The Impacts of Increasingly Complex Matchup Models on Baseball Win Probability

Baseball is a game of strategic decisions including bullpen usage, pinch-hitting and intentional walks. Managers must adjust their strategies based on the changing state of the game in order to give their team the best chance of winning. In this thesis, we investigate how matchup models -- tools that predict the probabilities of plate appearance outcomes -- impact in-game strategy and ultimately affect win probability. We develop four progressively complex, hierarchical Bayesian models that predict plate appearance outcomes by combining information from both pitchers and batters, their handedness, and recent data, along with base running probabilities calibrated to a player's base-stealing tendencies. Using each model within a game-theoretic framework, we approximate subgame perfect Nash equilibria for in-game decisions, including substitutions and intentional walks. Simulations of the 2024 MLB postseason show that more accurate matchup models can yield tangible gains in win probability -- as much as one additional victory per 162-game season. Furthermore, employing the most detailed model to generate win predictions for actual playoff games demonstrates alignment with market expectations, underscoring both the power and potential of advanced matchup modeling for on-field strategy and prediction.