from Amazon
Thursday, October 27, 2011
Batter-pitcher matchups
Colin says:
Once we have that expected value, we can also look at the TAv from that batter-pitcher matchup from all previous seasons. We can run this data from 1951 through 2011, giving us sixty years of data and over 16,000 data points to look at.
Using a technique known as ordinary least squares regression, we can see how well our expected TAv and our prior batter-pitcher matchup TAv predict future batter-pitcher matchup TAv. After controlling for whether the batter has the platoon advantage, what we find is that our log5 estimate of the outcome of a batter-pitcher matchup is 67 times more predictive than the batter’s past performance against that pitcher. Now, that’s slightly better for the batter-pitcher matchup data than we might have expected; there were on average 78 times as many PA for the log5 expectation as there were for the batter-pitcher matchup. (Since there are both batter PA and pitcher PA against used to generate the log5 expectation, I used what’s known as a harmonic mean to come up with the PA totals for the log5 expectation.)
We can conclude that one plate appearance against a specific pitcher is slightly more predictive than a plate appearance against any pitcher at all. But that effect is dwarfed by the number of plate appearances a batter makes against all pitchers
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But what about cases where a batter has really owned a pitcher in the past—just utterly demolished him? Let’s restrict ourselves to cases with a prior TAv of .520 against a pitcher, or twice the average TAv. (By happy coincidence, that’s just about two standard deviations above the average, for those of you who care about such things.)
Historically, these have been more predictive of batter success than ordinary batter-pitcher matchups. But they are still dwarfed by the predictive power of our log5 expectation, by a factor of about 24 times. A manager is likely doing himself a favor if he puts a guy with that kind of extreme success in the lineup in place of a batter who’s otherwise reasonably close in ability. However, such cases are extremely rare, and even in these extreme cases, the whole of a batter’s historic performance (combined with knowledge of the platoon advantage) is still a much better gauge of how a batter will perform against a pitcher going forward.
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The data isn’t telling us that batters can’t pick up certain cues about a pitcher, or that a pitcher’s repertoire is equally suited to all batters. However, 10, 50, or even 100 plate appearances aren’t enough to tell us whether what we’re seeing is one player with a special edge against another, or simply a small-sample-size fluke, and there’s too much at stake for La Russa and Washington to let themselves be overly swayed by such statistics to the detriment of their teams.
Thank you Colin for doing the work!
Moral of the story: take your noses out of your spreadsheets and index cards, and watch the baseball game instead.
Colin: I’d like to know the regression equation, of how much to weight the batter-pitcher matchup and how much to weight the log5 expectation.