Mike Sonne

Science and Baseball

Category: Baseball (page 3 of 4)

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

Who has the best stuff in baseball? – Volume 4

There seems to be something wrong with the Stuff engine this week… one pitcher is throwing off the numbers, and I’m getting a new leader with an astronomical score. Just going to check under the hood and see what’s wrong…

rich hill 1

Hmm.. at first glance, can’t seem to see anything. Wait a second… what is that… what the….

rich hill 2

Ah damn! Rich Hill! You’re breaking my stuff, man! I guess I can’t blame you. If I could make people fall over just from looking at the pitches I throw, I’d probably do it too. Why do you have to be so nasty?! Let’s just put things in perspective here for a second.

This is Rich’s fastball. Not overpowering by any means – according to FanGraphs, it averages around 90 mph. Now, let’s look at the curveball.

Well, that’s just not very nice. What a beast. The resultant separation between Rich’s curveball and his fastball rise is 24.76″ – the third best of any starting pitcher. However – what actually broke the metric was that Rich snuck in a 58 mph Eephus (according to FanGraphs). That would be a 30% change in velocity, and gave him a stuff score of over 3.5. To account for that, I’ve set a new standard, stating that a pitch must be thrown 30 times by a pitcher before it is included in the repetoire. So thanks, Rich. You made me change the rules. NO CHEATING (you still have the 9th best stuff of any starting pitcher).

Starting Pitchers

I mentioned earlier that Rich Hill had the third most separation between his fastball and curveball in the league. You know who is number one? None other than Toronto Blue Jays’ Aaron Sanchez. This is what his curveball looks like.

Relief Pitchers

The one obvious addition to this list is unfortunately Aroldis Chapman. He throws the ball really hard. Here he is giving up an RBI single to Devon Travis.


That’s all for this stuff report! It’s my last day of work as a post-doctoral researcher, and I must celebrate my entrance to the real world.

Who has the best stuff in baseball? – Volume 3

Welcome to the third installment of the stuff report. It’s kind of like Stuff’s return of the jedi – except with way less ewoks.

A couple of small changes this time around – to make the metric a bit more of a true leaderboard, I’ve implemented some inclusion criteria. For one, starters will only appear of they’ve made as many appearances as there have been weeks in the season. For relievers, they’ve had to have appeared in as many games as there have been weeks in the season. For the team averages, I’ve gone to a weighted average of stuff, based off the number of innings pitchers have thrown. So, for every team – every pitcher who has thrown any proprotion of an inning, has their Stuff score multiplied by the percentage of total innings their team has pitched. For example, if a pitcher has a stuff score of 1.0, has thrown 10 innings, and their team has thrown 100 total innings – their weighted contribution to the team’s stuff score would be:

Weighted Stuff = Stuff * (pitcher innings/total innings)

0.1 = 1.0 * (10 innings / 100 innings)

The sum of all pitcher’s weighted stuff scores are added together, to give a total for each team.

Starting Pitchers

 Compared to Volume 2 of the stuff report, there has been some significant subtractions from the list. Garret Richards and Chris Bassitt – both with elite stuff – have gone on the disabled list with elbow injuries, and will require Tommy John surgery. This leaves Noah Syndergaard and Jake Arrieta at the top of the leaderboard – somewhat running away from the rest of the pack. Their season average stuff has decreased in the past two weeks, but in both cases, the decline has been very small.

The best Stuff of any starting staff still belongs to the Mets. The Phillies also have a very exciting young pitching staff – and their top 5 ranking in the Starting Staff Stuff Metric gives a lot of reasons for hope in Philadelphia. Pulling up the rear of the starting staffs are the Blue Jays – though their Starting Pitcher’s performances this season have been amongst the very best in the league.

Relief Pitchers

Kelvin Herrera remains a very, very bad man at the top of the list of relief pitchers. Second on that list is Pirates reliever, Arquimedes Caminero. He has the best name in the bigs, and the second best stuff of all relief pitchers.

Throwing 99mph really does favour well for having your stuff rank highly.

With the weighted average for Stuff – the Cubs currently have the best bullpen in baseball. The dominance the Cubs have shown so far has allowed them to not rely on their bullpen as much as other teams, but as the season wears on – it looks like they will have yet another weapon to unleash on the National League. As Arolids Chapman pitchers more innings for the Yankees – you can expect that bullpen to rise up in the ranks as well.


