Modeling and prediction of tennis matches at Grand Slam tournaments

In this manuscript, different approaches for modeling and prediction of tennis matches in Grand Slam tournaments are proposed. The data used here contain information on 5,013 matches in men's Grand Slam tournaments from the years 2011-2022. All regarded approaches are based on regression models, modeling the probability of the first-named player winning. Several potential covariates are considered including the players' age, the ATP ranking and points, odds, elo rating as well as two additional age variables, which take into account that the optimal age of a tennis player is between 28 and 32 years. We compare the different regression model approaches with respect to three performance measures, namely classification rate, predictive Bernoulli likelihood, and Brier score in a 43-fold cross-validation-type approach for the matches of the years 2011 to 2021. The top five optimal models with highest average ranks are then selected. In order to predict and compare the results of the tournaments in 2022 with the actual results, a comparison over a continuously updating data set via a "rolling window" strategy is used. Also, again the previously mentioned performance measures are calculated. Additionally, we examine whether the assumption of non-linear effects or additional court- and player-specific abilities is reasonable.