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June 9, 2008

Ballad of the Fatigued

The Effects of Long Innings

by Eric Seidman

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Delivering to the dish with a 2-2 count, Wandy Rodriguez hit the outside corner with a 91 mph fastball with which Edgar Renteria could do nothing but whiff. This heater happened to be the 55th pitch that Rodriguez threw in the inning on August 1, 2007. While the pitch brought the inning to a close, it simultaneously placed Rodriguez atop a list of the pitchers who had thrown the most pitches in a single inning. Compiled by Retrosheet's David Smith and posted on the Inside the Book blog, the list is composed of the pitchers with the most pitches thrown in an inning from 2004-2007.

I decided to examine the Pitch F/X for Wandy's game. Analyzing the velocity and movement of Rodriguez's fastball, I was surprised to find that his fastball sustained its velocity and "bite" as he went deeper into the inning. However, during the rest of the game things changed a bit. In the second inning, his velocity lost three miles per hour, but his movement increased. It has been theorized before that some pitchers may throw with more movement when they tire due to a dropping of their arm angle; perhaps this happened here, as Wandy lost velocity but threw with more movement.

After several ideas were tossed back and forth in attempts to deduce causation, I decided to turn this into an extended study, looking at the 25-30 longest innings captured by the Pitch F/X system. First, though, we need to understand why this study matters from a mechanical and physiological standpoint; in other words, how throwing a baseball affects the body, and how throwing these long innings can cause even more problems for the pitchers who have to throw them.

The Science of Fatigue

To fully grasp the science behind fatigue, I turned to Will Carroll. He offered the following:

Baseball has conducted some internal studies on this, and it seems that there's a point where pitchers really begin to see the effects of in-inning fatigue. Since pitchers do essentially the same activity, though in very different ways, one of the commonalities I expected to see was a common fatigue point for their specific skill. Elite marathoners all tire at the same level (the legendary "wall" at the 20-mile mark). Sprinters and weightlifters all have a narrow range of anaerobic capacity. Pitchers, it seems, have that same type of common fatigue point. It was actually a bit higher than I expected.

Will then directed me to his father, Dr. Bill Carroll at the University of Mobile, who broke down the physiological aspects of fatigue as well as how it could come into play during these long innings with high pitch totals. According to Dr. Carroll, pitching is classified as anaerobic exercise due to the starts and stops. Because of the stoppages in intense, short-term exercise, fatigue can result from the depletion of muscle glycogen. Glucose is the only fuel source used to generate energy during anaerobic exercise; as these long innings continue, more glucose is needed.

Additionally, an increase in exercise intensity causes a buildup of lactic acid in the muscles. As the lactic acid continues to build the muscles will reach their lactic threshold. When the lactic acid in the blood is greater than the body can metabolize, fatigue and poor biomechanics can set in.

Beyondy Wandy

Intrigued by this information, and curious about how and where it may surface in the stats, I contacted Dave Smith regarding his list. He supplied me with a list of every inning in which a pitcher threw 40 or more pitches from April 2007 to May 20, 2008. While this might not seem a long stretch of time, it in fact included a multitude of pitchers. To view the whole list, click here.

Unfortunately, the Pitch F/X system did not track all of these games. On top of that, I needed to break the list down into starters, relievers, and the specific inning. For the purposes of my study, I ultimately opted to include pitchers for whom I had the Pitch F/X data, were starters, and who had thrown 40 or more pitches in the first inning. These criteria whittled the long list down to exactly 30 pitchers; the list included the likes of Bronson Arroyo, Derek Lowe, John Lackey, Jeff Francis, and Matt Cain, so it wasn't entirely made up of below-average performers. Ideally, I would have liked to use 30 right-handed and 30 left-handed pitchers to track and compare results and discrepancies between handedness; however, with the data available these current criteria work just fine.


Just like the Wandy research, tracking fastballs is the name of the game; while pitchers may differentiate in their secondary repertoires, everyone has a fastball. Once all of the numbers were compiled they were separated into two different files: one containing fastball data for the first inning, and one with fastballs for the rest of that game. This way we can track how the fastball changed-if it changed-in the actual inning as well as determine if it was affected later in the game. Perhaps the fatigue set in as the first inning progressed; or maybe it did not register until the next inning. While there are several aspects of pitching that could suffer from fatigue, velocity and movement are our primary analytical concerns right now.