Who has the best Stuff in Baseball? – Volume 2

As April comes to a close, the MLB season starts to pick up steam. Blue Jays fans eagerly await a game where they aren’t sitting under a roof. All baseball fans sit and wonder though… which Pitcher has the best stuff in baseball? You’re in the right place.

Starting Pitchers

Individual Pitchers

A bit of a somber start to this edition of the best Stuff in baseball, as our current leader, Chris Bassitt, has been put on the DL with elbow issues. Chris was roughed up by the Blue Jays in his last start, and news surfaced about the pain he’s been dealing with in his elbow. I hope for nothing other than a quick return to health for Chris. One of the most interesting debuts on this list belongs to Blake Snell – the Rays top pitching prospect. His debut against the Yankees resulted in exceptional stuff. Check out this curveball he used against Brian McCann.

Starting Staffs

The Mets assume their rightful place at the top of the MLB’s best Stuff rankings. Lead by Matt Harvey, Noah Syndergaard and Steven Matz, the Mets have the most elite stuff of any starting pitching staff. It looks like I’m not alone in thinking this.

Relief Pitchers

Individual Pitchers

The best stuff of any reliever belongs to Kelvin Herrera from the Royals. Herrera has long received praise from analysts, and with his elite fastball and massive amount of breaking distance, it’s not a big surprise.

In the AL East, it’s a bit scary to see how many elite relievers there are – with Craig Kimbrel getting better by the end of April, and Chapman still on the horizon.


The Royals bullpen continues to wear the crown for the best stuff of any relief corps. It will be interesting to see what happens when Arolids Chapman returns from the Suspended list – as not only do Bettances and Miller have elite Stuff, but John Barbato sits near the top of the list. The Yankees are aiming to play 5 inning baseball games.

What is Stuff?

What is Stuff

Who has the Best Stuff in Baseball? – Volume 1

Welcome to the bi-weekly Stuff report! I plan on posting this every 2 weeks to show off the Stuff metric (http://www.mikesonne.ca/baseball/22/), and answer the age-old argument – who has the best Stuff in baseball.

What is Stuff?

Stuff is an interaction between velocity, pitch usage, pitch movement, and change of velocity. Previous articles on the development of the stuff equation have found that it is significantly correlated with both K/9, WAR, and xFIP/ERA. The benefit of using the Stuff metric, is you could theoretically look at a pitcher’s arsenal in a bullpen session, and with the use of radar guns and spin trackers, could calculate their stuff. This has implications for both scouting, and rehabilitation.

How is Stuff calculated?

What is Stuff

How to interpret Stuff

These rankings are filtered in descending order, from the best stuff in the MLB to the worst. I have presented the raw values that went into the calculation (because these are more fun to look at than the z-scores). I have also provided the percentile for stuff – which is from 0 to 100%. If a pitcher has 95% stuff, that means that their stuff is better than 95% of all other major league pitchers. Percentiles are blocked in 1% increments, so that is why you may see more than 1 – 100% stuff pitchers.

Enjoy! Feel free to use these numbers on your site, your Twitter, or in arguments with your friends at the bar. Remember, it’s always better to win your arguments with science.

The Best Stuff

Starting Pitchers

Note – Starting pitchers had to make as many starts as there have been weeks in the season to be included.

Starting Pitchers – By Team

Relief Pitchers

Note – Relief pitchers had to make as many appearances as there have been weeks in the season to be included.

Relief Pitchers by Team

That’s the stuff report for now! Feel free to comment, or use these numbers – just throw me a shout out.

Twitter – @DrMikeSonne

Combining Arsenal Scores and Stuff to evaluate pitcher performance


The Arsenal Score is a metric which can examine how effective a pitch currently is, or how effective it could be. This metric is compiled from z-scores (a statistical measure of how far above, or below the mean a specific value is) of ground ball and swinging strike rates (Sarris, 2016). Eno Sarris put this metric together to see which players might be on the verge of a breakout, should they figure out control issues, improve their fitness and last longer in games. Eno has used the Arsenal score to rank pitchers from the 2015 season, proposing that pitchers like Chad Bettis, Rich Hill, and Rasiel Iglesias are on the verge of a breakout.

