Do Professional Baseball Players Play Mixed Strategies? Evidence from MLB

Abstract

Nash equilibrium in mixed strategies incorporates equalized payoff and serial independence for undominated strategies. We document strong evidence that pitchers in Major League Baseball not only throw fastball-series pitches too often but over-switch between them and breaking balls, not complying with mixed strategies in the pitch-type selection. Moreover, overconfidence and tiredness, rather than commonly assumed experience, are two underlying behavioral mechanisms explaining such deviations. In particular, power pitchers deviate more and fatigued pitchers alternate pitch type less. To address the selection bias, propensity score matching confirms main results persist. Our empirical evidence enriches the real-life mixed strategy applicability.

Keywords: mixed-strategy Nash equilibrium, minimax theorem, overconfidence, overthinking, fatigue

JEL Classification: C72, Z20