Mutual point-winning probabilities (MPW): a new performance measure for table tennis

We propose a new performance measure for table tennis players: the mutual point-winning probabilities (MPW) as server and receiver. The MPWs quantify a player's chances to win a point against a given opponent, and hence nicely complement the classical match statistics history between two players. These new quantities are based on a Bradley-Terry-type statistical model taking into account the importance of individual points, since a rally at 8-2 in the first set is less crucial than a rally at the score of 9-9 in the final set. The MPWs hence reveal a player's strength on his/her service against a given opponent as well as his/her capacity of scoring crucial points. We estimate the MPWs by means of maximum likelihood estimation and show via a Monte Carlo simulation study that our estimation procedure works well. In order to illustrate the MPWs' versatile use, we have organized two round-robin tournaments of ten respectively eleven table tennis players from the Belgian table tennis federation. We compare the classical final ranking to the ranking based on MPWs, and we highlight how the MPWs shed new light on strengths and weaknesses of the players.