My colleague Dan and I built the Stuff metric for a couple of different reasons. The first, and yet to be completed, was to look at how a pitcher’s stuff could influence their risk of injury. The second, was for a similar reason as to the development of the Arsenal score – how can we possibly find players who have electric “stuff”, yet are a mere tweak away from major league success. The stuff metric is developed in a similar fashion to the Arsenal score – we look at the z-scores of a pitcher’s velocity, change of velocity, velocity of breaking pitches, and amount of break (Sonne & Mulla, 2015). However, unlike the Arsenal score, we have no indication as to how these pitchers are influencing the hitter – if they causing swings and misses, or if they inducing ground balls. In a sense, this is a weakness of the Stuff metric compared to the Arsenal scores, but it could possibly be used sooner than the arsenal score – as minor league parks install PITCHf/x system and other tools for measuring pitch movement and velocity. Using the stuff metric, we’ve proposed possible 2016 breakout pitchers like Chris Bassitt and Mike Foltynewicz.

These two metrics try to get at similar answers, but go about it in a different manner. For this analysis, I wanted to see how these two metrics could be combined to predict pitcher success.


I used the stuff metric calculated for 2015 pitchers (found here: http://www.mikesonne.ca/baseball/22/) and the arsenal scores for pitchers in 2015 (found here: http://www.fangraphs.com/fantasy/the-change-arsenal-scores/). In both evaluations, a pitch had to be thrown 100 times to be eligible for further analysis. In total, 138 different pitchers were included in this analysis. To see how both new pitching metrics performed (Arsenal Scores and Stuff), I calculated the R2 between the metric and ERA, xFIP, k/9, and WAR. These result values were obtained from FanGraphs. To see how the combined metrics worked to predict pitcher performance, I used a multiple regression analysis, and developed separate equations for each of the FanGraphs result values, using the sum of Arsenal scores and Stuff value as inputs.

For further analysis of the combined metric model, the difference between predicted values and actual values was calculated for ERA, xFIP, and k/9. This analysis did not include WAR, as to allow for equal comparison between players who played different numbers of games.


Model Performance

In general, the Arsenal Score was a better predictor of pitcher performance than Stuff. Arsenal scores had higher R2 values when predicting xFIP, WAR and K/9, with Stuff having a slightly higher R2 value for ERA (Table 1). The new combined model was a better predictor than either metric alone, with the greatest improvement seen for WAR (an 11% increase in explained variance compared to a single input variable).

The combined Arsenal-Stuff model performed the best when predicting xFIP (accounting for 46% of the variance in xFIP). Predicted vs. actual values can be found in figure 1 for all result variables.

Table 1. R2 values between the input variables of Stuff / Arsenal Score, and result values of ERA, K/9, WAR, and xFIP. R2 values are also presented for the combined model, which uses both Arsenal Score and Stuff as an input.

Stuff 0.14 0.17 0.27 0.13
Sum Arsenal 0.12 0.37 0.33 0.44
Combined Model 0.19 0.41 0.44 0.46


stuff and arsenal

Figure 1. Relationships between predicted K/9, ERA, WAR, and xFIP and actual values. All predicted values are determined from a model that uses both Arsenal Scores and the Stuff Metric.

Player Identification

As a post-hoc analysis, I calculated the difference between predicted values and actual values. For ERA and xFIP, a lower value indicated the player’s predicted ERA or xFIP was lower than their actual results, which, could indicate that the player may perform better in 2016. A higher value may indicate that the pitcher may not have as favourable of results in 2016. The analysis is the opposite for K/9 – with higher values indicating that the pitcher should be expected to strike out more batters in 2016.

Table 2. The top 10, and bottom 10 predicted ERA errors. The top 10 represents pitchers who can be expected to have better results in 2016, with the bottom 10 predicted to perform with less success in 2016.

