Science and Baseball

Month: November 2016

Playoff Workloads in 2016

A lot was made of the heavy workloads that elite relievers performed in the 2016 post season. Aroldis Chapman, Andrew Miller, and Roberto Osuna had extended appearances of 2+ innings, when they had only thrown an inning at a time in the regular season. With everything on the line, teams were willing to push these elite arms to their limits. For the most part (save for one scary moment in the AL Wild Card game with Osuna), they all emerged unscathed, and probably went a long way to raising reliever salaries for future seasons.

By now, you have probably learned that my Fatigue Unit metric heavily favours relief pitchers. A study by Whiteside and colleagues (2016) 1, and my analysis of Driveline’s publically available data 2,3, have indicated that throwing on consecutive days, and throwing harder, are risk factors for Ulnar Collateral Ligament reconstruction. Relief pitchers are throwing more and more innings, and their rate of injury appears to be much greater than those of starting pitchers 4. These are the hard facts of relief pitching – see examples from Aaron Sanchez (94-95 mph as a starter, and 97-100 as a reliever).

Relief Innings pitched, and number of relief pitchers used through the 1965 to 2015 season (Keri & Neil, 2016). Relief pitchers are throwing more and more innings - and pitching in the bullpen may not be saving arms.

Relief Innings pitched, and number of relief pitchers used through the 1965 to 2015 season (Keri & Neil, 2014). Relief pitchers are throwing more and more innings – and pitching in the bullpen may not be saving arms.

Using Fatigue Units5, I wanted to look at the top workloads in the past post season, and furthermore, explore how those workloads compared to regular season workloads.


I was able to analyze the 2016 MLB regular season thanks to Michael Copeland (@jelloslinger). He pulled in pitch counts, by inning and game, for every game since the start of the 2015 season. For simplicity’s sake, I looked at the peak velocity and the average pace for all pitchers, downloaded from the Fangraphs website. Those were the data required to calculate FU’s for each pitcher. I then broke these data down by regular season games and post-season games.

Once cumulative fatigue units were calculated for each pitcher, I also calculated the average workload per game. The rest of the analysis was performed on pitchers who only pitched in both the regular season and the post season. I compared the average workload between regular season and post season performances. For an example, I also looked at how workloads changed throughout the season, and I’m going to present the data on how workloads changed throughout course of the season for a few select pitchers.

Results and Conclusions

Not surprisingly, the highest workload of the 2016 playoff season belonged to Andrew Miller and Corey Kluber. For Andrew Miller, the biggest change in his workload between the regular season and the post season, was his multi-inning appearances. In the playoffs, he averaged 0.8 FU’s per game, and in the regular season, he average 0.4 FU’s per game. His workload per game was doubled in the playoffs when compared to his regular season numbers. Andrew Miller’s playoff workload represented 25.2% of his entire regular season workload – during 10 games (compared to 70 games in the regular season).

As for Corey Kluber, his high workload was driven by short rest. Kluber pitched game 1, 4 and 7 of the World Series in 2016. In the regular season, Kluber pitched 100% of his starts on regular rest (a 5 day separation, minimum, between starts). During the playoffs, 50% of his appearances came on less than 5 days of rest. Kluber averaged 1.23 FU’s per appearance in the 2016 playoffs, compared to 0.74 FU’s per appearance in the regular season.

Going to game 7 of the  World Series, the Cubs had the greatest sum of fatigue units of all 2016 playoff teams. However, when looking at sum of fatigue units for every playoff teams, the Cubs accumulated 147% more fatigue units than the second highest team (the Toronto Blue Jays). When looking further into these findings – what drove these really high FU accumulations in the Cubs and Blue Jays, were a very high number of back to back relief appearances for both teams. The Cubs had 35% of all of their pitching appearances in the post season occur on back to back nights, a total of 26 pitcher appearances in the 2016 post season. Comparatively, Cleveland only had 11% of all of their pitching appearances occur on back to back nights.

I’m not one for hot takes, but I feel that I have to say something here. If workload has any sort of relationship to injury, Terry Francona’s management of his pitching staff, from a workload management perspective, is one of the most impressive baseball strategy events to occur in my recent memory. While the Cubs emerged the eventual World Series Champions, Joe Maddon had to repeatedly rely on the same pitchers (primarily, Aroldis Chapman) in high leverage situations, which lead to high usage during back to back games. If extreme workloads to lead to injury, the work done by Francona in the playoffs does appear to be a great template for managers in the future. If we’re being realistic though – flags fly forever, and when they haven’t flown in 108 years, it’s hard to say that there were any errors in workload management.

I still have to look further into the utility of FU’s as an injury prediction model. Currently, I believe it is a metric that more accurately represents physiological demands on the body, and more importantly, the musculature responsible for predicting the UCL.


