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January 21, 2013

Baseball Therapy

Pitchouts and My Underage Gambling Problem

by Russell A. Carleton

Last week, my colleague Sam Miller ran a few numbers on the pointless, yet poignant play that is the pitchout (a billion points to whomever catches that reference) and concluded that pitchouts are actually a net loser: they cost the defense/pitching team more in runs than they gain. Sure, individual pitchouts sometimes nab a would-be base stealer (and that's a good thing), but overall, managers guessed wrong so often that the expected payoff wasn't high enough to justify the strategy. Rule number one of strategic thinking is that just because you got lucky on a stupid bet, it doesn't negate the fact that it was a stupid bet.

Sam's math is relatively simple. He points out that pitchouts increase the likelihood that a runner will be caught from about 25 percent to 50 percent. Since the swing in value from a stolen base to a caught stealing is roughly .63 runs, if the manager has guessed right and the runner really is going on that pitchout, the gain is 0.158 runs. To do this, the manager must sacrifice a ball in the count, often meaning that the pitcher will either fall behind or sacrifice the advantage in the count for which he had worked so hard. Sam cites work by our own dearly departed Dan Turkenkopf (congrats Dan on getting hired by a team!) who found that changing a strike to a ball is worth .118 runs. Because about 63.7 percent of pitches go for strikes (I believe he speaks of non-contacted balls... adding in balls in play would change the calculus here, but also would negate the whole point of why we're discussing pitchouts), the manager is sacrificing a 63.7 percent chance at a strike, which is worth .075 runs.

Would you pay 75 cents for a chance at 158 cents? It depends on how good you think the odds are of winning. To figure out what the correct mathematical answer is, let's calculate the break-even point.

Oh yeah, by the way...

Warning! Gory Mathematical Details Ahead!
Cost of giving up a chance at a strike is 0.075 runs

Potential gain of guessing right and increasing the chance of a caught-stealing is 0.158 runs