  Rank Pitcher ERA Difference Predicted ERA ERA Arsenal Score Stuff
Room for Improvement 1 Chris Capuano -0.80 4.44 7.97 0.19 -0.62
2 Bud Norris -0.74 3.85 6.72 1.15 0.81
3 Keyvius Sampson -0.67 3.92 6.54 0.11 0.89
4 Hector Noesi -0.61 4.28 6.89 -2.06 0.41
5 Carlos Carrasco -0.48 2.45 3.63 14.33 1.43
6 David Hale -0.47 4.15 6.09 2.36 -0.35
7 Archie Bradley -0.46 3.97 5.80 1.51 0.38
8 Matt Garza -0.45 3.88 5.63 -0.92 1.25
9 Matt Moore -0.38 3.92 5.43 0.90 0.66
10 Michael Lorenzen -0.38 3.90 5.40 -0.59 1.10
Due for Regression 121 Jerad Eickhoff 0.29 3.76 2.65 2.05 0.85
122 Josh Tomlin 0.31 4.36 3.02 0.90 -0.58
123 Jake Arrieta 0.31 2.56 1.77 7.22 2.95
124 Jaime Garcia 0.33 3.63 2.43 4.14 0.67
125 David Price 0.34 3.70 2.45 1.61 1.11
126 Dallas Keuchel 0.34 3.76 2.48 6.04 -0.19
127 Brandon Morrow 0.36 4.28 2.73 -1.89 0.37
128 John Lackey 0.38 4.46 2.77 -2.30 -0.04
129 Steven Matz 0.44 4.02 2.27 1.02 0.36
130 Zack Greinke 0.52 3.45 1.66 3.04 1.48


Table 3. The top 10, and bottom 10 predicted xFIP errors. The top 10 represents pitchers who can be expected to have better results in 2016, with the bottom 10 predicted to perform with less success in 2016.

  Rank Pitcher xFIP Difference Predicted xFIP xFIP Arsenal Score Stuff
Room for Improvement 1 Allen Webster -0.40 4.30 6.02 -0.95 -0.95
2 Archie Bradley -0.34 3.85 5.15 1.51 0.38
3 Henry Owens -0.33 3.77 5.01 1.93 0.62
4 Carlos Carrasco -0.32 2.02 2.66 14.33 1.43
5 Hector Noesi -0.30 4.33 5.61 -2.06 0.41
6 Jarred Cosart -0.25 3.57 4.46 3.15 0.99
7 Keyvius Sampson -0.24 3.99 4.97 0.11 0.89
8 Garrett Richards -0.24 3.06 3.80 6.44 1.69
9 Matt Moore -0.23 3.91 4.81 0.90 0.66
10 Chi Chi Gonzalez -0.21 4.36 5.26 -1.98 0.00
Due for Regression 121 Chris Sale 0.15 3.08 2.60 6.49 1.49
122 Joe Blanton 0.16 3.56 3.01 3.99 -0.15
123 Jose Quintana 0.16 4.18 3.51 -0.91 0.33
124 Dallas Keuchel 0.16 3.29 2.75 6.04 -0.19
125 Tyler Duffey 0.16 4.35 3.64 -2.35 0.56
126 Clay Buchholz 0.17 3.98 3.30 0.40 0.57
127 Brett Anderson 0.18 4.29 3.51 -2.10 0.92
128 Jose Fernandez 0.19 3.24 2.62 5.38 1.33
129 Michael Pineda 0.19 3.65 2.95 3.07 0.26
130 Stephen Strasburg 0.20 3.35 2.69 4.40 1.61


Table 4. The top 10, and bottom 10 predicted K/9 errors. The top 10 represents pitchers who can be expected to have better results in 2016, with the bottom 10 predicted to perform with less success in 2016.

