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Title: Comparing dominance of tennis' big three via multiple-output Bayesian quantile regression models Authors:  Bruno Santos - University of Kent (United Kingdom) [presenting]
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, we delve into comparing some key statistics related to dominance over their opponents for the male players with the most Grand Slam titles, currently: Nadal, Djokovic and Federer. 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. 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. The results agree with the common intuition of Nadal's superiority on clay courts, Federer's superiority on grass courts and Djokovic's superiority on hard courts given their success on each of these surfaces; though Nadal's dominance in clay court games is unique. Federer shows his dominance regarding minutes spent on the court in wins, while Djokovic takes the edge when considering the dimension of relative points won, for most of the comparisons.