Science and Baseball

Category: Pitching (Page 2 of 3)

I HAD concerns about Marcus Stroman’s workload

A lot has been made about Aaron Sanchez’s workload this season. He’s entering uncharted waters for innings pitched, throws incredibly hard, and is insanely awesome. Little has been made about the workload Marcus Stroman has endured this season – where he just crossed the 200 inning threshold. Remember when he and Sanchez were yelling about 200 innings in the off season? It’s awesome to see their hard work rewarded this season.

Given the ACL injury Stroman sustained last season, a lot of his workload occurred behind the scenes under the watchful eye of Blue Jays’ physiotherapist Nikki Huffman (at the time, from Duke University). He only pitched 27 regular season innings in 2015 with the big league team. Despite the baseball reference page saying he had a limited workload for innings, he was without a doubt, using his arm. When Stroman first came up in 2014, he was used as a reliever, before getting his chance to start. This once again, limited his innings. I wanted to use Fatigue Units to examine changes in Marcus Stroman’s workload over the course of his professional career, and see if 2016 was a giant spike that could lead to future injury.

First of all, I had to take a few liberties with the data set. For minor league data, there are no values for pace, starting vs. relief innings, or total pitches. So, I had to make some changes. I once again used a linear regression approach, and tried to find out predictors for pitch counts in a season – using MLB data. I included games, games started, innings pitched, BB/9, and K/9 as input variables – all which ended up being significant predictors. Overall, this model produced an R2 of 0.98, with a standard error of 131 pitches. It isn’t perfect, but it will do for this application. estimated-pitches

The equation for predicting pitches from MiLB data is:

Pitches = -1.72 + 2.41 * K/9 + 0.62 * BB/9 + 15.60 * Games + 81.45 * Games Started

So, we’re now one step closer to calculating FUs. For the remaining information, I used the average fastball velocity from the MLB data, and the pace from the MLB data. I assumed there was greater care given to the type of pitching appearances (for example, how Sanchez’s MiLB starts were short in duration, but still 5 days apart). I made the assumption that all innings were starter innings, and used these for the calculation of MiLB FU’s. As a reminder, I am using “Predicted FU’s” from FanGraphs data – not the actual calculated FUs, so there can be an error of up to 3.5 FU’s. For a refresher – read up here.

Marcus Stroman Workloads


Without a doubt, 2016 is the highest traditional workload season that Stroman has seen. He has set career highs for pitches, and for innings. Compared to 2014 (his next highest season), 2016 represents a 23% increase in innings, and a 45% increase in the total number of pitches thrown.

Now, looking at FU’s, the story is not nearly as daunting.


His highest workload season before 2016 saw Marcus accumulate and estimated 32.6 FUs, where as he sits at 33.9 FUs in 2016. This only represents a 4% increase in peak workload. This is because in 2014, Stroman pitched more innings out of the bullpen, and in 2016, he works solely as a starter. As I had previously written – typically, someone who throws out of the bullpen throws at a higher effort level than when they are a starter. This is the same for Stroman – 95mph when he worked in relief with the Jays in 2014, compared to 93.5 when he worked as a starter in the same year.


Traditional workload metrics (innings pitched, and pitch counts) have long been researched, and the findings have all come back as being null – these metrics don’t help in injury prevention or prediction. Even less can be said about Fatigue Units – because there has been next to no research on this topic – other than what you have read on this website! That being said, this shows a very encouraging trend – that Stroman’s workload has been closely monitored by the Blue Jays staff, and he is not showing any signs of breaking down.

I once HAD concerns about Stroman’s workload increase, but I am comfortable in saying that those concerns have been alleviated.


Back to the FUture – Workloads since 2007

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!


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, or on Twitter @DrMikeSonne if you want to debate these findings!

Emergency Night before Pitch Talks Stuff Report


It has come to my attention that, while updating the Blue Jays Stuff report over at BP Toronto, I have neglected the MLB stuff report on this site. No time like the night before Pitch Talks to fill everyone in on who has the best stuff in the MLB!

Starting Pitchers

The man remains entrenched at the top of his loft perch – Jake Arrieta has the best stuff of all starting pitchers in Major League Baseball.  In fact, the top three are quite significantly higher than anyone else – Arrieta, Syndergaard, and Strasburg are the only starters who have flirted with the mythical 2.0 mark on the Stuff report all season long. For Jays fans, I would like to present how Syndergaard sits near the top of this list, and down at #108… well, you can guess who.

