  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.
