Estimating tennis player abilities and predicting match outcomes using Bayesian methods

Abstract

The main goal of this dissertation is to propose four Bayesian models with the aim of modelling tennis player abilities and predicting outcomes of tennis matches. The models are constructed in order of increasing complexity to strike a balance between computational cost and model performance, where each model builds on the preceding one by incorporating critical concepts drawn from existing literature. The proposed models, inspired by the works of Gorgi et al. (2019) and Bradley and Terry (1952), are reformulated within a Bayesian framework and incorporate concepts from other models, making a novel contribution to the statistical literature. These models are then fitted to an ATP tennis data set compiled by Kovalchik (2019), spanning the years 2000-2022. The model fits are evaluated based on MCMC convergence, Bayes’ Factors and posterior predictive checks. Additionally, the resulting posterior distributions of ability are interpreted by utilising sequence plots and highest posterior density intervals, emphasising whether the rankings obtained using these models are in line with the official leaderboards and provide clearer insights into the skill of the players. Finally, the models are employed to forecast ATP tennis match outcomes for the years 2023 and 2024, using data compiled by Sackmann (2024). The results indicate that the third most complex model, which integrates match statistics and time-varying player abilities, achieves the best model fit and the highest percentage of correct predictions, with accuracy rates reaching 78.1%. In contrast, the simpler models, while comparable in terms of fit, yield prediction accuracies of no more than 66.4%.