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I don’t believe pitchers should go past 100 pitches. That might seem like the view of a baseball luddite, but it’s quite simple. Throwing 100 pitches means six innings. Surviving six innings equates to 27 batters. Facing 27 batters impends the fourth time through the order. And that spells doom.

As a rule of thumb—not without exceptions—a decent reliever coming out of the bullpen will be better than all but the best of starting pitchers facing the fourth time through the order. Batters make adjustments, and there’s little a pitcher can do.

So I don’t think fatigue has much to do with the 100-pitch rule. However, I do think the subject of pitcher stamina is interesting in itself. Behold:

No pitcher fades as severely as Jonathan Sanchez.

Here’s how I arrived at that conclusion. First, I tried to correct the velocity using a similar method as outlined by Mike Fast yesterday, but only using the fastest 25% of pitches by every pitcher. Then, I took the 25% fastest pitches for every pitcher at every pitch count. This would hopefully provide an unbiased measure of fastballs as the game went on. I found the difference in velocity between each of those pitches and the average pitch velocity in each game.

Here’s how it looks on a league-wide basis:

There is a phenomenon with regard to the first pitch of a ballgame. Pitchers throw fastballs at an exceedingly high rate on the first pitch, and batters refuse to swing. I’ve noticed that some smart players (such as Derek Jeter) will take advantage of such predictability. After that, pitchers will work their hardest against the most difficult batters in the batting order from pitches 10-20, and then fade a bit as the game goes on, until they hit the fourth time through, when they really gear up.

Few are able to enter another gear like Justin Verlander:

I ran a regression of velocity on pitch count, controlling for the pitcher, and found that the following starters, over the course of 100 pitchers, will either gain a half a mile per hour in velocity or lose at least one mph.

 Velo Gain Per 100 1.2 1.1 Justin Verlander 0.9 0.7 0.7 0.7 0.7 0.6 -1.0 -1.0 -1.0 -1.0 -1.0 -1.1 -1.1 -1.1 -1.1 -1.1 -1.2 -1.2 -1.2 -1.3 -1.3 -1.3 -1.4 -1.4 -1.7 -1.8 -1.8 -1.9 -2.0 -2.2 -2.5 Jonathan Sanchez -2.7

One other notes of interest: there were reports early last season of a spike in Mike Minor’s velocity. Minor was reportedly a finesse pitcher coming out of Vanderbilt, but he debuted in the Majors throwing in the low 90s. By September, Minor complained of fatigue. As it turns out, Minor also fatigues rapidly within games:

Pitch counts aren't the only reason for fatigue; time is another potential culprit. To test for time's effect on velocity, I controlled for pitch count. At 10-15 pitches, a pitcher has generally been on the mound for about five minutes. My data showed that pitchers threw over a tenth of a mile per hour faster when they had been out there under five minutes than when they'd passed the five minute mark. In general, at the same pitch count, the more time has elapsed since a pitcher’s first delivery, the softer he throws.

Next week, I hope to look at how time between innings may impact velocity. The thing to keep in mind with all of this is that every pitcher reacts in his own way to these stresses.  The data would indicate that most all pitchers should be pulled before they reach the fourth time through the order, and that there's no way of telling how most any pitcher is throwing given his pitch count without an awareness of his individual history. The 100-pitch mark isn't when pitchers tire—different athletes tire at their own rates throughout the entire course of competition. The crucial factor here isn’t fatigue, but times through the order. Limiting pitchers to 100 pitches seems to be the right rule, but for the wrong reasons.

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greggborgeson
3/03
Great stuff! Do you have any data on how drop in velocity relates to effectiveness based on the velocity of the pitcher? In other words, if pitcher A starts at 95 mph and drops to 93 mph, is that a greater or lesser decline from a pitcher that starts at 89 and drops to 87?
jgreenhouse
3/04
Gregg, as Mike says, that would be tough to tease out from other effects, but that is the ultimate goal of this line of work.
mikefast
3/03
Gregg, when I looked at changes in effectiveness due to changes in velocity on a season level, I found that pitchers who threw slower were less affected by a loss in velocity.
http://www.hardballtimes.com/main/article/lose-a-tick-gain-a-tick/

Whether that applies equally well within a game, I'm not sure. It's tough to separate multiple effects that are going on as pitchers pitch deeper into the games (seeing same batters multiple times, fatigue, different quality of pitchers in the sample, changing temperature, pinch hitters, etc.).
metty5
3/03
"I donâ€™t believe pitchers should go past 100 pitches. That might seem like the view of a baseball luddite, but itâ€™s quite simple. Throwing 100 pitches means six innings. Surviving six innings equates to 27 batters. Facing 27 batters impends the fourth time through the order. And that spells doom"

Jeremy, I think this opening should have be done without the 6 innings part, and said rather, "Throwing 100 pitches equates to roughly facing 27 batters."

