Markov-chain Modelling and Simulative Assessment of the Impact of Selected Tactical Behaviours in Modern Tennis

Abstract

Game behaviour in net games or other game sports is often captured in the form of discrete performance indicators which represent frequencies or relative frequencies of key behavioural variables. In this regard however, discrete performance indicators are often of low practical relevance as they lack information on the sequence of actions and the underlying interaction of players in a match. Thereby, establishing a connection between performance indicators and sport success also remains an open challenge. In tennis, finite Markov chain modelling based on a transition matrix has shown promise in circumventing those issues. The transition matrix allows to capture equivalence classes of strokes as a sequence of states with the possibility of transitions between them, basically representing a rally. Furthermore, finite Markov chain modelling enables to determine the relevance of state transitions regarding performance. Since existing state transition models may be outdated a major aim of the current study was to establish a newly designed transition matrix which is representative of the game structure of tennis. The sufficiency of the transition matrix as a descriptive tool was aimed to be demonstrated using actual match data. Furthermore, the relevance of selected state transitions was determined using finite Markov chain modelling. Match data and emerging values for performance relevance were analysed with regard to the influencing factors sex and court surface. This revealed only minor differences regarding both factors, specifically indicating a convergence of game structure in men and women.