An Introduction to Fatigue Units: A New Method for Evaluating Workloads

Tom Verducci once wrote about how a 30% increase in innings pitched could lead to injury in young pitchers. Since he wrote that, many people have objectively determined that this is not the case (Carleton, 2013). Not all innings are created equally, and not all pitches put the same amount of stress on the human body.

As we have learned in many different ways that are not a lot of fun , both relief pitchers and starting pitchers can succumb to the effects of pitching (also read as, getting injured). This makes the Pitcher Abuse Point scale not appropriate for relief pitchers (see this article on Baseball Prospectus – (Jazayerli, 1998)). Other research has pointed to measures like innings pitched as being a poor determinant of workload in pitchers (Karakolis et al., 2016). Pitching on consecutive days, high velocities, and total pitches have been identified as risk factors for injury (Whiteside et al., 2016).

How do these risk factors come together to cause a pitcher to become injured? For one fatigue is identified as a major risk factor for Ulnar Collateral Ligament (UCL) injury in baseball pitchers.  Dr. Glenn Fleisig has stated that muscle fatigue could lead to joint laxity, and as a result, increase the amount of strain on the ligaments of the arm during throwing (Fleisig et al., 1995). Dr. Jeremy Bruce and Dr. James Andrews echoed these sentiments, stating fatigue of the flexor-pronator muscles of the forearm, would compromise joint stability and stress the UCL (Bruce & Andrews, 2014).

Using research from the field of biomechanics, exercise physiology, and sports medicine, I’ve tried to come up with a new workload metric.

Development of the Metric

Back during my grad school days, my friend and mentor Dr. Jim Potvin and I came up with a model that predicted muscle fatigue (Sonne & Potvin, 2016). This model outputs a value which represents the amount of force generating capacity that a muscle has lost. Relating this back to baseball – if a pitcher loses the ability to produce muscle force in their forearm muscles – those muscles can no longer contract and protect the UCL. If you’d like to get deeper into the topic of pronation and it’s protective effects, check out this article from the guys at Driveline Baseball (Buffi, 2015).

To put it simply, there are two ways that you can influence the amount of fatigue your muscles have. The first – you can increase or decrease your fatigue level by either increasing, or decreasing how active your muscle is. If you have your muscle on at 50% of its maximum for 5 seconds, compared to a contraction of the same duration at 30% of its maximum – the 50% contraction will be more fatiguing. The second way to change fatigue levels is the amount of rest you receive. If you have more time to rest, you will reduce your fatigue level. This is the principle that was expressed in the paper I wrote arguing against the use of pitch clocks in MLB from an injury prevention perspective (Sonne & Keir, 2016).

So, how do we get fatigue prediction into a metric that can help better understand workload in MLB and MiLB pitchers?

Step 1 – Predicting Fatigue

The first step was to develop a prediction of fatigue based on the pitching characteristics MLB pitchers. After a review of the relevant literature, I found a series of papers that looked at muscle demands during pitching. Using these time histories of muscle demands, I created inputs for my fatigue model, and produced predictions of how much muscle force one could expect a pitcher to lose during an inning. Here’s an example of what the predicted fatigue would have looked like during Marco Estrada’s 2015 ALCS Start against the Kansas City Royals (Sonne, 2016). 

Figure 1. Predicting Muscle Fatigue from PITCHf/x data

From the more advanced model, I distilled the findings down into regression equations to predict what the estimated maximum forearm muscle fatigue would be, averaged across 8 different muscles, using the inputs of:

  • Fastballs thrown per inning
  • Other pitches thrown per inning
  • Innings pitched in a game
  • Pace between pitches (from FanGraphs).

This left me with the following equation for predicted average fatigue (aFatigue):

The relationship between the predicted fatigue fatigue in this regression equation, and the maximum fatigue predicted by the Sonne & Potvin model was an r2 of 0.95. Keep in mind – this is from already modelled data, so the amount of variability is low – this is just an easier way to access the fatigue level for this type of work (pitching). 

Step 2 – Combining Games

Starting with the Fatigue Units (FUs) I described in part 1, I took a shot at modelling fatigue in every game from the 2008 to 2016 MLB seasons. I downloaded the PitchFX database, and extracted the number of pitches, batters faced, innings pitched, and total time for each inning, for every game. I broke this down by pitcher, game, and inning, and was left with an FU for each inning during each game. To get a cumulative FU for each game, I just added these inning FUs up for each pitcher.

Velocity has also been indicated as a risk factor for injury, and the source of greater UCL stress (Whiteside et al., (2016), Sonne (2016)). To add in the effect of high velocity, a scaling factor was created using the average velocity of 92.16 mph. The peak velocity during each appearance was scaled to this, creating a factor that ranged between 0.614, and 1.124. This value was multiplied by the FU in each inning to create a velocity scaled FU.

