Identifying patterns in squash contests using dynamical analysis and human perception

This report examines the space-time patterns of squash players as they move around the squash court in the context of a dynamical system. The phase relations that describe the squash dyad (i.e., where one player is in relation to the other player) demonstrated a strong tendency towards an anti-phase (180°) relation, as expected. When the data from a number of squash rallies (N = 47) were combined a second stable phase relation of 135° emerged, thus indicating the existence of a previously undetected lead-lag phase relation within the squash dyad. The lead phase relation belonged to the server of the rally in each instance. Further inspections of individual squash rallies demonstrated other properties consistent with a dynamical system description, namely the existence of phase fluctuations (i.e., increased variability in the phase relations), phase transitions (i.e., a switch between stable phase relations), and phase slippages as a result of a missing, or extra, phase cycle for one of the two players. Together, these results indicate that the space-time interactions of squash players might usefully be described in the context of dynamical principles of self-organizing (complex) systems. These findings furthermore suggest that the dynamical properties of the squash dyad may contain important information for identifying the squash patterns that we think we see using visual inspection. To examine this supposition we used the point-light method to represent the movements of the two squash players within a rally as contrasted against a distracter set of varying complexities. Interestingly, humans retained the ability to identify the squash dyad beyond chance even when the distracter set contained squash-like properties. Whether a dynamical analysis of these data is likewise discriminatory in its ability to detect squash behaviours from squash-like behaviours remains to be determined in future research.