  Rank Pitcher K9 Difference Predicted K9 K9 Arsenal Score Stuff
Room for Improvement 1 Tyler Wilson 0.52 6.76 3.25 -0.76 -0.55
2 Chi Chi Gonzalez 0.39 6.61 4.03 -1.98 0.00
3 Jose Urena 0.39 6.70 4.09 -1.99 0.24
4 Cody Anderson 0.38 7.01 4.34 -0.47 -0.12
5 Scott Feldman 0.36 7.91 5.07 1.52 0.71
6 Jarred Cosart 0.29 8.49 6.07 3.15 0.99
7 Aaron Sanchez 0.26 8.09 5.95 1.25 1.37
8 Archie Bradley 0.25 7.78 5.80 1.51 0.38
9 Kyle Ryan 0.25 6.39 4.79 -0.85 -1.42
10 Allen Webster 0.25 6.54 4.94 -0.95 -0.95
Due for Regression 121 Stephen Strasburg -0.20 9.10 10.96 4.40 1.61
122 Chris Archer -0.21 8.83 10.70 3.77 1.39
123 Tyler Duffey -0.22 6.72 8.22 -2.35 0.56
124 Chris Sale -0.22 9.66 11.82 6.49 1.49
125 Ian Kennedy -0.23 7.55 9.30 0.18 0.79
126 Vincent Velasquez -0.24 7.55 9.38 -0.11 1.00
127 Nate Karns -0.27 7.01 8.88 -1.35 0.54
128 Lance Lynn -0.28 6.70 8.57 -2.27 0.45
129 Drew Smyly -0.34 7.75 10.40 2.16 -0.17
130 John Lamb -0.62 6.49 10.51 -2.09 -0.24



This new model which incorporates both the Stuff Metric and the Arsenal Score improves predictions of ERA, xFIP, K/9 and WAR. By combining both of these metrics, the new model incorporates both the action of a pitch, plus the ability of a pitcher to induce swings and misses, and ground balls.

Examining the player rankings to determine which pitchers are both under performing and over performing based on the new model’s predictions, there are some interesting names that show up. Carlos Carrasco appears to be due for improvement based on ERA and xFIP. Matt Moore is slowly returning from injury, but could see improvements in 2016 based off of his Stuff and Arsenal Scores.

While pitchers like Zack Greinke, David Price, and Dallas Keuchel appear on the list of pitchers who could see regression in 2016, this is more due to the fact that they had other worldly, perhaps outlier seasons, than it is a commentary on them pitching above their ability. Zack Greinke has gone on the record saying that his 2015 season was an outlier, and “that he may not actually be that good (Rodgers, 2016”.  For Blue Jays fans, it is exciting to see how Aaron Sanchez’s stuff predicts he will have a better K/9 next season – though it’s to be seen whether he will pitch as a starter or reliever.

This model, much like the previous evaluations of Stuff and Arsenal scores, does not factor in control, deception or pitch sequencing. While model performance is strong, there is room for improvement of greater than 50% of explained variance. Pitching is complicated, and to achieve better predictions – models will need to grow increasingly complicated.


The combined Stuff/Arsenal score model improves predictions of ERA, xFIP, K/9 and WAR over the individual metrics on their own. This model was used to identify possible candidates for improvement and regression in the 2016 season. Future work should include a variety of more complicated measures to account for control, deception and additional game factors.


Rogers, J., 2016.  Zack Greinke on furthering his 2015 domination: ‘I’m probably not that good’. Retrieved from:

http://www.sportingnews.com/mlb-news/4695603-zack-greinke-stats-diamondbacks-projection-cy-young-chances, on February 21, 2016.

Sarris, E., 2016. The Change: Arsenal Scores. Retrieved from: http://www.fangraphs.com/fantasy/the-change-arsenal-scores/, on February 2, 2016.

Sonne, M.W., and Mulla, D., 2015. Revisiting the “Stuff” Metric. Retrieved from http://www.mikesonne.ca/baseball/22/, on December 21, 2016.


Additional Information

Difference between predicted and actual values – all pitchers included in the analysis.



Let it Happ-en

Full disclosure: When the Jays signed J.A. Happ to a 3 year, $36 million contract, my first thoughts were “that’s a lot of money for someone who didn’t blow the doors off the last time he was in Toronto”. I definitely had my doubts. Then, when David Price went to the Red Sox and the Jays signed Fausto Carmona/ Roberto Hernandez, and Brad Penny – I really started to wonder what was happening. However, when Mike Leake, Jeff Samardzija, and Johnny Cueto signed contracts for a combined 55.7 million dollars per year – things started to come into focus. Starting pitchers make a LOT of money. This article by Chris Rinaldi shows just how much money a starter can make by just being average (Mike Leake). So, I wanted to look a bit further into the J.A. Happ deal, and see just what the Jays were getting for their money, and how it might influence their chances of competing for a second straight AL East title.

