Penalty kicks involve a choice on both the goalkeeper's and kicker's part about whether to go left or right. Shooters tend to be stronger in one direction or another. Game theory predicts that, if goalkeepers and shooters are following optimal strategies, then attempts at either side are likely to be equally successful. (OB-Sklansky: do you see why?)
A study of 42 top players showed that this prediction was mostly correct.
I wonder if a similar study could be done for baseball. There seem to be more degrees of freedom--- I think that studying just pitch types would be insufficient, as the pitcher has some orthoganal control over where the ball crosses the plate.