The top starting staffs all reside in Chicago, with the Cubs at #1, and the White Sox at #2. This goes to show – stuff isn’t everything. The cubs are closing in on a 100 win season and the White Sox… well, they’re fighting to steer clear of the Twins at the bottom of the central.

Relief Pitchers

Chapman still sits at number 1, but Mauricio Cabrera seems hellbent on taking the reliever Stuff crown. Both of these arms have an average fastball velocity of over 100mph. That’s their AVERAGE fastball. To make it worse? They can both drop it down into the 80’s when they need to.

As for Bullpens, the Red Sox – buoyed by the electric arm of Craig Kimbrel – have risen to the top of the Stuff rankings. The Cubs are close behind, and the Jays lurk in fourth.


Are you coming to Pitch Talks? Do you have your tickets? If you order your tickets online, use the promo code “stuff” to get $5 off your ticket. See you there!

Giving a big FU to workload metrics in pitchers: Part 2b – Cumulative FUs from FanGraphs

To calculate individual game FU’s, you’ll have to download the pitchFx database. However, if you want to get an idea of how much fatigue a pitcher has accumulated during a season, there is an easier way.

I investigated how well Cumulative FU’s lined up with data I downloaded from FanGraphs from the 2015 season – particularly, the amount of Innings pitched, the pace of pitching, number of relief innings pitched, and total pitches thrown. Using a linear regression approach, I then figured out what the right coefficients would be to predict the cumulative FU’s. Here are the results:

table for regression

regression for cumulative FU's

Overall, the R2 value was 0.95, and the RMS error was 3.0 Cumulative FU’s. Not too bad. Looking a bit more specifically, relief innings pitched was the most significant individual predictor, at R2 = 0.43. The combined variables produce the most accurate replication of the Cumulative FU metric.

If you want to use this to estimate workload in pitchers, the formula is: Cumulative FU’s =-3.38 + 0.10 * IP + 0.43 * Relief IP + 0.12 * Pace + 0.004 * Pitches.

With all of this in mind – now, let’s take a look at some 2016 data.

I went on the FanGraphs site, and generated a custom report with IP, Pitches, Relief IP, and Pace included.

Once again, the list ends up being fairly reliever heavy. Erasmo Ramirez has the highest workload so far this season, with at total of 44.38 FU’s. The first starter that appears on the list is Christopher Devenski at number 2 – but he has started 25 out of his 93.1 innings have come as a starter. The first dedicated starter on this list is Trevor Bauer, all the way down at 62. Once again, he has pitched out of the bullpen at times this season. With only starting innings showing up, Justin Verlander is at 72, accumulating 32.3 FU’s on the season.

Catering to my Blue Jays friends, Roberto Osuna leads the team in FU’s, accumulating 34.5 on the season. He’s followed by Joe Biagini, with 33.6. Aaron Sanchez is at 26.7 on the season – which looks like it will be less than his 34.6 FU’s he accumulated during the 2015 season. Here are the Blue Jays cumulative FUs for the 2015, and 2016 seasons, respectively.

2015 jays

2016 jays

As with any metrics, tinkering will happen over time. Interesting to note between the 2015 season – while Sanchez has had a reduction in workload, look at the increase seen by Marcus Stroman. He made his miraculous return in September last year, only accumulating 7.53 FU’s in 2015. This year, he’s at 27.33 FUs.

Giving a big FU to workload metrics in pitchers: Part 2 – Cumulative FUs

Read Part 1 to see how FUs are calculated for pitchers during their appearances.

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. 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 paper). Pitching on consecutive days, high velocities, and total pitches have been identified as risk factors for injury – let’s try and combine them all into one metric.

Starting with the FUs I described in part 1, I took a shot at modelling fatigue in every game in the 2015 MLB season. 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, the paper on heart rate variability in pitchers illustrated there weas less HRV the day after an appearance – which returned to baseline after 4 days. 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 3. 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.

I’ve included an example of one pitcher from the 2015 season that I feel shows a good example of how this metric can be used (and how I feel moving a pitcher from the starting rotation to the bullpen doesn’t necessarily help their arm). Aaron Sanchez started the 2015 season as a starter for the Blue Jays, but injuries forced him to the disabled list after his June 6th start. When he returned on July 25th, Sanchez pitched out of the bullpen. To relate this back to the Whiteside article, which indicated higher velocities and fewer days’ rest were significant predictors of injury, Aaron averaged a peak fastball velocity of 95.5 mph as a starter in 2015, and 97.3 mph as a reliever. The average time between appearances was 5.5 days as a starter, but 2.4 days as a reliever.