I’ve written before about the stuff metric (a measure of a pitcher’s velocity, change of velocity, and range of pitch movement, combined with pitching strategy), so I wanted to use stuff to see how J.A. compared against these other multi-millionaires. Of the four free agents, Happ has the second best stuff (0.53 ) – slightly better than league average (Table 1), with the Shark having the best stuff (0.67). Leake and Cueto were third and fourth, respectively (0.23, and 0.00). Happ had the best xFIP of the group at 3.69, compared to 3.78, 3.93, and 4.31, for Cueto, Leake and Samardzija, respectively. What might be the most exciting number of all however, is that Happ provided 3.3 WAR in 2015, which was second in this group, behind Cueto (4.1). While Johnny Cueto may be worth 0.8 WAR above Happ – he is worth that much at a cost of nearly $10 million more per season.

Stuff for Mike Leake, Jeff Samardzija, Johnny Cueto and J.A. Happ, as well as relevant velocities and break distances.

Table 1. Stuff for Mike Leake, Jeff Samardzija, Johnny Cueto and J.A. Happ, as well as relevant velocities and break distances.

Finally, one thing I’ve been interested in presenting is how “stuff” ages. As you would expect if you’ve seen Jeff Zimmerman’s pitcher aging curves, velocity deteriorates with age – but so does stuff in general. If you’re signing a pitcher at around 30 years of age, you better not be doing it for his stuff, because it’s about to fall off a cliff. Take a look at how stuff has changed over the years for these 4 pitchers (Figure 1).

Changes in stuff and xFIP over time for 4 2016 MLB free agent pitchers.

Changes in stuff and xFIP over time for 4 2016 MLB free agent pitchers.

The moral of this story, is that J.A. Happ doesn’t have to be the Ace of the Toronto staff – but the salary that he is being paid is looking like a good deal compared to what some of the other free agents have signed for this off season. Would it have been nice to see David Price back in Toronto? For sure. J.A. Happ is going to do a great job for the Jays, and he puts them in a better financial position to resign Encarnacion and Bautista.


Chris Rinaldi – @simplybases
Jeff Zimmerman – @jeffwzimmerman

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

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


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

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

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


Data Acquisition

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

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

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

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

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


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

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


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

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

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



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

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


figure 5

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


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

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


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

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

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


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


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


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

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

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

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

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

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

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

[8]       J. Lemire, “Preventing Athlete Injuries With Data-Driven Tech – Athletic Business,” Athletic Business, 2015. [Online]. Available: http://www.athleticbusiness.com/athlete-safety/preventing-athlete-injuries-with-data-driven-tech.html. [Accessed: 21-Dec-2015].

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

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

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

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

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

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


Revisiting the “Stuff” Metric

This article was originally posted on FanGraphs: http://www.fangraphs.com/community/revisiting-the-stuff-metric/
This article was co-authored by Daanish Mulla – @DanMMulla

Last month, we wrote an article on calculating a pitcher’s “stuff”. We were quite pleased with how our equation performed with respect to predicting a pitcher’s strikeout rate and his xFIP. Part of the discussion surrounding the equation was what exactly is stuff? Well, in our case, stuff can be thought of as a three-dimensional shape, where the three axes of the shape represent a pitcher’s peak velocity, a pitcher’s change in velocity between their fastest and slowest pitch, and the amount of distance that their pitches can break. In other words, it aims to represent the range in pitch velocity and movement batters must account for during any given at-bat against a particular pitcher.

However, there was still some room for improvement, and with help from the FanGraphs community, we’ve slightly modified our equation to improve various performance predictions. The first major change came from comparing faster breaking balls versus slower breaking pitches with greater movement. In our original stuff metric, pitchers with a slow, looping breaking ball received more benefit than pitchers throwing a fast breaking ball. I queried the PitchF/x database to see how swinging strike rates and batting average changed against curveballs with respect to pitch speed during the 2014 season. Pitches that were thrown for at least 1% of all pitches were included in this analysis. As you can see in the figure, swinging-strike percentage increases exponentially after 75mph, and is nearly 15% higher at 85mph than at 75mph. This encouraged us to find a better way to account for faster breaking balls.

