Are Points in Tennis Independent and Identically Distributed? Evidence From a Dynamic Binary Panel Data Model

Abstract

AbstractThis article tests whether points in tennis are independent and identically distributed (iid). We model the probability of winning a point on service and show that points are neither independent nor identically distributed: winning the previous point has a positive effect on winning the current point, and at “important” points it is more difficult for the server to win the point than at less important points. Furthermore, the weaker a player, the stronger are these effects. Deviations from iid are small, however, and hence the iid hypothesis will still provide a good approximation in many cases. The results are based on a large panel of matches played at Wimbledon 1992–1995, in total almost 90,000 points. Our panel data model takes into account the binary character of the dependent variable, uses random effects to capture the unobserved part of a player's quality, and includes dynamic explanatory variables.KEY WORDS: Binary choiceDependenceDynamic panel dataLinear probability modelNonidentical distributionRandom effectsTennis