I’ve compared his numbers against those of David Price – a known workhorse who remained in the starting rotation for multiple teams all year long.

figure 1 - price vs sanchez

Figure 1. Aaron Sanchez and David Price’s cumulative FU workloads during the 2015 season.

Despite Sanchez being moved to the bullpen, you can see that his cumulative FU’s still increase over the course of the season. Sanchez missed nearly two months in the 2015 season – and this can be seen in the plateau between May and July. When he returns from the bullpen, his workload begins to increase again, and matches the increasing trajectory of FUs generated by Price.

Given the research reported by Whiteside et al., (2016), and inferred from the Motus data collected at Driveline  – 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. Let’s take a look at how Cumulative FU’s can capture the workloads of all major league pitchers from the 2015 season, and compare them back to the traditional metrics.

First, I wanted to see if the Cumulative FU was just a surrogate for IPs or pitches thrown – if it was, there is no point in using this metric! To do this, a Pearson correlation was used, and the R2 was calculated. Just as a note – this is not “innings pitched”, it represents “innings appeared in”. My thought process was – if a pitcher is coming out for an appearance, they perform the same warm up pitches, and bullpen work, regardless of how many outs they record. If a pitcher throws 30 pitches, while getting shellacked and does not record an out – this should still count towards the cumulative innings total on the season.

Cumulative FU’s were significantly correlated with other workload metrics, but not enough to believe they’re just a replication. After all, if you throw a lot of innings, that does represent a higher workload… it just may not capture the whole story. Looking at IP and total pitches, these measures explained 36.5% and 29.5% of the variance in cumulative FU’s, respectively. The number of outings in a season explained 65.2 % of the variance in cumulative FU’s, and the average number of days between appearances explained 27.9% of the variance in cumulative FU’s.

I examined the top workload pitchers for each of these metrics as well. I broke these metrics down by month of the season, so the cumulative workloads could be analyzed over time.

figure 3 - cumulative pitches

Figure 2. Cumulative Pitches Thrown during the 2015 season – top 10 pitchers. 

figure 2 - cumulative innings

Figure 3. Cumulative Inning Appearances in the 2015 season, broken down by month.figure 4 - cumulative fatigue units

Figure 4. Cumulative FU’s for the 2015 season – top 10 pitcher workloads.

Once again, I don’t think it would surprise anyone to see Clayton Kershaw at the top of the innings pitched workload metric, or Jake Arrieta as the pitcher with the most total pitches thrown. These are both work horses for their respective teams. However, in both innings pitched, and total pitches, you will noticed that there are no relief pitchers.

Looking at cumulative FUs (Figure 4), Dellin Betances – he of 76 total game appearances, and Jeurys Familia (appearing in over 80 games for the Mets) appear at the top of the list. This is followed by Travis Wood (who appeared as both a reliever and a starter for the cubs), and finally, by Clayton Kershaw. Starters Price, Arrieta, Keuchel, Volquez and Cueto round out the list. This workload metric appears to show more favour for relievers, who appear on short rest schedules, often throw harder, appear in more games than starting pitchers.

Let’s look one step further, and see who has the highest workloads between the 2007 and 2015 seasons. First of all – who cumulatively had the highest workload during this time, and second – who had the highest average workloads during this time period.

Table 1. Top 10 for cumulative FU’s between 2007 and 2015 (in blue). Top 10 for average cumulative FU’s in a season between 2007 and 2015 (in red).

table 1 - cumulative fu's

Francisco Rodriguez has kind of run away with the cumulative FU crown – accumulating 366.19 FUs over the past 9 seasons. Serving as a closer – and surely, an elite closer, K-Rod has consistently averaged less than 3 days between appearances (on average, 2.7 days between appearances). Jonny Venters has the highest average season FU, at 49.64. His average days between appearances during those years with the Braves was 2.37. This is concerning, given his flame out of the major leagues due to injuries.

Depending on how you think about workload, these lists may surprise you. The overall cumulative workloads have half relievers, and half starters. The highest yearly averages all belong to relief pitchers, without a single starter in this list.

