On the distribution of rally length in professional tennis matches

In the literature, information on the rally length distribution is quite incomplete, fragmented and non-homogeneous. In this paper we fill the gap deeply analyzing the distribution of rally length in professional tennis matches in the following directions: i) we provide the empirical distribution of the rally length, not only for some categories, but for each single length; ii) we consider different distributions for men and women and for different surfaces; iii) we find the statistical distribution best fitting the data for each surface; iv) we show how the rally distribution depends on some variables, such as the probabilities of winning a point at serve and players' heights; v) previous points are based on a much larger sample size than other works leading to very reliable results. Our analyses point out that the best distribution for rally length is a zero-one-modified Geometric distribution, whose parameters are functions of the probabilities of winning a point at serve and of the players' heights. Results suggest that the the players' heights is the most impacting variable on the rally length distribution.