They first analysed over 3 million pitches thrown in major-league baseball games between 2002 and 2006. For each type of pitch, they measured the batter's "OPS" – a number that represents how likely a batter is to reach a base or to make a big hit. They found, on average, that fastballs tended to give batters 20 per cent higher OPS than curveballs.Read the entire thing for the (predictable) caveats and nay-saying. OPS isn't the be-all end-all of baseball stats, for one.
If pitchers played according to minimax, the OPS for curveballs and fastballs should be the same, but in fact pitchers gave batters a slight edge by throwing too many fastballs.
Levitt and Kovash then looked at whether or not pitchers chose their pitches as unpredictably as minimax theory says they should. They found that when a pitcher threw a fastball, his next pitch was 4 per cent less likely to be a fastball as well. If pitchers played truly rationally, there would be no such bias towards switching the type of pitch. "Pitchers are being just a little too cute on the mound when they're switching back and forth so often," says Kovash.
I wonder how a pitcher who dialed up pitches totally randomly would fare in the bigs. It could be pretty interesting: randomness means the possibility of, say, throwing five fastballs in a row, then a curve, then four more fastballs. There'd be no such thing as a "fastball count," and a batter who thought that a curveball was "due" would fall prey to the gambler's fallacy.