Background
In recent years the usage of video based tracking systems (such as Prozone, Deltatre and AMISCO Pro) in sporting events increasingly established in order to provide objective performance information to sports coaches. Based on the above merits, extensive efforts were and are directed to sought and ascertain the feasibility of different diagnostic tools that will provide researchers a landscape into the detection of patterns formation in sport settings (Mackanzie et al., 2013). Especially many studies in the field of soccer were investigated (Sampaio et al., 2012; Couceiro et al., 2014). More recently, an increasing number of researchers view a soccer match from a dynamical system perspective to get a more holistic comprehension of the soccer matches (Grehaigne et al., 1997; Mc Garry, 2002; James et al., 2012;). The core theme of dynamical system perspective is to analyze the dynamic constellation of the soccer players based on the spatio-temporal position data. The purpose of this study is to analyze the tendency of the dynamic constellation (based on position data) of the players in a soccer match to recur to a former constellation. Further analyzing the property of recurrence in a soccer match may be a successful method to attain a better understanding about the predictive capacity of performance in soccer. Many dynamic processes in physics, meteorology, biology and neuroscience were modeled by recurrence analyses (RQA) and recurrence plots (RP) in recent years (Marwan et al., 2007) So far, there was no approach to apply this tool in team sport and specifically in soccer. This study aims at exploring the appropriateness of recurrence analyses to describe characteristics of soccer matches.
Methods
The positional data from 22 players in 12 soccer matches from German Bundesliga season 2009/2010 provided by AMISCO were used for recurrence analyses. Pre-processing and the analyses were realized by a self-developed application. Distance Plots and thresholded plots for the 12 soccer matches were created. Further a moving windowed RQA for soccer matches was developed.
Results
Recurrence plots showed common and individual pattern of the matches. Qualitatively it is possible to identify distinguished color bands in the distance plots corresponding to certain events like free and corner kicks as well as goals. The threshold plots show typical pattern like diagonal and vertical lines of recurrence plots and further specific characteristics of soccer games. The development in the density of recurrence points per second over the course of game typifies the match. Certain events in the game receive significant lower recurrence points in the seconds around the event than position play does. Partially significant correlations are recorded between the game statistics and the RQA parameters. The parameters show significant differences between the first five minutes of the game and the second five minutes of the match.
Discussion and conclusions
The recurrence analysis is a new and appropriate method to model soccer games. Further the recurrence parameters supply descriptions which have an importance for the soccer match. Higher recurrence rates in the initial match phase may be caused by tactical efforts due to surprise the opponent and score an early goal. Significant correlations between match statistics and recurrence parameters prove validity of modeling soccer with recurrence analyses. Thus, there is an improved description of soccer as a complex system with dynamic interactions and emerging behavior based on recurrence analyses.