Modelling the interaction in game sports - relative phase and moving correlations.

Model building in game sports should maintain the constitutive feature of this group of sports, the dynamic interaction process between the two parties. For single net/wall games relative phase is suggested to describe the positional interaction between the two players. 30 baseline rallies in tennis were examined and relative phase was calculated by Hilbert transform from the two time-series of lateral displacement and trajectory in the court respectively. Results showed that relative phase indicates some aspects of the tactical interaction in tennis. At a more abstract level the interaction between two teams in handball was studied by examining the relationship of the two scoring processes. Each process can be conceived as a random walk. Moving averages of the scoring probabilities indicate something like a momentary strength. A moving correlation (length = 20 ball possessions) describes the momentary relationship between the teams' strength. Evidence was found that this correlation is heavily time-dependent, in almost every single game among the 40 examined ones we found phases with a significant positive as well as significant negative relationship. This underlines the importance of a dynamic view on the interaction in these games. Key PointsGame sports.Mathematical modelling.Relative phase.Random walks.