Professionals do play Minimax: Revisiting the Nash equilibrium in Major League Baseball

We present a game-theoretic model of baseball as a two-by-two normal-form game between pitchers and batters, where batters decide whether to swing or hold, and pitchers choose whether to throw inside or outside the strike zone. We use machine learning to label pitches that have not been swung at. Our approach enables testing of the predictions derived from the Minimax Theorem for both players. The hypotheses of equality of payoffs across actions and the absence of serial correlation hold for the majority of players. Batters exhibit lower swing rates than theoretical predictions, while pitchers tend to throw inside the strike zone more frequently than expected.