# How fatigue affects a pitcher’s fastball

 Ben Sheets contemplates pitchers fatiguing. Brewers vs. Astros May 4, 2008 (Icon/SMI)

How pitchers tire is one of the great unknowns left in baseball. Ideally, you could measure fatigue by ERA inning by inning, but the problem is not only does fatigue factor in, but so do adjustments by hitters who have now seen the pitcher multiple times.

So when you hear an announcer say something like “The third time through the order Joe Pitcher has a .320 batting average against” it is hard to say if the cause is pitcher fatigue or hitter familiarity. A better method would be to track the pitcher’s stuff and see how it changes the deeper in the game he goes. This completely removes the batter from the equation and we can isolate pitcher fatigue. With piles of PITCHf/x data rolling in, we have the perfect information to begin to isolate pitcher fatigue.

###### Method

For this study I am using 2008 PITCHf/x data up to June 1. Only pitchers who started and who threw at least 80 pitches will be considered, to remove emergency starts and starts by a swing man. This left me with 1,058 starts. I am going to exclusively look at fastballs, so cutters and sinkers have been removed. I then average every fastball thrown in the first 10 pitches and create a baseline for the pitcher that day. So if a pitcher threw six fastballs in the first 10, those six are averaged to create the baseline. I then divide every group of 10 pitches afterward by the baseline and create a percent to determine how fatigue is affecting the pitcher for that group.

###### Speed

After following the prescribed method for initial speed of the fastball, I combined all the groups for the 1,058 starts and this is the result.

I am actually displaying error bars on this graph, but because of the sample is so large, the statistical error is so small you can’t see it. Because the average fastball is around 90 mph, a difference of one percent is a little less than one mph. So after the baseline 10 pitches, the average fastball increases every so slightly in the next 10 and then slowly dips down until around 100 pitches, where the pitcher has lost about half a mph.

Looking first at the slight increase in the beginning, this is implying that, on average, starters need a little time to warm up before their fastball peaks. Once the pitcher is warm, it is a slow decline to the finish line without the rapid decrease that one might have guessed. At the end, the pitcher generally has lost little off his fastball. While looking at a combined result is interesting, we can also use this method to look at individual pitchers to see how fatigue affects them.

Ben Sheets has long been known as a slow starter and despite what he says (warning audio link), it appears that the data back that up. Sheets’ fastball this year is starting off slightly above 93 mph but after a few pitchers he cranks it up near 95 and it never dips back below the starting point.

I have to wonder if Sheets is purposely doing this to keep the gas tank from being empty as the game wears on. In any case, if you are an opponent you might think about going up hacking early, because it is only going to be more difficult as the game moves on.

On the opposite end of the spectrum is A.J. Burnett, who has the reputation of fading as the game goes on. In fact, it appears that he pretty much starts out with his peak fastball and then it drops more than a mph at the end of the game, though the path is not nearly as nice as the path Sheets takes. Again, if you are facing Burnett it pays to make him work as you are likely to get a slower fastball as he throws more pitches.

In his day, no pitcher was the work horse Randy Johnson was. Age and a balky back have sapped him of some of his greatness, but you can still see some of that rubber arm in him. After peaking quickly, he settles in at almost the same speed he starts the game with.

Even as he gets late into the game, he shows very little sign of losing speed. The Diamondbacks have been pretty careful with Johnson this year, which obviously is the right plan with his history. Still, it appears if they really need him to stretch out in an important game. he still has the ability.

On the other hand, 22-year-old Jair Jurrjens of the Braves shows a steep decline in his fastball after the 90-pitch mark. Like Sheets, he appears to need a few pitches to get going and he peaks relatively late, but then drops off very fast near the end, losing nearly two mph off his peak fastball. Is this due to lack of endurance or age, or is it that he isn’t used to throwing this many pitches in a game? I can’t say for certain, but the Braves would do well to keep a close eye on Jurrjens once he nears the century mark.

The story of Daisuke Matsuzaka throwing 250 pitches in one game while is high school has been widely reported, so I thought it would be interesting to see how his fastball changes as the game wears on. After a slow build to a peak at around 45 pitches, Matsuzaka declines relatively quickly until he has lost a mph from his starting speed and nearly two mph off his peak. I’d love to see a plot for how his fastball changed after the 200-pitch mark but, sadly, that isn’t available.

###### Movement

So speed is obviously an important component in throwing a good fastball, but movement is important, too. How does fatigue affect the movement of the pitch? Because different pitchers throw from different arm angles, I am going to use total movement of the fastball compared to a ball thrown without spin instead of breaking the movement up into horizontal and vertical pieces. Running on the same sample as before produces some interesting results.

Well, that is something new. It appears that pitchers’ fastballs move the most right out of the gate and decline quickly compared to the fastball decline. The average movement of a fastball is about 11 inches, so here a percent decrease is a little more than a tenth of an inch of movement lost. Because loss of movement is a lot larger than loss of speed, it appears that might be a better gauge to determine when a starter is getting tired. Those who like to watch MLB’s gameday should be able to roughly track a pitcher’s movement throughout a game, as that is one of the variables it displays every pitch.

###### Conclusions

In general, pitchers lose very little speed on their fastballs as the game goes on. After a short time to fully warm up, pitchers are still throwing nearly as hard at the end of the game as at the beginning. While this varies greatly from pitcher to pitcher, it doesn’t appear that tracking the speed of the fastball is a good way to determine how fatigued a pitcher might be. Movement of the fastball seems to decline much more rapidly and might be a better indicator. While it is currently hard to measure a pitcher’s control with the PITCHf/x data, if a pitcher is losing movement on his fastball, you can imagine that it would be more difficult to locate that pitch.

Studying fastballs is just one step toward really understanding how pitchers fatigue, but it is an important first step. Perhaps soon a method will become available to determine how much less effective an individual pitcher is after a certain number of pitches. Not only could this help managers decide when to pull the starter, but also whether a move to the bullpen might be necessary for a pitcher.

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