Bivariate Modeling of Tennis First Serve Dependence Using Copula Approach: Insights from Grand Slam Tournaments

Abstract

Modeling performance in tennis has traditionally relied on multivariate statistical techniques, often assuming normality in data distribution. However, these assumptions may not always hold, particularly in the case of binary match outcomes and interdependent performance metrics such as service and return success rates. This study introduces a copula-based approach to model the dependency structure between first serve performance and match outcomes using data from major Grand Slam tournaments: US Open, Australian Open, French Open, and Wimbledon. Applying various marginal distributions (Normal, Log-Normal, Gamma, Weibull, and Logistic) and selecting the best fit using Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC), we construct an optimal copula model for each tournament. We explore elliptical and Archimedean copulas to capture the underlying dependence between serve success rates and match results. Our findings indicate the Frank copula best fits all tournaments, demonstrating a significant positive dependence between serve performance and winning probability. The novelty of this study lies in the application of copula modeling to tennis match analytics, a domain where it has received limited attention, particularly in the context of women matches. Unlike conventional multivariate models, copulas allow for flexible dependence structures without requiring normality assumptions, providing a more accurate representation of real-world data. This approach offers valuable insights for coaches, analysts, and sports strategists by quantifying the impact of serve efficiency on match success. Our findings suggest that optimising first serve performance and return capabilities can significantly enhance a player's likelihood of winning, offering a data-driven framework for strategic decision-making in professional tennis.