6th inning – which ever value was the lowest.

For release point, I calculated the resultant distance of the release point (at z0, x0), from 0.0 (Figure 1). I also examined the change in vertical release point (z0) between the first inning, and the minimum of the 5th and 6th innings. Using the horizontal release point, and the vertical release point, I also calculated the absolute release angle (normalizing for left-handed and right-handed pitchers).

Demonstration of how calculations were made for the vertical release point, resultant release distance, and release angle.

Figure 1. Demonstration of how calculations were made for the vertical release point, resultant release distance, and release angle.


For this analysis, the independent variable was inning (first inning, minimum of 5th/6th inning).

To examine the effect of inning, I performed a dependent samples t-test on variables of peak velocity, resultant release point, vertical release point, and release angle, with p < 0.05. I also calculated Cohen’s D to determine the effect size of the inning.


Peak velocity significantly decreased between the first inning (91.19 ± 2.91 mph) and 5th/6th inning of the start (90.61 ± 3.01 mph, p< 0.05; d=0.20) (Figure 2). Vertical release point significantly decreased from 5.9 ± 0.35 feet to 5.84 ± 0.36 feet (p < 0.05, d=0.17)(Figure 3a). Resultant release point also decreased from 6.15 ± 0.35 feet to 6.09 ± 0.35 feet (p < 0.05, d=0.18) (Figure 3b). All of these changes were statistically significant, however, represented small effect sizes.

Release angle was significantly different between the first and final inning, moving from 74.9 ± 6.17 degrees to 75.1 ± 6.31 degrees. This represents a release angle that is closer to the vertical plane, or, closer to the midline of the body. While this change was statistically significant, the effect size was negligible (d=-0.04) (figure 4).

Figure 2. Fastball velocity significantly decreased between the first inning (91.19 ± 2.91 mph) and the minimum between the 5th and 6th inning (90.61 ± 3.01 mph) (p < 0.05). This represented a small effect size, of 0.20.



Figure 3. Both vertical release point, and resultant release distance decreased between the first inning and the 6th inning, representing a possible change in pitcher kinematics. This represented a small effect size, of 0.18 and 0.17, respectively.

Figure 3. Both vertical release point, and resultant release distance decreased between the first inning and the 6th inning, representing a possible change in pitcher kinematics. This represented a small effect size, of 0.18 and 0.17, respectively.


figure 5

Figure 4. Release angle increased (representing a release point closer to the midline of the body) between the first and final inning, though the effect size for this relationship was negligible.


In line with previous research on baseball pitching and fatigue, fastball velocity decreased between the beginning and the end of the average game. A decrease in release point distance and height also indicates that kinematics have changed during the course of a baseball game.

The following examples are from pitchers in the top ten for fatigue related changes between innings. Andrew Heaney has a nearly 2mph decline between the 1st and the 6th inning (Figure 5a), and Ervin Santana has his resultant release point decrease by 2.21% (Figure 5b). In both cases, it could be expected that performance would be impaired by these fatigue related changes. Conversely, Jacob deGrom actually increases his release point by 0.58% (Figure 5d), and Max Scherzer increases fastball velocity by 0.38% between the first and 6th inning (figure 5c). In general, 70% of pitchers experience a decreased velocity between the first and final inning, 85% of pitchers have a decrease in their resultant release point, and 83% of pitchers have a decrease in their vertical release point.


Figure 4. Release angle increased (representing a release point closer to the midline of the body) between the first and final inning, though the effect size for this relationship was negligible.

The velocity change demonstrated in this analysis represents a decrease of only 0.5 mph from the first to the 6th inning. This represents approximately a 1% change in velocity. Previous research has shown up to a 5mph decrease in velocity, decreasing from 90 mph to 85 mph during spring training games [10]. This greater decrease in velocity may represent decreased conditioning from the pitchers at this time of the season. Crotin, et al., [11] found that fastball velocity increased during a season, as a result of conditioning and improved strength. These factors may wash out some of the differences that could be seen throughout the course of a game, when average velocities are calculated over the course of an entire season and by inning, like in this analysis.

The pitchers included in this analysis represent a highly elite subset of the population. Previous research that has examined fatigue in baseball pitchers has included pitchers in spring training [10], college [9], or even Japanese high school players [12]. The fatigue effects for the elite population may not be as severe, as elite athletes are able to moderate the detrimental effects of fatigue when performing their sport specific task [13].