Even more concerning about the top seasonal workloads is the injury history of these pitchers – Venters and Manness needed Tommy John surgery after huge workload seasons, Trevor Rosenthal is down with a shoulder injury currently, and Belisaro flamed out of major league action. Carlos Marmol eventually lost all of his ability to throw strikes and is no longer on a major league roster. Even Francisco Rodriguez – who has remained relatively injury free (aside from a back injury) – is now throwing his fastball 5mph slower than he did in 2007. This is a legitimate concern for the number 3 pitcher on this list, the Blue Jays Roberto Osuna. As a teenager, Osuna had one Tommy John surgery – which is a risk factor for subsequent UCL reconstructions. Bear in mind – this list, and assessing workload with injuries, is completely anecdotal at this point. Much greater analysis is required to see if this workload metric is an indicator of injury potential.

The next step – making this method easy to use, and finding out where threshold values lie. As for now, I can say based on these numbers – this is what different workload levels look like:


From a pool of 1869 pitchers, over the span of 9 seasons, this is the range we are seeing for cumulative FU’s. The average FU in a season is 18.35, and the maximum is 61.63 – from the 2011 season, which proved to be Chris Carpenter’s final season as a full time, major league pitcher. If someone gets to a level of 40, you can consider that a very high workload season.

Like all metrics, there is a long way to go for us to understand what exactly all of these numbers mean.

If you have any feedback, or questions about this method – shoot me an email (, or send me a tweet @DrMikeSonne.

If you’re curious, here are the data for different workload metrics.


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.

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.

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

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

Giving a big FU to workload metrics in pitchers: Part 1 – Fatigue Modelling

This is a three part series on the development and evaluation of a new workload metric in baseball pitchers.

So, back in the day – 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 – Dr. 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).

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.

Now, currently – the fatigue model runs in MATLAB, which is definitely not software we’d expect to appear on most pitching coachs’ computers. In fact, it’s usually so expensive that only academics or engineering companies will have access to it. I wanted to come up with a way of helping people determine the fatigue levels in their pitchers without a lot of cumbersome technology.

I used the same subset of data from the paper on pitch clocks – 75 American League starting pitchers from the 2014 season, with their average pace, pitches thrown, and innings per start reported from the FanGraphs website.

Included these values as the inputs from the fatigue model which I ran in Matlab, and generated regression equations from the outputs. These inputs were:

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

This model output a predicted maximum fatigue level for 8 different forearm muscles (Brachioradialis, Flexor Digitorum Superficialis, Flexor Carpi Radialis, Pronator Teres, Extensor Digitorum, Extensor Carpi Radialis Longus and Brevis, and Supinator), but for the sake of this application – I’m just going to look at the average fatigue of these 8 muscles as the dependent variables for the fatigue model. Here is a figure from my pitch clock paper to explain how the fatigue modelling process worked (Sonne & Keir, 2016).

from pitch clock paper


Of the four included predictor variables, only fastballs per inning, and pace between pitches emerged as significant predictors of fatigue level. These predictors were highly significant though, with 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).

The predictive equation for average forearm muscle fatigue is:

fatigue equation

For example, pitcher A threw 15 fastballs in an inning, pitching the ball every 21 seconds. As a result, he has a predicted average forearm fatigue level of 11.06%. To examine the contribution of the individual components to this prediction, I looked at the correlation between fatigue and each independent variable. The number of fastballs thrown predicted 81.7% of variance in fatigue, with number of other/breaking pitches, # innings, and pace explaining 6.0%, 15.1%, and 24% of the variance in fatigue, respectively.

For the final model which only included # of fastballs thrown, and pace, this is how things shaped up. For every 1 second increase in pace, there was a 0.23% decrease in the amount of predicted fatigue (when # of pitches was held constant at 15 per inning). For every one fastball increase, there was a 0.32% increase in fatigue (when pace was held constant at 18 seconds per inning).

Fatigue Pitchers

Predicted average forearm fatigue while pace was held constant (18 seconds between pitches) for an increasing number of fastballs per inning pitched (red). Predicted average forearm fatigue while # of pitches per inning was held constant (15 pitches per inning) and pace was gradually increased from 8 second between pitches, to 30 seconds between pitches (green).