Though, I really enjoyed the rest of the piece.
jgreenhouse
3/04
Yeah, you're probably right. I sometimes try to be clever with my lead-ins, and that can come as a fault. Thanks for the comment.
kingcharlesxii
3/03
One of the most interesting articles I've read this year, thanks!
danmckay
3/03
Wow, really interesting stuff to think about. Thanks.
MindRevolution
3/03
Sounds like the real optimal point would be to limit pitchers to about 2 innings since many pitchers are losing it after 40 pitches or so. Of course that would be a roster construction problem.
JeffreyLyon
3/03
You assume all pitchers are created equal. I'll take Halladay at 60 pitches over (insert generic reliever's name here) any day of the week.
jgreenhouse
3/04
But Jeff, that's not realistic. Because if you take the 5 man rotation that has Halladay, you also have to take a 5th starter like Josh Towers or something. I don't think we should dismiss such radical strategies out of hand.
JeffreyLyon
3/04
I think you misinterpret my point. I'm not saying "a starter at 60 pitches is better than a reliever." I'm saying that there are varying levels of ability in pitchers: a pitcher that is starting to lose effectiveness may still be a better option than the fresh pitcher you chose to replace him with. I can absolutely believe that a 5th starter that is starting to tire is a weaker option than a fresh reliever. I don't, however, believe it is optimal to put a blanket cap across all pitchers. Hallady simply comes across as the most obvious example as a pitcher who is still going to perform better after 60 pitches than many other fresh options you may have.
jgreenhouse
3/05
BrewersTT
3/03
I wonder whether those deltas of +/- 1.0 or so are statistically significant. Also, could they be a result of the error introduced by (necessarily) using the same 25% cutoff for isolating everyone's fastball?
jgreenhouse
3/04
Can you be more specific? I have the data and would be willing to test what theories you may have.
tbwhite
3/03
It seems like there could be a selection biases in play. Generally, pitchers only throw 100 pitches if they have been effective. So, is the data really showing that the pitchers are tiring, or is it just that bigger pitch counts are correlated to having good days ? If you're having a good day maybe it's because your secondary pitches are working that day, and that allows you to dial back a bit on your fastball. Likewise if your secondary stuff isn't working then maybe you try to make up for it with a little extra on your fastball. I can also imagine that if higher pitch counts are associated with pitcher effectiveness, then there could be a correlation to the pitcher working with a larger lead, in which case perhaps they dial it back if they are working with a 5 run lead.

For example in 2010, Sanchez's K:BB ratio goes from 1.81 to 2.04 to 2.13 to 3.54 for pitches 76-100. Does that suggest Sanchez really develops pinpoint control as the game goes on ? Of course not, he throws a lot of pitches when he's throwing well and has good control.

Was the data used for this just from 2010, or does it encompass all of Sanchez's career ? Because his first two years he was largely used as a reliever, which could also bias the results for the lower pitch counts.
jgreenhouse
3/04
Compensating for one pitch with another on a given day is an intriguing thought.

Data is mostly from 2009-2010. I normalized velocity by game, though, so starting vs. relieving shouldn't matter. I'm confident in saying that Sanchez fades at an exceptional rate throughout the game.
tbwhite
3/04
I'm curious what would happen if you limited the sample to starters, and only starts where they exceeded some minimum number of pitches or IP to help control for "having it" vs "not having it". Maybe only look at starts with > 75 pitches, something like that. Of course that might wreak havoc with your sample size.
jgreenhouse
3/06
No, that's absolutely something I should have done. I plan to revisit this topic sometime soon, so I'll look into it.
3/03
Love the article. Looking forward to more. tbwhite raises some really good points that make the causality difficult to establish, but I would imagine that extreme cases (over several seasons) are of value in determining which pitchers likely have unusual fatigue patterns.
lichtman
3/04
Jeremy, does the chart which shows a general decline after a short uptick in the first 20 pitches control for the pitcher? If not, then the chart is suspect since there is likely a different pool of pitchers at each pitch count.