Whiteside D, Martini D, Lepley A, Zernicke R, Goulet G. Predictors of Ulnar Collateral Ligament Reconstruction in Major League Baseball Pitchers. Am J Sports Med. 2016;44(9):2202-2209. [PubMed]
Sonne M. Pitch Velocity and UCL Stress using the Motus Sleeve: Further interpretation from Driveline data – Mike Sonne. Science and Baseball. Accessed November 30, 2016.
O’Connell M, Boddy K. Elbow Stress, Motus Sleeve, and Velocity. Home – Driveline Baseball. Published October 28, 2016. Accessed November 30, 2016.
Keri J, Paine N. How Bullpens Took Over Modern Baseball. FiveThirtyEight. Published August 15, 2014. Accessed November 30, 2016.
Sonne M. Giving a big FU to workload metrics in pitchers: Part 2 – Cumulative FUs – Mike Sonne. Science and Baseball. Published September 1, 2016. Accessed November 30, 2016.

Pitch Velocity and UCL Stress using the Motus Sleeve: Further interpretation from Driveline data

As previously mentioned, there really isn’t anything better than getting your hands on new data. That new data smell, the excitement of telling someone that the singular of data is datum. I was really excited to see a follow up study (O’Connell, Hart & Boddy, 2016) to the Bauerfeind study that examined the influence of pitch velocity on arm stress (O’Connell & Boddy, 2016). After reading the article, there were some really surprising findings that I wanted to look into further. More specifically – the claim this study replicated the findings of Post et al (2015), and found a non-significant relationship between elbow valgus torque, and ball velocity.

The study can be found here:

But, here are some of the key findings.

  • A “very small” relationship between the stress metric, and pitch velocity of r2 = 0.21
  • “This contradicts a commonly believed hypothesis that when comparing pitchers across a population the ones who throw the hardest also experience the greatest stress. We are only looking at elbow stress, this may not hold up when looking at both elbow and shoulder stress. But this is a very interesting finding nonetheless!”

First of all, I wanted to look at simply the interpretation of these data. The r2 statistic infers how much of variable A can we infer from variable B. For example, if our r2 value is 0.5, that represents that variable B accounts for 50% of the variation in variable A. When studying human movement, Vincent and Weir (2012) proposed threshold values of r2 = 0.25 to 0.49 as low, 0.49 to 0.64 as moderate, and greater than 0.81 as strong. However, they included this caveat:

“Values lower than (0.25), if they are statistically significant, can be useful for identifying nonchance relationships among variables, but they are probably not large enough to be useful in predicting individual scores. However, in conjunction with more than one predictor variable (multiple regression)… even individually modest predictors may be useful”

– Vincent & Weir, 2012, page 117.

The values reported in their text are r values, but I have adjusted them to be r2 values.

So, let’s look at these results – a “very small” relationship, and “similar to the findings of Post et al., 2015”. Post et al (2015) found

“very small r2 values, indicated that very little of the variance in joint kinetics can be explained by ball velocity… the correlations between ball velocity and both elbow-valgus torque and shoulder external-rotation torque were not significant”

The values reported by Post et al (2015) were an r2 of 0.04, and p=0.053, or, 4% of elbow valgus torque could be explained by ball velocity, and this relationship was not statistically significant. This is where I have some concerns with the interpretations of the newest study from O’Connell and Boddy (2016). Their study reveals a statistically significant relationship between ball velocity and arm stress, in the low range of correlational strength (r2 = 0.21).  Interpreting these results in their current form, these findings indicate that 21% of arm stress can be predicted using ball velocity alone. So, ignoring any differences in mechanics between pitchers, fatigued state, or pitcher body size, we already have a model that predicts 21% of our dependent variable. As someone who has spent a good amount of time wrestling with data, attempting to prove hypotheses about muscle fatigue, I would typically kill for a relationship with this strength! The findings of the O’Connell & Boddy study do not replicate those of Post et al., 2015 – they illustrate a link between arm stress and pitch velocity – and that is without moving on to some methodological concerns.

The beauty of blogging, and posting open source data to try and further science, is that you live in a state of constant, dynamic, peer review. In many ways, this is vastly superior to the traditional publication model, where studies are reviewed by academics, then go to sit on bookshelves and are never looked at again. When open data is published, it gives others a chance to chime in on the results.

Looking at the data that went in to calculating the r2 value of 0.21 between stress and velocity, a couple of things emerge. First of all, not all pitchers have the same contribution to the means. Two pitchers only threw 6 pitches, while one threw 19 pitches. If pitch velocity only indicates 21% of the variance in arm stress, there are clearly other factors at play. If we have an unequal number of pitches between our participants, we’re leaving room for error, by having someone with greater stress contributions from other variables swaying our correlation, one way, or the other. To try and accommodate for this, I removed the two pitchers from the analysis who only threw 6 pitches. I then took the average velocity, and stress, from the top 9 velocity throws from all other pitchers, and put them into the correlation with an n=15. The correlation between velocity and stress now goes up to r2 = 0.32, or 32% of the variance in arm stress is accounted for by ball speed. Including all of the pitches individually, and only using the top 9 pitches from each pitcher (an n=97), we end up with a correlation of r2 = 0.37 between velocity and arm stress.