Looking at the velocity and vertical movement on the fastballs for all 30 pitchers, blind to handedness or any other split, here are the overall averages per nine pitches:

Pitches   Velocity   Vertical Movement
 1-9        89.79         9.28
10-18       90.01         9.26
19-27       90.60         8.87
28-36       91.89         8.81
36+         93.17         8.44

The velocity increase can be attributed to one of two factors: either the increase is accurate, and these pitchers threw harder as the inning progressed, or the guys who threw harder were more likely to throw more fastballs. Since the latter might exaggerate the results, here are the average velocities and movements split by those who threw 27 fastballs or fewer, against 27 or more fastballs as their long inning went on:

Pitches   Velocity   Vertical Movement
 1-9        88.97         9.46
10-18       89.07         9.47
19-27       88.97         9.17

Pitches   Velocity   Vertical Movement
 1-9        90.72         9.06
10-18       91.09         9.00
19-27       90.97         8.72
28-36       91.89         8.68
36+         93.17         8.44

For those who threw 27 fastballs or less, the velocity of the pitch essentially stayed stagnant while the movement didn't decrease until the latter third of their pitches. The second table shows a consistent decrease in movement, while the velocity stays in the same range until the 36+ mark. The reasoning for this is consistent with the overall results; the pitchers who threw harder would use their fastballs more often. We can also see that those who used the fastball less often threw a little slower, but had more vertical movement on their pitches, while those who threw more fastballs threw them at higher velocities but with initially less and ever-decreasing movement.

What about the splits for these two groups as the game went on? The tables below show the average velocity and movement for each group as their subsequent innings progressed:

Inning  <27 FB   27+ FB
 1       89.19    91.06
 2       88.40    89.47
 3       89.05    89.88
 4       89.24    89.04
 5       88.92    89.73
 6       87.76     N/A

Vertical Movement
Inning  <27 FB    27+ FB
 1       9.41      8.91
 2       9.59      8.13
 3       9.42      6.99
 4      10.59      7.77
 5      10.64      5.34
 6       9.66       N/A

To return to our initial look at Wandy Rodriguez in his long inning-afflicted outing, he showed a decrease in his velocity and movement in the second inning, but a leveling out as the game continued. The under-27 fastballs group threw at about the same velocity in the first through fifth innings, before seeing their velocity drop in the sixth. The group of pitchers with 27 or more fastballs experienced a significant hit from the first in the second inning, but essentially sustained the same velocity through the second through fifth inning; nobody in this group pitched into the sixth inning.

In terms of movement, the two groups moved in opposite directions. The under-27 fastball group seemed to increase their vertical movement as their innings progressed-until the sixth, when they were likely exhausted-while the pitchers from the 27-plus group lost a lot of movement between innings two and three and innings four and five. They did shoot up again from the third to the fourth inning, but from the first to the fifth they lost in total some 3.57 inches of vertical movement, while the under-27 group gained 1.23 inches.

Velocity Splits

Since it has been apparent that the increase in velocity in certain cases can be chalked up as those who throw harder utilizing the pitch more often, let's take a look at the inning results for different velocity ranges:

Pitches   <88.5   88.5-91.5  >91.5
 1-9      86.45     90.18    91.61
10-18     86.36     90.49    92.00
19-27     87.17     90.38    92.25
28+        N/A      90.42    92.94

Vertical Movement
Pitches   <88.5   88.5-91.5   >91.5
 1-9       9.31      9.45      9.02
10-18      9.17      9.08      9.54
19-27      8.09      8.93      9.06
28+         N/A      8.51      8.96

With regards to the long-pitch inning, those who threw the slowest experienced virtually no change from pitches 1-18; however, from pitches 19-27 they threw harder but straighter, gaining one mph but losing one inch of movement. Those in the middle range threw at the same velocity, but lost movement at every interval. The hard throwers increased velocity at every interval and, with the exception of the 10-18 mark, threw within a pretty narrow range of 8.96-9.06 inches of vertical movement. The outlying interval saw this group throw an average of 92 mph with 9.54 inches of vertical movement.

What about the rest of the game?

Inning <88.5   88.5-91.5    >91.5
 1     86.54     90.35      92.05
 2     86.27     88.87      91.16
 3     86.56     89.20      90.81
 4     86.54     88.80      90.79
 5     84.99     89.37      90.39
 6     84.26     88.92       N/A

Vertical Movement
Inning <88.5   88.5-91.5    >91.5
 1      9.06      9.13       9.19
 2      9.21      8.49       9.21
 3      9.13      7.91       8.81
 4      9.89      9.57       8.59
 5     10.71      9.11       7.85
 6      9.14     10.08        N/A

Each group lost velocity between the first and second inning, with the slowest group losing the least. The medium group lost movement, but the others stayed about the same. Looking at the slower group, their velocity leveled out in the third and fourth innings before significantly decreasing in the fifth; the middle group essentially leveled out from the third to sixth inning; the hard throwers lost velocity as the game went on and none of them pitched in the sixth inning.