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Secondly, the original metric did not account for pitch frequency. The Pitch Arsenal metric was improved from it’s original state by accounting for this, and realistically – a pitcher should be given more credit for a great pitch that they throw frequently, as opposed to a great pitch that they rarely throw. To account for this, pitches were classified as either off-speed/breaking or fastballs. The sum of pitch uses for each of these classifications was then used to modify the values in the equation. With that in mind, here’s how we have proposed to modify the stuff equation.

For a pitch to be included in the analysis, it had to be thrown by the pitcher 100 times. Just like the original stuff equation, z-scores were determined for the fastest pitch the pitcher threw, and for the amount of movement that could be seen with respect to that fastball, from the remaining pitches.  For further analysis, only qualified starters were used (those who threw 162 innings in the 2015 season).

Furthermore, z-scores were also determined for the % change in speed between the pitcher’s fastest and slowest pitch. Another z-score was determined for the velocity of the fastest pitch, between curveball, slider, or knuckle-curve. Frequencies were determined for the proportion of fastballs thrown by a pitcher, and the remaining non-fastball pitches. The z-score for velocity was multiplied by the fastball percentage, and the remaining z-scores were multiplied by the non-fastball frequency. The z-scores for peak velocity of breaking pitch and change in velocity were used to determine “pitch strategy” – either, power breaking ball, or change in speed. Whichever z-score was greater, was used in the final stuff equation.

So, the final “stuff” equation is as follows:

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To begin validation of the equation, the stuff value was then correlated with K/9 for all qualifying starters. This resulted in a predicted R value of 0.53 (figure 2), compared to the value of 0.42 from the original stuff equation.

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We’ve since applied the stuff equation to all pitchers from 2007 to 2015 to try and get an idea of the range of the metric. Here’s what we found. For interpretation of this figure, if a pitcher has a stuff value of 0.90, his stuff is better than 75% of all pitchers since 2007. If the value is 2.0, they have stuff that is better than approximately 99% of all pitchers since 2007. To put that in perspective, that means their stuff is better than nearly 4000 other starting pitchers. You’ll notice that in our list of the top 30 pitchers from 2015 – all of these pitchers fall within the top 15% range of stuff. These are elite pitchers with respect to this metric.

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These data have a wealth of applications, such as how a pitcher returns from injury or has even changed his repertoire between years. For example, the jump Chris Bassitt made from 2014 to 2015 – going from someone in the bottom half of the metric to the 99th %ile. Similar to the Arsenal score, there is an application of these data in determining a pitcher on the verge of a breakout (perhaps the Joe Kelly of the second half of 2015 is the real Joe Kelly).

However, we felt that it would be in our best interest to let the community decide just how useful the metric was, so we’re making our evaluation data from 2007 to 2015 available in the form of a Google sheet. Simply select the pitcher you’d like to evaluate, and their stuff scores and xFIPs will be graphed for you. We’ve also posted the entirety of stuff scores from the 2015 season.

2015 Season


Stuff worksheet


Philosophically, we feel that the stuff metric has a great benefit for advanced scouting, because it relies on measures that are solely dependent on the pitcher, and not an interaction of the pitcher and the hitter. Thanks to the FanGraphs community, r/baseball, and Eno Sarris for all of the support with this project.

Get Nasty: Quantifying a Pitcher’s “Stuff”

This article was originally posted on FanGraphs – http://www.fangraphs.com/community/get-nasty-quantifying-a-pitchers-stuff/
This article was co-authord by Daanish Mulla (@DanMMulla)

A New York Times article by John Branch in October 2015 discussed the elusive definition of the pitching term “stuff”. Talk of “plus stuff” and feelings of “all the stuff being there” was scattered throughout the article. Despite interesting commentary discussing the ability for pitchers to over-power hitters, there was no true definition of the nastiness of a pitcher’s stuff.

Earlier this November, Eno Sarris wrote an article examining who had the best changeup in the 2015 season. This was evaluated by looking at the difference in speed and movement with respect to the pitcher’s fastball. This made us think, to truly quantify “stuff”, you would first need to understand what goes into a pitcher having a truly dominant repertoire.

Our definition of a pitcher’s “stuff”, or their overall nastiness, was based on three different factors: 1) fastball velocity; 2) change of velocity of a secondary pitch with respect to the fastball; and 3) movement with respect to the fastball. We downloaded all of FanGraphs’ PITCHf/x data from 2008 to 2015 to attempt solving this problem.

