Football Match Dynamics Explored by Recurrence Analysis - Lames, Martin; Hermann, Sebastian; Prüßner, René; Meth, Hendrik (Frontiers in Psychology, 2021)
A widely accepted notion of football matches in Performance Analysis (PA) is to consider them as dynamic interaction processes with emerging behaviour (Gréhaigne et al., 1997; McGarry et al., 2014). Describing and analysing these processes requires specific methods. Recurrence analysis is a technique for analysing complex systems in many domains like astrophysics, earth sciences, engineering, biology, cardiology or neuroscience (Marwan et al., 2007). Its general idea is to examine the recurrence behaviour of a system, i.e. when, how often and how close its trajectory in a phase-space returns to a previous state. Positional data of 21 football matches of a German Bundesliga team were examined. Field player’s xy-positions in each second of the match made up the phase space. For each pair of seconds the average distance of the players between their positions on the field in these two time-points was calculated. Recurrence plots (RPs) were obtained by colour-coding these distances. With a recurrence threshold of rt = 9 meters and a minimum line length of lmin = 3 seconds general recurrence parameters were calculated characterizing the individual recurrence behaviour of each match. Three football specific recurrence parameters were defined characterizing recurrence properties of open play. RPs showed commonalities (typical features indicating set plays and continuous game) as well as specific structures per match (number, distribution, and sequence of typical features). Recurrence parameters showed several significant correlations to popular performance indicators like number of goals or passes completed. In extending samples and design of recurrence studies there is a great potential of recurrence analysis to increase the practical and theoretical potential of performance analysis.