Pitcher fatigue, batted balls, and DIPS

Are you tired, Mr. Starter?† I’ve been asking this question of my magic spreadsheet for a while now, and last week, during my look at fatigue factors like pitch count, days of rest, mileage on the arm for the season, and number of times through the lineup, I promised a follow up study on how fatigue affected what happens to a batted ball.† Here it is.
I isolated all batted balls from 2000-2006 (isolated is a strong word: that’s still 500K+ events!)† Like in my last two articles, I first calculated the batter’s and pitcher’s GB rate, LD rate, and FB rate (including pop ups), and then the expected probabilities of each for such a matchup, using the odds ratio method.† Then I took the natural log of that number.† I entered this into a binary logit regression as a control for batter and pitcher tendencies, and then on top of that entered my fatigue variables.† Pitch count was present in all the regressions, then one of the other fatigue variables (rest, mileage, times through order, number of pitches thrown last time out), and then the interaction of pitch count and whatever fatigue measure was under consideration.† (In my day job, we call this a modeator analysis.)
First, what effect does pitch count have on the batted ball profile in general.† As the game wears on, there’s an effect for pitch count such that grounders go down and fly balls go up.† How poetic.† Line drives don’t seem to respond to pitch count.
Let’s talk about mileage.† Like last week, I kept the sample to guys who went a maximum of 10 days between starts on the season to get rid of players who had “hidden mileage” in AAA or the bullpen, plus those who had been injured.† The results: as the season wears on, and the pitcher has more pitches on that arm, there’s a very real effect.† When the ball comes off the bat, it’s more likely to be a flyball and less likely to be a grounder.† Of course, the effect is not going to overwhelm a pitcher’s own tendencies to induce ground balls, but it’s certainly not going to help.† Tired pitchers get the ball up in the zone more often and that’s more likely to be hit in the air.† Now, last week, I didn’t find that there was a significant increase in home runs (or anything other than walks), in terms of outcomes, but batted ball percentages are usually much more statistically stable than are outcome measures.† It’s possible that what used to be ground ball outs are becoming fly ball outs, but I’m not convinced.
Next, let’s talk about rest.† Turns out that days of rest didn’t have any effect whatsoever on the batted ball profile, once you control for batter and pitcher matchup.† In my previous study from last week, I found that a short-rested pitcher was more likely to give up a home run.† So, while he might not throw any more fly ball pitches, his pitches that do go for fly balls are more likely to leave the yard.† A ground ball pitcher likely†wouldn’t have the same problem, because… well a mistake on a ground ball pitch is going to just be a slightly harder hit ground ball… maybe a better chance for a single.† This also brings up the old chestnut about starting sinkerballer pitchers on short rest because their ball is “heavier” and sinks better, leading to more ground balls.† I decided that was worth a look.††I restricted my sample to pitchers who had GB percentages over 50% for the year.† That’s not an exact proxy for sinkerballers, but I’m guessing there’s a few sinkers and splitters being thrown there.† The result: no effect.† Looks like the sinker is sinking any more heavily because of the short rest, but it doesn’t seem to harm the pitcher either.
Finally, let’s talk about the number of times that the pitcher has seen this guy before in this game.† Because I’m controlling for the expectations of this pitcher/batter matchup and for pitch count, any effects for time through the lineup are likely due to the pitcher actually gathering intelligence about the batter.† Are there effects?† Yes, there are.† As the lineup cycles around more, the batter is more likely to hit a ground ball and less likely to hit a line drive.† (That’s a good trade for the pitcher!)† So, it looks as though the pitcher is actually gathering some sort of intelligence on the batter and is perhaps gaining some small advantage.† Oftentimes, Sabermetric analysis has a tendency to reduce at bats to simple agglomorations of probabilities.† Here’s some evidence that we need to take a look at the mental aspect of the game.† Of course the batter and pitcher are trying to learn about one another.† It looks like the pitcher is the one who has the advantage.† Perhaps a pitcher gets the batter out with his “stuff” early and his brain late.
One more area of interest.† Does fatigue affect DIPS?† For a long time, it’s been assumed that balls in play went for hits at a rate that had more to do with the defense than the pitcher.† That’s been based mostly on season-to-season intercorrelations.† But, what about within a game?† The answer is… yes, there is an effect.† At lower pitch counts, a ball in play is less likely to be a hit, again, controlling for batter/pitcher rates.† Additionally, there’s an effect for number of times through the lineup (already controlling for the fact that there will be a pitch count effect.)† So, we would expect that starters who are efficient with their pitch†count†to have a lower BABIP overall.† Fresher pitchers throw pitches that are better able to be turned into outs.† This might explain my question concerning Troy Percival.
There are a few more factors that could be studied.† I didn’t consider age (younger pitchers probably bounce back faster) nor body type (through BMI?), and I haven’t yet looked at relievers.† And then there’s the work that’s sure to come from the Pitch F/X folks who can break this stuff down on a molecular level.

