The Impacts of Increasingly Complex Matchup Models on Baseball Win Probability

2025-11-21

AI Summary

Traditional baseball win-probability models neglect the dynamic pitcher-batter interactions and strategic rationality inherent in in-game decision-making. Method: We propose four progressively sophisticated hierarchical Bayesian matchup models that jointly incorporate hierarchical prior modeling, subgame-perfect Nash equilibrium, baserunner advancement probabilities driven by player steal tendencies, and Monte Carlo simulation. The models integrate pitcher-batter attributes, platoon effects, and recent performance to enable real-time, strategy-aware adaptation. Contribution/Results: In simulated 2024 MLB postseason scenarios, the optimal model yields an average of 1.0 (±0.1) additional wins per season relative to baseline. Moreover, its win-probability forecasts align closely with market odds (Spearman’s ρ = 0.92), demonstrating dual efficacy in both strategic decision support and probabilistic win modeling. This work is the first to embed game-theoretic equilibrium concepts within a hierarchical Bayesian baseball framework while explicitly modeling dynamic baserunning behavior.

Technology Category

• Game Theory and Economic Paradigms: Behavioral Game Theory
• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Bayesian Learning

Application Category

• User Modeling, Personalization and Recommendation: Metrics for user behavior and evaluating success
• Web Mining and Content Analysis: Models for Web evolution
• Economics, Online Markets and Human Computation: Uses of LLMs and GenAI for marketplace design, bidding, and strategic interactions

Abstract

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.

Problem

• Investigating how matchup models impact baseball in-game strategy decisions
• Developing hierarchical Bayesian models to predict plate appearance outcomes
• Evaluating how accurate matchup models affect win probability through simulations

Innovation

• Hierarchical Bayesian models predict plate appearance outcomes
• Game-theoretic framework approximates subgame perfect Nash equilibria
• Models combine pitcher-batter data with base-running probabilities