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

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