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.

在职业网球中，通常公认服务器具有最初的优势。确实，服务器赢得了大多数积分，这使得服务成为这项运动中最重要的要素之一。在本文中，我们着重于发球优势在赢得积分中的作用，这是反弹时间的函数。我们提出了贝叶斯等渗逻辑回归模型，以获取发球点的概率。特别是，我们通过B样条基函数与运动员特定基函数系数的线性组合来分解获胜概率的对数。此外，我们通过在样条系数上施加约束来确保发球优势随拉力长度的增加而减小。我们还考虑了每个玩家的集会能力，并研究了不同类型的法院如何影响玩家的集会能力。