Bayesian isotonic logistic regression via constrained splines: an application to estimating the serve advantage in professional tennis

TL;DR

This paper introduces a Bayesian isotonic logistic regression model using constrained splines to analyze how serve advantage in tennis varies with rally length, accounting for player and court effects.

Contribution

It develops a novel Bayesian constrained spline approach to model serve advantage as decreasing with rally length, incorporating player-specific and court-specific effects.

Findings

Serve advantage decreases with rally length.

Court type influences rally ability.

Model applied successfully to Grand Slam data.

Abstract

In professional tennis, it is often acknowledged that the server has an initial advantage. Indeed, the majority of points are won by the server, making the serve one of the most important elements in this sport. In this paper, we focus on the role of the serve advantage in winning a point as a function of the rally length. We propose a Bayesian isotonic logistic regression model for the probability of winning a point on serve. In particular, we decompose the logit of the probability of winning via a linear combination of B-splines basis functions, with athlete-specific basis function coefficients. Further, we ensure the serve advantage decreases with rally length by imposing constraints on the spline coefficients. We also consider the rally ability of each player, and study how the different types of court may impact on the player's rally ability. We apply our methodology to a Grand Slam singles matches dataset.