Turns out that Steven Levitt, the economist half of the Freakonomics duo, recently co-produced a paper examining whether or not pitchers (and football teams) follow game theory. The bottom line? “Pitchers appear to throw too many fastballs; football teams pass less than they should.”

"Game theory," in this case, refers to the economics principle that "[i]n the perfect world of game theory, two players locked in a zero-sum contest always make rational choices. They opt for the “minimax” solution — the set of plays that minimizes their maximum possible loss – and their play selection does not follow a predictable pattern that might give their opponent an edge." The researchers examined every MLB pitch from 2002 to 2006, grouped them by pitch type, then looked at OPS per pitch type. According to them, fastballs are overused (and pitchers are too predictable in general) to the tune of about 2 losses per team per year (of course, if every team corrected, you'd simply come to a new equilibrium with fewer runs scored).

The linked piece is just an abstract, so go ahead and read through it - it's interesting stuff, and definitely points to a possible Moneyball-like arbitrage situation, in which whatever team learns to exploit these findings first will gain a significant - and essentially cost-free - advantage.