A Stochastic Analysis of Some Two-Person Sports II

We establish a general formula for the game-winning probabilities in table tennis, which extends previous results by Schulman and Hamdan (1977). We use this formula to derive the probability distribution (and hence the expectation and variance) of the number of rallies necessary to achieve any given score. Our results also encompass, with minor modifications, similar results for the game of tennis. We use these findings to investigate (theoretically, and via Monte Carlo simulations) the implications of recent rule change imposed by the International Table Tennis Federation (ITTF). Finally, we briefly indicate how our results can lead to more efficient estimation techniques of individual players’ abilities.