Using 120 years of Major League baseball data, we re-examine the apparent and widely presumed performance advantage of left-handers. We verify the previously known phenomenon that left-handers hit better than right-handers, but we show this advantage exists only because they face pitchers with the opposite hand far more often; they are not innately more talented. We find, however, that left-handed pitchers are indeed better than right-handed pitchers, and we show the perhaps unusual result that a player`s throwing hand plays a role in the quality of his batting. We further show that switch-hitting is largely ineffective, and we explore a symmetry puzzle in which batters of a given hand facing pitchers of a given hand do not bat similarly to batters of the other hand facing pitchers of the other hand. Taken together, we show that the handedness advantage in baseball is about more than the batting hand. Three handedness factors matter: the matchup advantage, the pitcher quality, and the natural handedness of the batter. Of the 40,320 possible rank orderings of the eight combinations of these three handedness factors, our theory predicts one specific order and finds that it indeed holds across the 1.8 million matchups of 15,000 players.
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