Simulation of Tennis Behaviour Using Finite Markov Chains

Markov chains are a well-known tool in mathematical modelling. In performance analysis, finite Markov chains and the connected transition probabilities can be used to evaluate game behavior. Herein finite Markov chains are especially suited in the modelling of net games like tennis, due to their structure as an alternating sequence of discrete strokes. Finite Markov chain modelling thereby can be used as a descriptive tool, as well as to gain insight in the relationship between sports behavior and outcomes. The transition matrix can be used to display the frequency of game actions in relation to the respective game structure. Likewise, the model calculations from the theory of Markov chains enable determining the relevance of actions therein, concerning overall performance. To permit the usage of finite Markov chain modelling, adherence to the Markov property, often described as the property of “memorylessness”, must be assured. Present study implemented finite Markov chain modelling for elite level tennis at the Australian and French Open. The goal of the present study was to verify the usage of Markov chain modelling in tennis, using a newly designed transition matrix. Furthermore, the aim was to gain insight in the game structure of tennis. Results showed that the new model adhered to the Markov property in an extent, which allowed the usage of selected model predictions for the analysis. Further the analysis revealed insights in the current game structure of tennis, as well as connected influence of the factors court surface and gender of players.