So, when brainstorming ideas for how to use the fatigue model as a workload metric, I bounced a few ideas off of some colleagues as to how I should name this fatigue based workload metric. There were some great ideas that emerged, but ultimately the best one was Fatigue Units – or, FU’s (Thanks, Jenn!).

So, that’s it for now – this is an example for quantifying forearm muscle fatigue in pitchers without needing to know how to program or use Matlab. In part 2, I’m going to propose a method for tracking FU’s over the course of a season, and in part 3 – I’m going to finish this off by providing some spreadsheets to help you track FUs in your pitchers.


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 medicine23(2), 233-239.

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. Ergonomics59(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.


Who has the Best Stuff in Baseball? Volume 7

The Stuff report gets back on track! Let’s figure out who has the best Stuff in Major League Baseball.

In case you’ve forgotten, the Stuff metric was designed to help our friends in colour commentary with their commonly used cliche’s about what pitchers have great “stuff”. The metric looks at a pitcher’s ability to generate velocity, change in velocity, and break distance between their arsenal of pitches. The exact math can be found in the first stuff article, or throughout the rest of the Stuff reports on this site.

Let’s get into it.

Starting Pitchers

The leader of the pack remains Jake Arrieta, followed by Noah Syndergaard. However, all of the drama this week has centered around the ever climbing Aaron Sanchez – who is now up to #7 on the Stuff list. Aaron is being moved into the Blue Jays bullpen – where, his stuff will likely get better (his velocity increased from 95 to 97 last year when he was in the bullpen), but who knows about the long term implications for injury prevention. I’ve argued that moving to the bullpen probably doesn’t decrease stress on the arm. Leaving the rotation doesn’t help the Jays with their overall starting Stuff, that’s for sure – but take a look who is at the top of the list. Now, let’s look at relievers.

Relief Pitchers

There’s no surprise that Aroldis Chapman is leading the league in Stuff – he’s thrown the hardest pitch ever recorded.

However, a new challenger to the StatCast throne makes his first Stuff Report appearance – Mauricio Cabrera, with his 100mph average fastball falls in line just behind Chapman with Stuff of 2.24.

I mentioned earlier to look at the top of the team Stuff rankings – the Cubs sit number 1 for the starters. Well, they sit # 1 for the relievers. The Chicago Cubs are unequivocally, the kings of Stuff. They have a preeeeetty good team over there on the North Side.

Learning more about Stuff

A metric is only good if it is both reliable (it measures the same thing, over and over again), and valid (what it claims to be measuring is actually being measured). I’m sure there are a lot of people who have their own thoughts over how Stuff should be quantified – BUT THEY DIDN’T MAKE A WEBSITE ABOUT IT, SO HAH. I wanted to check out just how well the Stuff metric has performed this season.


My initial thoughts were that I had needed an entire season of data to make sure we got a reliable measure of Stuff – but then this season, I’ve been trying to write Stuff reports every 2 weeks (that hasn’t always worked out on, but you can find my Stuff reports on the Blue Jays over at Baseball Prospectus Toronto. In total, there have been 8 stuff reports since the start of the year, so let’s look at all of the starters and relievers who have appeared in each of them.

Overall, there were 110 Starting Pitchers who have registered stuff values in the 8 Volumes of the Stuff Report. There were 135 relief pitchers. The average (SE) Stuff for these starting pitchers was 0.50 +/- 0.08, and 0.51 +/- 0.08 for relievers. Over the course of those 8 reports, There has been a general decline in Stuff – with Stuff peaking for both starters and relievers in Volume 2, and gradually declining since.


Figure 1. Average (SE) Stuff for Starters and Relievers over the biweekly stuff reports since the start of the season.

With respect to the reliability of the metric – how much did a pitcher’s stuff change on a biweekly basis? I looked at all of the Starting and Relief pitchers who qualified, and I calculated the coefficient of variation of their Stuff (Standard Deviation / Average). For starting pitchers, the CV was 30%, and for relief pitchers, the CV was 22%. That was pretty shocking! I thought with the fewer number of pitches that a reliever throws, they would be much more variable – but that isn’t the case.