When your model can account for 37% of the variance between one variable and another, you are definitely on to something. This is statistically significant, and when visualized (Figure 1), it becomes quite clear that a relationship exists. In fact, this number appears to be nearly an exact replica of another study, where Hurd et al., (2012), found a relationship of r2 = 0.37 between pitch velocity and elbow adduction moment.


Figure 1 Correlation between Arm Stress and Ball Velocity, for top 9 velocity throws (n = 15 pitchers, 97 pitches)

So, what about the other variables that the Motus sleeve spits out? I can’t tell you with 100% certainty what arm slot, or shoulder rotation means from these data, but I included ball speed, arm speed, arm slot, and shoulder rotation, in a multiple linear regression model to predict Stress. Once again, I used the top 9 velocity pitches from 15 pitchers to do this analysis.

To put all of the variables on the same scale, I converted them all into z-scores – this will give us standardized coefficients that we can compare against one another in our regression output.

In summary, this model produced an r2 value of 0.55, with Arm Slot and Shoulder Rotation not being the weakest predictors of arm stress, and arm speed having a negative relationship with arm stress (Figure 2).


Figure 2. Predicted and actual UCL stress (z scores), from input variables of ball velocity, arm slot, arm speed, and shoulder rotation.

Regression Statistics
Multiple R 0.74
R Square 0.55
Adjusted R Square 0.53
Standard Error 0.67
Observations 97
df SS MS F Sig. F
Regression 4 49.78 12.44 28.06 0.00
Residual 92 40.80 0.44
Total 96 90.58
Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0%
Intercept 0.01 0.07 0.17 0.86 -0.13 0.15 -0.13 0.15
MPHz 0.83 0.09 9.77 0.00 0.66 1.00 0.66 1.00
ArmSpeedz -0.47 0.08 -5.90 0.00 -0.62 -0.31 -0.62 -0.31
ArmSlotz 0.16 0.08 1.97 0.05 0.00 0.32 0.00 0.32
ShoulderRotationz 0.11 0.05 2.10 0.04 0.01 0.22 0.01 0.22

It is quite clear that there are other variables not being measured that will help produce a better model of arm stress, but from the main predictor of arm stress right now remains ball velocity. These data collected using the Motus Sleeve, on one of the more advanced populations of pitchers that have been researched, echoes many of the findings that Hurd et al., (2012) produced in a lab setting. It is important to understand how statistics are interpreted, and what assumptions go in to calculating results.

This study goes deeper into understanding the stress on the arm during pitching (as this is tracked from actual bullpen sessions, and not flat ground throws like in the Bauerfeind study). Other studies that have examined the risk of UCL injury in youth pitchers, have identified fatigue, stature, and cumulative pitch effects as risk factors for injury (Chalmers et al., 2015).


In summary, pitch velocity shows a significant relationship with arm stress, using the Motus Sleeve. If you throw harder, chances are, you will have higher levels of stress on your UCL. It is important to properly condition and be strong, so you can withstand these stresses. There are many other factors that go in to determining just how much stress is on the UCL, but these must be further studied by hard working groups like Driveline, and researchers in other facilities.

Here are the data I used for the analyses above.


Chalmers, P. N., Sgroi, T., Riff, A. J., Lesniak, M., Sayegh, E. T., Verma, N. N., … & Romeo, A. A. (2015). Correlates with history of injury in youth and adolescent pitchers. Arthroscopy: The Journal of Arthroscopic & Related Surgery31(7), 1349-1357.

Hurd, W. J., Jazayeri, R., Mohr, K., Limpisvasti, O., ElAttrache, N. S., & Kaufman, K. R. (2012). Pitch velocity is a predictor of medial elbow distraction forces in the uninjured high school–aged baseball pitcher. Sports Health: A Multidisciplinary Approach4(5), 415-418.

O’Connell, M., Hart, S., & Boddy, K. (2016). Elbow Stress, Motus Sleeve, and Velocity. Retrieved from, November 4, 2016.

O’Connell, M., & Boddy, K. (2016). Can You Reduce Pitching Elbow Stress Using a Sleeve? Retrieved from, November 4, 2016.

Post, E. G., Laudner, K. G., McLoda, T. A., Wong, R., & Meister, K. (2015). Correlation of shoulder and elbow kinetics with ball velocity in collegiate baseball pitchers. Journal of athletic training50(6), 629-633.

Sonne, M.W. (2016). UCL Stress and Velocity Increases. Retrieved from, on November 4, 2016.


Vincent, W., & Weir, J. (1999). Statistics in kinesiology. Human Kinetics. Champagne, Illinois.

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