Who Does What to Whom in Tennis? A Threshold-Crossing Stochastic Model of Tennis Rallies

In this paper, we view a tennis rally as a succession of shots, played alternatively by two players, whose aim at each shot is to put as much pressure on the opponent as possible while keeping the ball ”in” the court. A compound effect arises since, as the rally unfolds, the cumulative pressure makes it ever harder to hit a shot in the court. To capture these features of a rally, we propose a threshold-crossing stochastic model where, for each shot in a rally to be in the court requires the pressure imparted by the player executing the shot to cross a threshold whose expected value depends on the cumulative pressure of the previous shots. We show how to estimate these thresholds using data on the length of rallies in professional men tennis matches and how to use these thresholds to recover profiles of play for each player indicating who does what to whom in a tennis rally.