Football Match Dynamics Explored by Recurrence Analysis

Abstract

A widely accepted notion of football matches in performance analysis (PA) is to consider them as dynamic interaction processes with emerging behaviors. The description and analysis of these processes requires specific methods. Recurrence analysis is a technique for analyzing complex systems in many domains like astrophysics, earth sciences, engineering, biology, cardiology, and neuroscience. Its general concept is to examine the recurrence behavior of a system, as in when, how often and how close its trajectory in a phase space returns to a previous state. The aim of the study is to apply recurrence analysis to football matches. Positional data from 21 football matches of a German Bundesliga team were examined. The phase space was made up of the field players' x,y-positions at each second of the match. For each pair of seconds, the average distance of all the players between their positions at these two time points was calculated. Recurrence plots (RPs) were obtained by color-coding these distances. With a recurrence threshold of rt = 9 m and a minimum line length of lmin = 3 s, general recurrence parameters were calculated to characterize the individual recurrence behaviors of each match. Three football-specific recurrence parameters were defined to represent recurrence properties of open play. RPs showed commonalities (typical features indicating set plays and continuous gameplay) as well as unique structures during each match (number, distribution, and sequence of typical features). The recurrence parameters showed several significant correlations with traditional performance indicators like number of goals and passes completed, e.g., the correlation between number of goals and recurrence rate is r = −0.622 (p = 0.003). By extending the sample and design of recurrence studies, there is great potential for recurrence analysis to improve both the practical and theoretical potential of performance analysis.

MATHMOD 2022 Discussion Contribution Volume

“…Instead, the calculations and plots were executed programmatically and with the help of mathematical programming and visualisation libraries (e.g. Lames et al, 2021). This circumstance is consistent with the authors' knowledge that, at the time of writing, no tool exists for carrying out recurrence analyses in professional football.…”

“…Applications of the recurrence method in professional football can be found in the work of Lames & Plück (2015), Stöckl et al (2017) and Lames et al (2021). The results of these studies are promising, as they demonstrate the representational capacity of RPs in football matches (Lames & Plück, 2015), the unpredictability of the players' behaviour (Stöckl et al, 2017), significant correlations with common performance indicators (Lames et al, 2021) and a correlation of RPs and RQA parameters to open play (ibid.…”

Implementation of Recurrence Analysis algorithms in a dashboard for practical application in Football

“…Instead, the calculations and plots were executed programmatically and with the help of mathematical programming and visualisation libraries (e.g. Lames et al, 2021). This circumstance is consistent with the authors' knowledge that, at the time of writing, no tool exists for carrying out recurrence analyses in professional football.…”

“…Applications of the recurrence method in professional football can be found in the work of Lames & Plück (2015), Stöckl et al (2017) and Lames et al (2021). The results of these studies are promising, as they demonstrate the representational capacity of RPs in football matches (Lames & Plück, 2015), the unpredictability of the players' behaviour (Stöckl et al, 2017), significant correlations with common performance indicators (Lames et al, 2021) and a correlation of RPs and RQA parameters to open play (ibid.…”

Collective behavior of stock prices in the time of crisis as a response to the external stimulus

“…However, in applications to data which are far from representing low dimensional deterministic dynamics, the ARQA results can be rather independent of D, so that unembedded ARQA performs just as well on experimental series [37]. Such an approach has yielded satisfactory results in previous research [38,39], and specifically in analysing financial time-series [31,33,[40][41][42]. For this reason, we also opt for employing ARQA without embedding.…”