Now, how does the stuff metric continue to hold up against performance metrics – primarily, K/9 and bb/9. I looked at the average Stuff over the course of the season (calculated by taking the average of each of the 8 volumes – not the overall season average), and also, the average absolute coefficient of variation, and correlated these with K/9 and BB/9. Similar to previous evaluations of the metric, there was a moderate, positive correlation between stuff and K/9 for both starters and relievers (r = 0.35 for starters, and 0.30 for relievers). Looking at the variability of Stuff in starting pitchers – there’s a significant positive correlation between BB/9 and variability (r = 0.16), and a negative correlation between K/9 and variability (r = -0.26). The moral of that story? It appears if what is coming out of your hand is consistent, you may have an edge for striking people out, and you may have better control. Now, when looking at these variability measure in relief pitchers – the relationship disappears (an r of 0.02 for both BB/9 and K/9).

Starters - Stuff k:9 Relievers - Stuff k:9

Figure 2 – Stuff vs. K/9 for Starters (Blue) and Relievers (Red).

I haven’t had a chance to look at it yet, but the next step is to see how Stuff changes as a response to injury. Here’s a graph of Brett Cecil’s stuff – he went on the DL a few months ago with a Lat tear. Also included is Marco Estrada – a starter who has had a bad back injury, and is likely fighting a trip to the DL. Finally, Aaron Sanchez – someone who has dominated and remained healthy all year.

Case Studies

Figure 3 – How does Stuff change for pitchers who are healthy, pitchers fighting a stint on the DL, and pitchers who have missed time with an injury?

The Stuff metric was originally developed to quantify anecdotal claims about a pitcher’s repertoire, but I believe it has a lot more utility than that. Identifying workload and injury is the next step in Stuff.

UCL stress and Velocity increases

The dudes over at Driveline gave us scientists the best present we could ever hope for – data. They tested out the new Bauerfeind EpiTrain Powerguard to see if it was effective in reducing elbow stress. To test out the device, they paired it with the Motus Throw Sensor – a device designed to measure stress on the elbow. This device has been tested in the field by Dr. Bryan Cole, and you can find the results over at Beyond the Box Score.

Up here in Toronto, you can’t go 5 minutes into a Blue Jays conversation without hearing about the dilemma the team faces regarding Aaron Sanchez. The young ace Sanchez, is without a doubt, the best pitcher on the team, and arguably one of the top 5 starting pitchers in the American League this season. Last year the Jays spent a ton of prospect capital to go out and get an ace in the trade market – this year, they’re talking about moving the Ace they already have into the bullpen.


Aaron Sanchez. Look at him. He’s perfect in every way. Long live Sanchez! (photo – PETER LLEWELLYN/USA TODAY Sports)

I’m not convinced that this is going to work to reduce stress on Aaron’s arm. Will he throw fewer innings? For sure – but as I’ve tried to demonstrate – fatigue accumulation in the arm doesn’t necessarily depend on the number of innings you pitch, but more on the number of pitches you throw in an inning. Sanchez has been known to dial up his fastball to 100mph out of the bullpen, and this left me asking the question – despite limiting his innings, is Aaron Sanchez going to be exposing his arm to more stress by throwing out of the pen? (From Brook’s Baseball – in 2016, Sanchez’s sinker has averaged 95.26 mph, compared to 97.1 mph in September of 2015 – when Sanchez was used as a reliever). Let’s look at the driveline data to see if we can figure this out.

In the driveline study, 5 pitchers threw 20 pitches each. Some had Powerguard on, some didn’t – but for the sake of this study, I’m going to ignore that factor (they didn’t find there was a reduction in stress, anyway). First, I looked at the relationship between stress and the other variables that came out of the Motus Throw Sensor. There was an R2 of 0.84 between pitch velocity and elbow stress – that means, 84% of the stress on the UCL can be accounted for by the velocity of the pitch. If someone throws harder – they’re going to have more elbow torque, and greater UCL stress. The rest of the variables – they get a bit hazier.

Figure 1

Peak UCL Stress vs. Pitch Velocity – from 5 pitchers, throwing 20 times each. The UCL stress is calculated from the MotusThrow Sensor.

Arm speed has an inverse relationship with elbow torque. Greater arm speeds appear to have less UCL stress, but arm speed only accounts for 25.5% of the variance in UCL stress (an R2 of 0.25). Arm slot accounted for none of the variance in UCL stress (so no fancy graph for this one). Finally, shoulder rotation angle accounted for 34.8% of the variance in UCL Stress. I’m not entirely sure what “shoulder rotation angle” is defining here, so I’m just going to leave it for now. Essentially, with a greater shoulder rotation angle, there is greater UCL stress.