Less can be learned from the movement as the game went on because the numbers fluctuate more. Other than the hard throwers, who lost both velocity and movement as the game progressed, everyone who threw 91.5 mph or less saw their velocity level out, but failed to sustain any pattern of movement. The hard-throwing group was affected the most in these splits. As the first inning progressed they threw harder and sustained their bite, but as the game progressed they lost speed and movement to the point that none of them lasted more than five innings.

Subsequent Starts

So far we have examined the effects of these long, high-pitch innings on the innings themselves as well as during the remainder of those starts. We have not yet discussed the idea that significant effects might not register until the next time these pitchers toe the rubber. Perhaps nothing new will be discovered but finding answers stems from asking questions; this question should be taken into account.

Of the 30 pitchers used in this study, 18 also had Pitch F/X data for their very next start. I took a look at the game scores for the group in both the long-inning game and their next start, and found that the means were 28.0 for in the first start, and 46.3 in the second. Comparing the means of two different datasets, we can say with 95 percent degree of confidence that the long-inning start would produce a game score between 21 and 34, whereas the subsequent start would be between 38 and 55. From that, clearly these pitchers seemed to improve in terms of their overall results the next time out, but how did their velocities and movement fare?

I separated the pitchers into two groups: those with subsequent game scores of at least 50, and those below 50. Having divided them into these two groups, let's take a look at the average velocity and movement in the first inning of the long-inning game of those who would go onto have a game score of 50 or better in their next start:

Subsequent Game Scores of 50 or more
Pitches  Velocity   Vertical Movement
 1-9       90.22       10.14
10-18      90.41       10.69
19-27      90.83       10.66
28+        91.38       11.93

As a group, their velocity increased as their long inning progressed and, despite a drastic increase in movement during pitches 28 and up, all four intervals experienced very high amount of vertical movement. How would this compare to those who would go onto have subsequent game scores below 50?

Subsequent Game Scores Below 50
Pitches  Velocity   Vertical Movement
 1-9       89.03         8.61
10-18      89.40         8.28
19-27      90.93         7.67
28+        91.86         4.99

Ignoring the velocity, let's go right to the vertical movement. The greatest amount of vertical movement amongst this group is 1.5 inches below the minimum in the group with Game Scores of 50 or better. Based on this it seems that those who went on to succeed in their next start had pretty ridiculous movement in the long-inning start, despite the 40-plus pitches thrown in that first inning.

When looking at the same group breakdown but comparing the velocity and movement for the rest of the game we get very similar results: Those with a subsequent Game Score over 50 threw with a ton of vertical movement as the game progressed, while those who struggled in their next start not only lost movement as the game went on but their maximum amount of vertical movement was nowhere near the other group's lower end. The most vertical movement that the below-50 group had was 9.83 inches; the lowest for the other group was 9.42 inches; and other than the 9.83, all other innings fell short of the 9.42 minimum. These results further support the idea that those who will not be affected too much by the long-pitch inning are those who have a ton of vertical movement.

Conclusions and Analysis

Overall, those who rely on velocity and not movement to make their fastball successful will likely fatigue as the game goes on-regardless of whether or not they're arguably improving as the actual long inning goes on-losing velocity in the process. Without velocity, and already lacking significant movement, these pitchers in theory will not nearly be as effective. Those throwing at slower velocities but with more movement can get by much better; they weren't relying on fastball velocity to begin with, so a progressive decrease shouldn't really have too much of an impact on their performance, especially if a very high amount of movement is sustained.

Though this is still a small sample to work with, and concrete decisions should not be based off of these results, we can form a few ideas. Managers may want to consider not bringing a hard thrower back out after a long, high-pitch inning like this, as the results suggest that this kind of pitcher's velocity will decrease in turn, meaning he will be throwing straighter and without the velocity needed to make these straighter pitches as effective. Another important considerations is that perhaps pitch counts should be examined on an inning-by-inning basis rather than an accumulative basis; throwing 91 pitches over seven innings, with an equal spread of pitches per inning and adequate rest between those innings would be much better on a pitcher than 90 pitches through six innings, where 40 come in one inning.

Of course, velocity and movement are not the only two ways to analyze fatigue. Next week I will look at how the time differential may affect these pitchers by using the MLB.TV broadcasts to measure time. Similarly, I will watch each of these long-pitch innings and chart when pitchers miss their spots, as well as how those missed spots correlate with release points. If anyone has any other ideas for me to potentially analyze, please e-mail me.

Eric Seidman is a contributor to Baseball Prospectus. He can be reached here.

Eric Seidman is an author of Baseball Prospectus. 
Click here to see Eric's other articles. You can contact Eric by clicking here

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