I’ve done a bunch of work modelling fatigue in pitchers, including the study used to suggest Pitch Clocks would lead to increased fatigue ¹ , how pitches per inning influences fatigue levels ² , and a new workload metric based on fatigue ³ .  For a lot of these simulations, I used average pitch counts and paces from FanGraphs. This provides an overall picture of the estimated fatigue in a pitcher, but doesn’t really account for the individual variability associated with a game. I was originally trying to get a bigger picture idea of how fatigue accumulated during pitching – so this was appropriate. However, I missed out on some pretty cool looking graphs – which depending on who you talk to, is the entire point of science.

Last week, I tweeted out a few graphs that looked at predicted forearm fatigue in pitchers from games during the 2014, and 2015 season. Here was the first one:

Playing around with data visualization – Marco Estrada’s predicted forearm muscle fatigue during his game 5 gem from the 2015 ALCS. pic.twitter.com/fWqH0JaqWm

— Mike Sonne (@DrMikeSonne) December 2, 2016

In game 5 of the ALCS in 2015, Marco Estrada went 7 and 2/3 innings, staving off elimination and sending the series back to Kansas City. Estrada started out fast, and never gave up a run until the 7th inning. It was a sign of things to come – absolute clutch pitching performances that buoyed the Blue Jays pitching staff in the 2016 season. Here’s how I was able to get these simulations.

Methods

The first step in this method was to get the pitch types, sequence, and time of each pitch during an outing. From the MLB’s gameday data, I was able to pull this sequence out by querying the database by pitcher and game. Here’s the MySQL Query I used for that purpose:

select pitches.sv_id, atbats.inning, atbats.outs, pitches.pitch_type, atbats.des, atbats.pitcher from atbats, pitches, games where pitches.ab_id = atbats.ab_id and atbats.game_id = games.game_id and games.game_id = ‘23910’ and atbats.pitcher = 462136 order by atbats.inning, atbats.outs ASC

This produced a result that looked like this:

Figure 1. Sample output from the MySQL query posted in the snippet above.

Every pitch, organized by inning and sequence, for an individual pitcher in an individual game. That value on the left – the sv_id from the gameday atbats table, contained the date (YYMMDD_HHMMSS). Everything I needed to calculate the amount of time between each pitch.

From the paper on pitch clocks and fatigue, I had created a time history of muscle demands for a series of forearm muscles. These were defined as either fastball type pitches, or breaking type pitches. In the graphs, figure A are the demands for fastballs, and figure B are the demands of curve balls / breaking pitches. These time histories are from a series of studies, summarized in the pitch clock papers.

So, back to the Gameday database. I exported the demands from the query into Matlab. I coded each pitch as being either a fastball or a breaking ball, then attached the appropriate amount of rest after each pitch. Here’s an example from Marco Estrada’s ALCS game:

Figure 3. Pitch selection and rest time from Estrada’s game 5 of the 2015 ALCS. All pitches coded as a 1 were fastballs. All pitches coded as 2 were breaking pitches. These were used to simulate the time histories of demands for Estrada, and then determine the predicted fatigue level. 

Figure 4. Muscle demands by pitch  during a 12 pitch first inning. The first pitch of the game lead to a ground ball out. The next 7 pitches resulted in a strike out, followed by a 4 pitch strike out. You can see the larger gaps between pitches as being reflective the time between batters. 

The largest numbers in this time history represented the time between innings. What I have learned from this is, is just how fatiguing it can be for a pitcher to have a long inning, followed by a short half inning where his team goes three up three down.

At this point, I had everything I needed to predict fatigue in a pitcher. Using the EMG demands from figure 4, the three compartment fatigue model was able to generate an example of how much muscle force would be lost at a given time based on the previous history of muscle demands. For Estrada, his peak fatigue came during the 5th and 7th innings of the game. During these innings, he threw 14 and 17 pitches – the highest per inning in the game. In the 5th inning, he threw more fastballs than breaking pitches, which resulted in higher fatigue levels.

Interestingly. innings where pitchers throw more fastballs have higher fatigue levels. Greater homogeneity in pitch selection has been identified as a risk factor for UCL reconstruction by Whiteside and colleagues (2016) ⁴  have higher fatigue levels occur when pitchers throw more fastballs.

Conclusions

This methodology could now allow for examination of fatigue during starts where a pitcher was hurt, or from a series of starts where a pitcher became hurt. If at the start of the season, a pitcher had his EMG activation levels recorded during a bullpen session, these accurate demands could be substituted into the model for a more accurate fatigue prediction. For now – this is a fun new way to look at a pitching performance.

If you have any requests for simulations, let me know!

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:

https://www.drivelinebaseball.com/elbow-stress-motus-sleeve-velocity/

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.

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).

Conclusion

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.

References

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 Surgery, 31(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 Approach, 4(5), 415-418.