Also, what effect do you think temperature has on this? It would be nice to separate out day and night games to see whether you can tease out the temperature effect, although fatigue in day games might come into play also.
3/04
Do you have data showing that a ~5-10 degree drop in temp. causes a significant change in pitch velocity?
jgreenhouse
3/04
MGL, yes, I've controlled for pitcher with that chart and controlled for that pitcher's velocity within each game. I'm not sure I did either the correct way, however.

My original purpose for this article was actually to find the role of temperature on pitcher fatigue, so it's funny you ask that. I spent a day looking for something and couldn't find anything for a multitude of reasons. I did not separate out day and night games when I looked at it, which I probably should have. I do not know what the best way for testing temperature would be. Please let me know if you have any ideas on how I might go about it, because I find the topic interesting, but I'm rather stumped.
lichtman
3/04
I would start by separating day and night games for a start, although, as I said, fatigue in day games might be a confounding factor.

Otherwise, just run some kind of regression on pitch speed and temp controlling for the other factors of course.

As I personally hate regressions, I would simply split each pitchers games into 2 groups for day games and 2 groups for night games - below a certain temperature and above a certain temperature. You would have to do it for home games, otherwise the stadiums would be a confounding factor (the warm games would tend to be in different stadiums than the cold games).

If you did that, you would have to control for time of the year as well, otherwise your warm games would mostly be in the middle of the season and the cold games at the beginning and end, which could be a confounding factor as well.

Shouldn't be too hard to find a way to see effect of temp on overall velocity and the trends during a game.

Didn't someone have an article a while ago on pitch speed and temp? Also, someone can Alan Nathan could tell you the physical effect of changes in temp on pitch speed due to the differing air density, but that would not include any effects on the pitcher (like being looser in warmer weather or less fatigued in colder weather, etc.).
jgreenhouse
3/06
Yeah, running a regression on this stuff is tough. Lot of noise. It's mainly about how I can control for stuff to isolate temperature. And of course physics guys could tell you how temperature actually affects a ball's velocity and stuff.
lichtman
3/04
If you are asking me (MGL), I don't know. That is what I am asking!
ecudmarsh
3/04
great article,BP has been killing it lately
ecudmarsh
3/04
by thge way, does anyone know whatthe numbers in parenthesis under user-names mean?
TangoTiger1
3/04
deepblue64
3/04
It's basically your id in the membership database, related to how long you have been a member with some oddities.
BrewersTT
3/07
Jeremy, in response to your question above (I can't get the Post Reply button to work for me or I'd have responded directly), my question about statistical significance is directed at the regressions underlying the table showing velocity changes after 100 pitches. When I see a delta of somewhere around +/- 1 mph compared to 85 to 95 mph initial values, with data as noisy as these probably are, I wonder whether the regressions' coefficients are statistically different from zero, and if they are, whether they're stable enough to put faith in their fit at the edges of the dataset.

The other half of my question had to do with the 25% cutoff for identifying fastballs. I certainly understand the merits of choosing one cutoff, but unavoidably there some folks will have a lot of other pitches mixed into that group, others fewer. Therefore, if a pitcher's mix of pitches changes at all as the game moves along, this alone could possibly produce both the small deltas found within any one pitcher's data and the differences across pitchers. In other words, the findings could be an artifact of that assumption.

It's a good article and I'm glad to see such work, so I'm not trying to attack it. But it's our job as the readership to probe the science and make sure it stands up.
jgreenhouse
3/09
Thanks.

The coefficients are statistically significant for the guys I showed in the sense that their p-values are less than .05 or whatever. I'm not sure if that's really what you're getting at, though.

The mix of pitches thing is an issue, but check out the Sanchez graph. He's never thrown harder than 93 past 80 pitches, and he routinely throws 94-95 to start the game. And part of the point I was trying to make is that all pitchers tire at different rates and stuff, so of course I agree choosing one number like 25% as a cutoff isn't great. Wakefield's distribution was definitely messed up. Maybe I should've chosen top 50% of all pitcher's fastballs.

Hope my tone isn't somehow coming off defensive or anything. I really appreciate all comments.
BrewersTT
3/09
Thanks for your response, Jeremy. I have no better suggestion than 25%, and I'm sure trying to settle on exactly the right pitches for each individual would be a huge undertaking. Simplifying assumptions are a part of life. The only thing that pricks my ears up about it is the fact that the loss of velocity is so often so small, relative to the initial velocity. Upon finding a small difference, or a gentle curve, amidst lots of noise and assumptions, it's often tough to be sure it's a real effect. It sounds as though you've thought about that. Very interesting stuff.