UCL Stress vs. Arm Speed (in angles per second), calculated from the MotusThrow Sensor.


UCL Stress vs. Shoulder Rotation, calculated from the MotusThrow Sensor.

The idea that UCL injuries are more prevalent in higher velocity pitchers is not a new one (Keller et al., 2016). Researchers from the University of Michigan found that one of the most significant predictors for elbow injury was ball speed (Whiteside et al., 2016). However, how does a change in ball speed influence UCL stress?

I used the driveline data, and I rank ordered UCL stress, and Velocity. So – there is a 1 through 20 for Velocity and Stress – which I’ll refer to as individual velocity and individual stress. I then ran a Spearman’s correlation on these data.

Ranked intra-pitcher UCL stress compared to ranked intra-pitcher pitch velocity.

Ranked intra-pitcher UCL stress compared to ranked intra-pitcher pitch velocity.

There was an R2 of 0.17 – essentially stating that an internal increase of velocity is associated with 17% of the increase in UCL stress. As you can see in this graph, this is not the strongest of relationships. Does a pitcher ramping up and throwing harder, within his own capacities increase stress on the arm? Possibly, but I don’t think it’s that clear.

There are a lot of other factors that go into determining how stress may change between the role of a starter and a reliever. Particularly, relievers (and relievers in the proposed role that Sanchez will fill) will be coming in for high leverage situations. Working in such a stressful situation can change kinematics, as Bill Marras’ group found when exposing those who were lifting boxes to highly stressful work environments (Marras et al., 2000). When preventing injury, recovery is one of the most important aspects of health. Relief pitchers can perform on up to three consecutive days – and while pitching only 1 inning at a time (in most cases), they still need to perform warm up pitches. Their workload is definitely different than a starter’s, but I don’t think there is enough evidence out there to support that switching from a starting role to a reliever’s role is that much of a reduction in demands on the arm.

The Blue Jays hired a high performance team to help make scientific decisions when it comes to things like monitoring a pitcher’s workload. They have a really hard decision ahead of them, and the long term health of Aaron Sanchez depends on them making the right choices.


Marras, W. S., Davis, K. G., Heaney, C. A., Maronitis, A. B., & Allread, W. G. (2000). The influence of psychosocial stress, gender, and personality on mechanical loading of the lumbar spine. Spine, 25(23), 3045-3054.

Keller, R. A., Marshall, N. E., Guest, J. M., Okoroha, K. R., Jung, E. K., & Moutzouros, V. (2016). Major League Baseball pitch velocity and pitch type associated with risk of ulnar collateral ligament injury. Journal of Shoulder and Elbow Surgery, 25(4), 671-675.

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.

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.

Who has the best Stuff in Baseball? – Volume 5

Volume 5 of the stuff report means that we are now 10 weeks into the MLB season.  Remember when it was cold and snowy, and we all just wanted baseball season to start? Let’s look at who has the best stuff in the MLB – 10 weeks into the season.

Starting Pitchers

The king has returned, and reigning 2015 Stuff champion Jake Arrieta has risen to the top of the 2016 Stuff list. The strength of Arrieta’s stuff comes from his premier breaking pitch velocity. His resultant break distance also ranks in the top 20, at over 20″ of separation between the fastball and breaking ball. The newest addition to the list is Jon Gray from the Rockies. Gray hasn’t put the whole package together quite yet, but with a Slider like this one – you can see the potential in his arsenal.

In terms of a starting staff, the Tigers have the best Stuff in the MLB – with a rating of 0.21 Stuff units per inning. This is buoyed by the resurgent Justin Verlander and new kid on the block, Michael Fulmer. The Cubs with Arrieta and Lester are close behind at 0.20.

Relief Pitchers

Unsurprisingly, Arolids Chapman has finally made his way to the top of the Stuff list for relief pitchers. Following close behind, is Matt Bush.  However, Johnny Barbato has also risen up the stuff list.

Barbato has a great curveball, which has 21.6″ of separation between his fastball and his curve. Combined with Elite Stuff pitchers Chapman, Miller, and Betances – the Yankees bullpen is loaded with great stuff. In terms of the entire bullpen. The best stuff for the pen still belongs to the Cubs – buoyed by Rondon, Grimm and Strop – all of which have Elite stuff (a value over 1.0).

Curious as to how Stuff is calculated? Check this primer out for a refresher.

What is Stuff

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