Whiteside et al., (2016) showed reduced time between appearances was a significant predictor of UCL injury. Furthermore, other research has shown heart rate variability in pitchers was reduced in the day day after an appearance – which returned to baseline after 4 days (Cornell et al., 2017). To include this in the cumulative FU, if a pitcher appeared in 2 games, back to back, they had a multiplier of 5. If their last appearance was between 2 and 4 days ago, they had a multiplier of 2. If their last appearance was 5 days or greater, the multiplier was 1. The velocity scaled FU was then multiplied by the rest multiplier, giving a cumulative FU for each game. These game cumulative FUs were then all added together, giving a season FU for each pitcher.

Step 3 – Filling In the Blanks

I didn’t have access to the PITCHf/x data from the minor leagues. To estimate workloads (pFatigueUnits), I created a regression equation with the dependent variable of Fatigue Units from the 2016 season, and various outcome metrics as the independent variables (Innings Pitched, Games, Games Started, Games Relieved, Walks/inning, Strikeouts/inning, WHIP, and Batters Faced/Inning). This resulted in a regression equation that looked like:

This prediction of fatigue units correlated well with the calculated fatigue units, with an r2 0.98, and a standard error of 1.2 FUs. Pulling in all of the data from all levels of the minor leagues, and grouping it by pitcher and year, I was able to generate an estimated fatigue unit for each player. If a pitcher played at multiple levels within a season, the estimated fatigue units could be used to get a more accurate idea of their overall workload.

Here’s an idea of the top 20 workload seasons according to the Fatigue Unit Metric.

Fatigue Units by Season
Rank Season – Name Fatigue Units Innings Pitched Games
1 2010 – Jonny Venters 27.12 89.2 81
2 2011 – Jonny Venters 26.54 88.0 85
3 2008 – Carlos Marmol 26.29 87.1 82
4 2008 – Jeff Bennett 25.79 101.1 76
5 2009 – Justin Verlander 25.58 240.0 35
6 2010 – Carlos Marmol 25.29 77.2 77
7 2013 – Trevor Rosenthal 25.24 75.1 74
8 2008 – Grant Balfour 24.96 81.3 66
9 2008 – Chad Durbin 24.91 87.2 71
10 2010 – Roy Halladay 24.87 250.2 33
11 2015 – Travis Wood 24.48 100.2 54
12 2012 – Justin Verlander 24.44 238.1 33
13 2010 – Matt Belisle 24.36 92.0 76
14 2015 – Dellin Betances 24.13 84.0 74
15 2008 – Mark Buehrle 24.08 218.2 34
16 2010 – Brian Wilson 24.04 74.2 70
17 2012 – Kelvin Herrera 23.80 84.1 76
18 2011 – Craig Kimbrel 23.72 77.0 79
19 2014 – Yordano Ventura 23.63 183.0 31
20 2009 – Ryan Madson 23.59 77.1 79

Step 4 – Evaluating this metric as it pertains to Ulnar Collateral Ligament Injuries

At last! We have made it to the part about whether this model has any implications for injury identification. To do this, I calculated the percentiles for fatigue units – so, a 75th %ile fatigue unit season means that this season has a higher workload than 75% of all other seasons. I did the same for innings pitched. In both situations, I binned all seasons in 10% ranges.

For each player season, I examined if a pitcher had Tommy John Surgery (TJS) that season, the next season, or the second season after that. I gave this type of resolution to account for instances where a pitcher would attempt to rehab for a season, then have surgery the following season; or, fought through a year of injury before finally having TJS. Thanks to the fact that Jon Roegele is a brilliant human being, and included FanGraphs ID’s in his Tommy John Surgery list, this was pretty easy to do. To give some context on the usefulness of the Fatigue Units metric, I compared the injury rates against innings pitched.  

These are the results (Figure 2):

Figure 2. Fatigue Units and Innings Pitched (by %ile), compared to rate of Tommy John Surgery incidence in subsequent two seasons.

When using innings pitched as the workload metric, those who pitched in the 90th %ile of innings per season (more than average of 184 innings), these pitchers were 1.7 times more likely to have Tommy John surgery in the next two seasons than a pitcher who threw less than the median number of innings in a season (an average of 72 innings). Those in the 90th %ile of innings pitched had Tommy John Surgery 5.1% of the time, in either the next season, or the season after. Comparatively, pitchers who were in the 90th %ile of Fatigue Units were 2.7 times more likely to have Tommy John Surgery in one of the next two seasons. Approximately 6.5% of the pitcher seasons that produced a 90th %ile workload resulted in Tommy John Surgery in one of the next two seasons.


Looking at the list of pitchers from Step 3, you can see there are some names that really jump out at you. Johnny Venters is attempting a comeback with the Rays this season, but his ascension to elite relief pitching was wiped out as quickly as it started due to an elbow injury. Carlos Marmol broke down, and is no longer an elite pitcher. Jeff Bennett punched the F out of a wall and got suspended for it. Actually, he tore his labrum in 2010 – but this study was just looking at the UCL injuries.