O’Connell, M., Hart, S., & Boddy, K. (2016). Elbow Stress, Motus Sleeve, and Velocity. Retrieved from https://www.drivelinebaseball.com/elbow-stress-motus-sleeve-velocity/, November 4, 2016.

O’Connell, M., & Boddy, K. (2016). Can You Reduce Pitching Elbow Stress Using a Sleeve? Retrieved from https://www.drivelinebaseball.com/can-reduce-pitching-elbow-stress-using-sleeve/, 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 training, 50(6), 629-633.

Sonne, M.W. (2016). UCL Stress and Velocity Increases. Retrieved from http://www.mikesonne.ca/baseball/ucl-stress-and-velocity-increases/, on November 4, 2016.

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

Well, now that we know what Brandon Morrow’s stuff looked like with the Jays in 2010, let’s move on to understanding pitcher workloads since 2007.

First – a foray back into my thought process for the days of rest penalty in the metric. If you look back to the second article on Cumulative FU’s, I proposed that for consecutive day appearances, the FU’s be multiplied by 5. For 2 to 4 days of rest, the FU’s were multiplied by 2. For the standard, every 5th day – there was no multiplier for the FUs.

When I looked at the predicted FU’s for all pitchers (and as you’ll see shortly), the high use relievers – 80-100 innings in a season – had the highest workloads – significantly higher workloads than starters for the most part. I thought, I may have to make an adjustment to the metric – but I wanted to look at starter vs. reliever injury rates first.

I downloaded Jon Roegele’s Tommy John Surgery (TJS) list (@MLBPlayerAnalys), and then classified pitchers as relievers (if 80% of more of their innings came from relief innings), or starters. I compared numbers from the 2007 to 2016 seasons. Only pitchers who pitched 10 innings in a season were included in the analysis.

I looked at the sum of innings pitched and the number of TJS that occurred for all pitchers, and came up with a ratio of innings per TJS, for both starters, and relievers.

There were a total of 125092 innings pitched by Relievers during this time period, and 290401.1 innings pitched by starters. During that time, 151 relief pitchers required TJS, and 141 starters required surgery. This worked out to a ratio of 848.4 innings per TJS for Relievers, and 2059.6 innings per TJS. These data should likely be vetted a bit more carefully before they’re viewed as gospel – but this is a scary number. Aren’t reducing innings and pitches during the season supposed to protect relief pitchers’ arms?

I have argued that pitchers often throw harder when they move to the bullpen, and that this extra velocity places more stress on the UCL. In that same time period (2007, to 2016), relief pitchers threw their average fastball at a velocity of 91.5 +/- 3.35 mph, and starters threw their fastball at an average speed of 90.7 +/- 2.6 mph. Maybe, just maybe – those back to back to back appearances that relievers can make are worse for their bodies than the 6 innings pitched every 5 days?

Anyway – let’s move on to the workload metrics since 2007!

Starters

Team Workloads

The 2011 Rays take the cake for total workload for starting pitchers. Lead by David Price and Big Game James Shields, the Rays starters were not only good – they worked hard in the 2011 season. Overall, the highest average workload belonged to the tigers – particularly in 2014 and 2015 seasons.

Individual Workloads

The highest workload for a starting pitcher belongs to Justin Verlander in 2011. In fact, it is alarming to see just how many times Verlander and Sabathia’s names show up in the top 25 of this list. Those guys were horses in their prime – and it’s unknown how those huge workloads contributed to both of their recent injury problems. Conversely – how much of their durability during that time was because they worked so much, and had great pitching fitness?

Relief Pitchers

Bullpen Averages

The Rockies 2012 bullpen put in the most about of work during the past ten years. This was a direct result of a really bad starting rotation – only one pitcher cleared 100 innings pitched. The relief core was totally hung out to dry on this team. Overall, the Nationals had the highest yearly workload average for their bullpen (though this is driven by the late 2000’s when they were not very good).  There is a general trend for bullpen workloads to increase in the past 10 years – with 2015 having the highest workload for relievers in that time frame.

Individual Workloads

At first glance, I have to say – these numbers looked just… wrong. Then, I looked again – and they didn’t change.

Francisco Rodriguez put up an INSANE workload in 2010 – 62.84 – with nearly 1800 pitches, and over 100 innings. That’s a lot of exposure to high pressure situations, back to back days, and pitches per inning. The set up men, and the swing men – those who pitch more than an inning in relief, appear to have the highest workload levels. Something else that came up this weekend – was the topic of Dellin Bettances. After giving up a walk off in his third day of work in three days, people talked about his over use with the Yankees. In the past 3 years – no one has a higher workload than Bettances.

You are welcome to question the FU’s! Hit me up at michaelsonne@gmail.com, or on Twitter @DrMikeSonne if you want to debate these findings!