For a pitch to qualify for this analysis, it had to be thrown by an individual pitcher at a frequency equal to, or greater than, the average frequency for that pitch to be thrown throughout the entire data set. For example, in our data set, the curveball was thrown at an average of 12% of the time by all pitchers. Thus, a pitcher’s curveball was only considered if it was thrown at a frequency of greater than or equal to 12%. We then determined the maximum and minimum velocity for all eligible pitches for each pitcher. Working off of the fastball, we then determined the maximum change in movement in both the X direction, and the Z direction, for any qualifying pitches. We then calculated the maximum resultant movement for these values. Z-scores were then calculated and summed from the following factors to get a final pitcher “stuff” score: 1) maximum velocity; 2) change in velocity between maximum and minimum velocity; and 3) maximum resultant movement.

Here is an example as to how a pitcher with elite stuff performed in this analysis. David Price had a great year with the Blue Jays and Tigers. From FanGraphs data, his maximum pitch velocity was 94.1 mph, and the minimum pitch velocity was 85.2 mph – a difference of 8.9 mph. Working off the fastball, the greatest x direction break on a pitch was 15.1”, and the greatest z direction break was 10.9”.  This produced a resultant change in movement of 18.6”.

These values translated to a z scores for velocity, change in velocity, and resultant movement of 0.969, -0.08, 0.91, resulting in a stuff value of 1.80. Comparatively, another Blue Jays starter who struggled in 2015 was Drew Hutchinson. Hutchison had a fastball velocity of 92.4 mph, an offspeed pitch of 84.3 mph, an x direction break of 7.1, and a z direction break of 9.8. Corresponding z scores for velocity, change in velocity, and resultant break were 0.392, -0.24, -0.08, resulting in a stuff value of 0.1.

To break down how well our stuff rating was performing, we correlated stuff with K/9. Pitchers included in this analysis were all starting pitchers who pitched 90 innings in a season, between the 2008 and 2015 season. Average stuff and average K/9 was calculated during this time. Overall, the correlation was r = 0.42 (Figure 1). For the sake of these graphs, knuckleballers Tim Wakefield and R.A. Dickey were not included, as the stuff metric had them rated lower than -4 per season.

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Figure 1. Stuff vs K/9, between the 2008 and 2015 MLB season.

Here’s the top 25 starting pitchers from the 2015 season ranked by their stuff. While overall, we think this is a good starting point for evaluating a pitcher’s repertoire, there are a few notable pitchers that the stuff calculation doesn’t seem to do justice. Chris Archer, who has had his slider called one of the best pitches in all of baseball, has only a 1.12 stuff value, and is ranked as having the 67th best stuff. Max Scherzer, who threw two no-hitters, is ranked as only having the 60th best stuff.

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Table 1. Top 25 stuff for pitchers, with raw data on velocity and break

What’s worth stressing however, is that this metric serves to evaluate the individual pitches within their repertoire. There are pitchers which would be scouted to have the ability to throw hard, with lots of break. Pitching is clearly an art form that involves more than those two things, thus players like Mark Buerhle (-2.7), are clearly someone who has mastered the art of pitching, without having great stuff.  When comparing stuff against xFIP, correlation coefficients are smaller (r = -0.33) (Figure 2). Much like K/9 does not directly predict pitcher success, neither does stuff.

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Figure 2. Stuff vs. xFIP, between the 2008 and 2015 season.

We believe there’s great use for this metric. We think this metric can provide insight into how stuff changes with age, how stuff changes after a pitcher is injured, and how it can let a coach know when a player has returned to pre-injury form, and how a pitcher’s consistency with their stuff relates to success. As with any ranking that appears on the FanGraphs website, we’re sure that there will be debate – however, we are looking forward to the input from the community into how we can improve this technique.


Branch, J. (2015). The Mysteries of Pitching, and All That ‘Stuff’. Posted online, October 3, 2015.http://www.nytimes.com/2015/10/04/sports/baseball/the-mysteries-of-pitching-and-all-that-stuff.html

Sarris, E. (2015). The Best Changeups of the Year by Shape and Speed. Posted online, November 9, 2015. http://www.fangraphs.com/blogs/the-best-changeups-of-the-year-by-shape-and-speed/

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