Despite the easy access to PitchFX data, there are concerns with the accuracy and reliability of the system. For one, the release point displayed by the PitchFX system is at a distance of 50 feet from the plate. Typically, pitchers release the ball at 54-55 feet from the plate, so the true release point is not exactly known [14] Additionally, inter-stadium differences may also contribute to inaccurate PitchFX data – as cameras are not always in the exact same place in all stadiums.


Examining PitchFX data for fastball velocities and release points, averaged by inning for qualifying starters in the 2015 season, have produced results comparable to more controlled, lab based studies, on fatigue during pitching. However, limitations with the PitchFX system, and averaging data throughout the entire season can possibly remove some of the differences that could possible be seen as a pitcher fatigues. Additional research should be performed to examine in-game changes in velocity for both good, and bad starts, to see if fatigue effects are more prominent as a pitcher becomes less effective.


[1]       R. M. Enoka and J. Duchateau, “Muscle fatigue: what, why and how it influences muscle function.,” J. Physiol., vol. 586, no. 1, pp. 11–23, Jan. 2008.

[2]       G. S. Fleisig, J. R. Andrews, C. J. Dillman, and R. F. Escamilla, “Kinetics of baseball pitching with implications about injury mechanisms,” Am. J. Sports Med., vol. 23, no. 2, 1995.

[3]       L. A. Hiemstra, I. K. Lo, and P. J. Fowler, “Effect of fatigue on knee proprioception: implications for dynamic stabilization.,” J. Orthop. Sports Phys. Ther., vol. 31, no. 10, pp. 598–605, Oct. 2001.

[4]       F. Ribeiro, J. Mota, and J. Oliveira, “Effect of exercise-induced fatigue on position sense of the knee in the elderly,” Eur. J. Appl. Physiol., vol. 99, no. 4, pp. 379–385, 2007.

[5]       M. Sharpe and T. Miles, “Position sense at the elbow after fatiguing contractions,” Exp. Brain Res., vol. 94, no. 1, May 1993.

[6]       H. B. Skinner, M. P. Wyatt, J. A. Hodgdon, D. W. Conrad, and R. . Barrack, “Effect of fatigue on joint position sense of the knee,” J. Orthop. Res., vol. 4, no. 1, pp. 112 – 118, 1986.

[7]       R. F. Escamilla, S. W. Barrentine, G. S. Fleisig, N. Zheng, Y. Takada, D. Kingsley, and J. R. Andrews, “Pitching biomechanics as a pitcher approaches muscular fatigue during a simulated baseball game.,” Am. J. Sports Med., vol. 35, no. 1, pp. 23–33, Jan. 2007.

[8]       J. Lemire, “Preventing Athlete Injuries With Data-Driven Tech – Athletic Business,” Athletic Business, 2015. [Online]. Available: [Accessed: 21-Dec-2015].

[9]       M. J. Mullaney, “Upper and Lower Extremity Muscle Fatigue After a Baseball Pitching Performance,” Am. J. Sports Med., vol. 33, no. 1, pp. 108–113, Jan. 2005.

[10]     T. a Murray, T. D. Cook, S. L. Werner, T. F. Schlegel, and R. J. Hawkins, “The effects of extended play on professional baseball pitchers.,” Am. J. Sports Med., vol. 29, no. 2, pp. 137–42, 2001.

[11]     R. L. Crotin, S. Bhan, T. Karakolis, and D. K. Ramsey, “Fastball velocity trends in short-season minor league baseball.,” J. Strength Cond. Res., vol. 27, no. 8, pp. 2206–12, Aug. 2013.

[12]     L.-H. Wang, K.-C. Lo, I.-M. Jou, L.-C. Kuo, T.-W. Tai, and F.-C. Su, “The effects of forearm fatigue on baseball fastball pitching, with implications about elbow injury.,” J. Sports Sci., pp. 1–8, Oct. 2015.

[13]     M. Lyons, Y. Al-Nakeeb, and A. Nevill, “The impact of moderate and high intensity total body fatigue on passing accuracy in expert and novice basketball players.,” J. Sports Sci. Med., vol. 5, no. 2, pp. 215–27, Jan. 2006.

[14]     M. Fast, “The Internet cried a little when you wrote that on it – The Hardball Times,” The Hardball Times, 2010. [Online]. Available: [Accessed: 21-Dec-2015].


Newer posts »

© 2024 Mike Sonne

Theme by Anders NorenUp ↑