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Mixed strategies are a key component of game theory. Investigations into whether or not people use optimal mixed strategies have largely been limited to laboratory settings and have produced mixed results. Recently, the empirical framework has been extended into professional sports.  This study uses pitch-level data from Major League Baseball games to see if pitchers mix their pitches optimally.  The scope of this study is limited to the first pitch of a plate appearance and finds that pitchers are mixing optimally to have success on the first pitch of the plate appearance, but the null hypothesis of optimal play for the plate appearance outcome is rejected.

Keeping the Hitter Off Balance: Mixed Strategies in Baseball