Comparing dominance of tennis' big three via multiple-output Bayesian quantile regression models

Abstract

Tennis has seen a myriad of great male tennis players throughout its history and we are often interested in the discussion of who is/was the greatest player of all time. While we do not try to answer this question here, we delve into comparing some key statistics related to dominance over their opponents for the male players with the most Grand Slam titles, currently: Djokovic, Federer and Nadal, in alphabetical order. Here we consider the minutes played and the relative points in each of their completed matches, as a measure of dominance against other players. We consider important covariates such as surface, win or loss, type of tournament and whether their opponent was a top 20 ranked player in the world or not, to create a more complete comparison of their performance. We consider a Bayesian quantile regression model for multiple-output response variables to take into account the dependence between minutes and relative points won. This approach is compelling since we do not need to choose a probability distribution for the joint probability distribution of our response variable. Our results agree with the common intuition of Nadal's superiority in clay courts, Federer's superiority in grass courts and Djokovic's superiority in hard courts given their success in each of these surfaces; though Nadal's dominance in clay court games is unique. Federer shows his dominance regarding minutes spent in the court in wins, while Djokovic takes the edge when considering the dimension of relative points won, for most of the comparisons. While minutes can be directly connected to style of play, the relative points dimension could express more directly different levels of advantage over their opponent, in which Djokovic seems to be the overall leader in this analysis.