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6 Responses to Pitcher fatigue, batted balls, and DIPS

  1. dan says:

    “And then thereís the work thatís sure to come from the Pitch F/X folks who can break this stuff down on a molecular level.”
    Not sure if this is just a complete coincidence, but Josh Kalk began that exact project today at THT, using fastball velocity (inconclusive) and movement (seemed to function as fatigue indicator). Read the article, it’s quite good.

  2. Pizza Cutter says:

    I read it and enjoyed it. And yes, it’s just a coincidence… unless he’s been spying on me.

  3. Eric Seidman says:

    Haha, nah, I talk to Josh a lot. Between you, he, and myself, we’ve really done a ton on pitcher fatigue.

  4. joe arthur says:

    Pizza,
    very interesting work, and a good framework. But I suspect still more rigor is required.
    1) I didn’t notice that you say in your articles that you control for platoon advantage in your models. Platoon advantage/disadvantage appears to have some impact on batted ball type:
    2000-2007
    (starting pitchers,when batter swinging away; no bunts)
    GB/FB/pop/LD %
    LHPvLHB 51/27/6/16
    LHPvRHB 45/31/7/17
    RHPvRHB 48/30/7/15
    RHPvLHB 48/30/6/16
    The platoon advantage is not random by pitch count. It didn’t occur to me until I ran the numbers, but pitches 1-15 are likely to be against batters 1-4 in the lineup,16-30 relatively likely to be against batters 5-8 and so on. You’ve controlled for batter quality, but there is some platoon-advantage discrepancy which oscillates through the pitch counts …
    platoon disadvantage
    pitch RHPvL LHPvR
    01-15 56.5% 76.4%
    16-30 46.3% 80.2%
    31-45 48.3% 79.6%
    46-60 48.8% 78.6%
    61-75 47.3% 80.0%
    76-90 49.7% 78.3%
    91-105 47.9% 79.1%
    106-120 49.4% 77.3%
    121+ 48.4% 78.3%
    2) you probably know much more about this than me, but how exactly do you use the odds ratio to compute expected result when there are multiple possible outcomes?
    a) unless you do some further adjustment, individual odds ratio calculations of expected GB% + expected FB% + expected LD% will not add up to exactly 100%. Do you have a further step to normalize the expectations back to 100%, and if so, how do you do it?
    b) along the same lines (that the total of expected outcomes between batter and pitcher should sum to 100%), what is the most appropriate model for defining those outcomes? Do you have a more accurate model for batted ball outcomes if you leave out expected walks and strikeouts, or if you leave them in?

  5. Pizza Cutter says:

    The platoon advantage wasn’t something I’d considered. Figure that might be conflated with pitch count in that some teams flip spots in the order for some of their hitters based on the pitcher on the mound. The Indians used to do this in the 90s with Manny Ramirez (righty) hitting above Jim Thome (lefty) when there was a lefty on the mound and the other way around with a righty.
    I suppose I could simply adjust by taking the batter’s probabilities against left-handed pitchers (or righties, whatever) and the pitcher’s… you get the idea, and using those as the basis for my predicted ORs.
    As to the odds ratio question, when looking for significant effects, it wasn’t as important that the probabilities all add up to 100%, but rather that the coefficient on the OR be near 1.0. So, in this specific case, it’s not necessary to adjust. However, the point could come up in other situations. If I were trying to project stat lines (which I did in the first article on the subject), you can adjust for this by simply adding up the probabilities (let’s say that they all add up to 96.7%) and re-adjust based on that. (So, if the prediction came out to 20%, re-adjust by taking .2/.967)

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