Given the research reported by Whiteside et al., (2016) (reduced time between appearances, throwing with harder velocities), and inferred from the Motus data collected at Driveline (O’Connell et al., 2016)  – I do not believe that Bullpen work should be viewed as a “break” from the starting rotation. There are unique demands associated with this type of pitching, and the workloads that the pitchers are subjected to when pitching in relief are not accurately captured by traditional metrics such as pitches thrown, or innings pitched.

Is there anyone to worry about in the 2017 season?


Fatigue Units by Season
Rank Name 2015 2016 Total
1 Travis Wood 24.48 20.13 44.61
2 Dellin Betances 24.13 20.15 44.28
3 Chris Sale 21.92 21.51 43.43
4 Max Scherzer 20.38 20.16 40.54
5 Chris Archer 21.18 18.93 40.11
6 Johnny Cueto 21.85 17.92 39.77
7 Jeurys Familia 21.04 17.97 39.02
8 Yordano Ventura 19.49 19.24 38.73
9 Jake Arrieta 21.70 16.55 38.25
10 Randall Delgado 19.26 18.71 37.98
11 Roberto Osuna 18.00 19.82 37.82
12 Cole Hamels 19.93 17.57 37.50
13 Brad Brach 18.14 19.15 37.29
14 Zach Duke 17.12 19.84 36.97
15 Addison Reed 15.54 21.17 36.72
16 David Price 19.45 17.22 36.67
17 Erasmo Ramirez 17.74 18.83 36.57
18 Hector Santiago 19.95 16.60 36.55
19 Kyle Barraclough 15.99 20.50 36.48
20 Madison Bumgarner 18.35 18.03 36.38

Part of the reason that pitchers pitch a lot, is because they are very good (or because their manager loves them). If you look at the list of pitchers who have accumulated the highest workloads in the past 2 seasons, you can see some really, really good pitchers. Remember, the fatigue units metric associated with a better idea of UCL injury than Innings pitched, but in the best situation, the most extreme workloads were only associated with less than 6% of UCL injuries in the following seasons. That being said, there are concerns with young pitchers throwing lots of innings, particularly in high leverage situations, on back to back days. For example, Roberto Osuna has the 11th highest workload in the past two seasons, during his age 20, and 21 seasons. No one else on this top 20 list is under 25. Kyle Barraclough has also put up a significant 28% increase in his workload between 2015, and 2016. Addison Reed and Hector Neris have also had significant jumps in their workloads between 2015 and also had a significant jump in his workload. If you’re interested, take a look through the top 250 of 2015 and 2016, here.


Sometimes my work on here gets a bit of heat for not being “Rotographs” enough – but I hope this gives you a better idea as to understanding the risk when drafting a fantasy pitcher – and that innings pitched may not be the number one thing to look at when you’re establishing risk on a relief pitcher. The plan this year is to monitor workload for pitchers using fatigue units, so stay tuned for more!


Bruce, J. R., & Andrews, J. R. (2014). Ulnar collateral ligament injuries in the throwing athlete. Journal of the American Academy of Orthopaedic Surgeons, 22(5), 315-325.

Buffi, J. (2015). Can Forearm Pronation Prevent Tommy John Surgery? Driveline baseball blog, posted June 18, 2015.

Carleton, R.A., (2013). Baseball Therapy Fact or Fiction: The Verducci Effect. Baseball Prospectus, posted on January 28th, 2013.


Cornell, D. J., Paxson, J. L., Caplinger, R. A., Seligman, J. R., Davis, N. A., & Ebersole, K. T. (2017). Resting Heart Rate Variability Among Professional Baseball Starting Pitchers. The Journal of Strength & Conditioning Research, 31(3), 575-581.


Fleisig, G. S., Andrews, J. R., Dillman, C. J., & Escamilla, R. F. (1995). Kinetics of baseball pitching with implications about injury mechanisms. The American journal of sports medicine, 23(2), 233-239.

Karakolis, T., Bhan, S., & Crotin, R. L. (2015). Injuries to young professional baseball pitchers cannot be prevented solely by restricting number of innings pitched. J Sports Med Phys Fitness.

Jazayeril, R. (1998). Pitcher Abuse Points – A New Way to Measure Pitcher Abuse. Baseball Prospectus, published June 19, 1998.

O’Connell, M., Boddy, K. (2016). Can You Reduce Pitching Elbow Stress Using a Sleeve? Driveline Baseball Blog, posted July 20, 2016.

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.


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. (2016). Pitching Velocity and its Effect on UCLE stress using the Motus Sleeve. Driveline Baseball Blog, posted July 27, 2016.


Whiteside, D., Martini, D. N., Lepley, A. S., Zernicke, R. F., & Goulet, G. C. (2016). Predictors of Ulnar Collateral Ligament Reconstruction in Major League Baseball Pitchers. The American journal of sports medicine, 0363546516643812.

Ergonomist (CCPE) and Injury Prevention researcher. I like science and baseball - the order depends on the day. Twitter: @DrMikeSonne

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5 years ago

Excellent research!

Thank you for sharing your findings and I look forward to seeing how our understanding matures over the season through this lens.