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June 11, 2003

Lies, Damned Lies

Batter vs. Pitcher Matchups

by Nate Silver

Don't tell anyone, but I really enjoy watching Randall Simon hit. The loose, goofy motion in his stance as the ball approaches the plate; the flyswatter swing; the big-stepping follow through, his blubber, after half a second in gelatin-like suspension, mimicking the motion of his bat. It's a lot of fun to watch, especially when Simon manages to make contact, which happens more often than you'd ever expect.

I've had the occasion, however, to watch Simon against Kerry Wood a couple of times this year, and from Randall's point of view, the results have been disastrous: zero-for-six with four strikeouts. Not just any kind of strikeouts, mind you, but ugly, pirouetting, breeze-generating, no-chance-in-hell strikeouts, the sort that make you think that Simon could face Wood 500 times and go oh-fer.

I didn't mind this, really; Wood is one of my favorite pitchers. But this particular matchup was interesting to watch because Simon and Wood are such an odd couple: Simon swings at everything, and never draws any walks, but by virtue of his superior hand-eye coordination, manages to keep his strikeout rate very low. Wood, on the other hand, is one of the toughest pitchers in the league to make contact against--though sometimes that's because he isn't throwing the ball anywhere near the strike zone. In any event, Simon's performance against Wood looked so bad than I began to wonder whether the batter isn't at some sort of systematic disadvantage in pairings of these types of players.

To study the question, I'll leverage from a technique that Gary Huckabay and I introduced last month in a 6-4-3 column, comparing the actual performance observed when certain types of batter-pitcher pairings occur against the results predicted by Bill James' log5 formula. Instead of dividing players up based on groundball and flyball rates, this time we'll look at a quick-and-dirty index of plate discipline. Ladies and gentlemen, introducing PDQ:

PDQ = SQRT(BBRate * KRate)

PDQ, or plate discipline quotient, is the geometric mean of a player's walk rate and his strikeout rate. I have some hesitancy about grouping strikeouts and walks together under the same metric--the research I've done for PECOTA suggests that the characteristics operate somewhat independently of one another: an 'impatient' hitter can find himself with either a low strikeout rate (think Nomar Garciaparra) or a high one (think Cory Snyder), depending on the other skills that he brings to the table. Nevertheless, this metric has the virtue of convenience, and using a geometric mean instead of an arithmetic one ensures that we identify players who both strike out and walk a lot (or a little), rather than being exceptional in one category but average in the other.

I went about dividing up hitters and pitchers based on their 2002 PDQ's as follows:

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