Dynamic Minimax Behavior in Professional Tennis Serves Open Access
Kim, Minjoo (Fall 2025)
Abstract
This thesis examines whether professional tennis players follow mixed-strategy minimax behavior in their serve decisions and how the two-stage structure of serving shapes equilibrium play. Building on Walker and Wooders (2001), who test minimax in a static 2x2 framework using first-serve outcomes, I develop a two-stage dynamic model in which a first-serve fault transitions the game into a second-serve subgame with its own payoff structure. In this model, the first-serve payoff is the total probability of winning the point, a risk-return object that combines the serve-in rate, the win probability conditional on an in-serve, and the continuation value of reaching the second serve. Using point-level data from ten men’s singles matches at the 2022 Wimbledon Championships, I these components by serve direction and test three implications of the model. First, second serve win probabilities are statistically indistinguishable across directions, consistent with static minimax in the terminal subgame. Second, directional mixing differs sharply between first and second serves, with second serves reallocating probability mass toward safer body serves. Third, although a naïve static test based only on first serves that land in would reject payoff equalization across directions, dynamic point-level win probabilities on first serves are approximately equalized. A simple risk-return decomposition shows how heterogenous fault rates and conditional success rates, combined with the second-serve continuation value, sustain these equalized payoffs.
Table of Contents
Introduction.................................................................................................................................. 1
Literature Review........................................................................................................................... 3
Model............................................................................................................................................ 5
Data.............................................................................................................................................. 9
Empirical Strategy ........................................................................................................................ 11
Results......................................................................................................................................... 14
Testing for Second Serve Minimax ................................................................................. 14
Testing for Structural Difference of First and Second Serves ............................................ 16
Testing for First Serve Minimax ..................................................................................... 17
Discussion .................................................................................................................................... 23
References..................................................................................................................................... 26
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