A Markov Chain Model of Elite Table Tennis Competition

Abstract

The evaluation of the structure of sports performance is one of the important functions of diagnostics in competitive sport. Especially in game sports, it is important to obtain diagnostic information on competition because of the interactive process between the two teams or players. This interaction cannot be simulated or replicated in training or test situations. When it comes to table tennis, performance diagnostics offers many different techniques and methods to analyze a game. In this context, problems mostly occur in adequately modelling the game. Moreover, the approaches lack a scope of uniform performance criteria. According to a stochastic performance diagnostic concept (Markov Chain) for game sports, we developed four different state-transition-models to describe tactical behaviour in table tennis: (1) game action, (2) stroke position, (3) stroke direction and (4) stroke technique. Afterwards we formalized these models by means of finite Markov Chain (stochastic modelling) to determine the relevance of tactical behaviour to performance by simulation. In this study, 152 games of the top 50 ranked male players in the world were analyzed. The results suggest that in international-level table tennis, the diagonal game from backhand to backhand (“stroke position”), strokes into the long backhand zone (“stroke direction”), and especially the topspin stroke for shake-hand players in general (“stroke technique”), are the most important winning tactical strategies. In comparison with traditional methods used in elite table tennis the approach described here is valuable in quantifying and comparing the relevance of various tactical behaviours to performance.