Abstract: B. Cotuk, E. Yavuz (2007)

OBJECTIVE The analysis of football in the framework of dynamical systems enhances the comprehension of the time dependent, non-linear and complex interactions which structure the game (Eckmann et al., 1987). In this context detection of transitions in system dynamics by Recurrence Plot Analysis (RPA) may convey crucial information about the changing states of play (Grehaigne et al., 1997). As the struggle for ball possession is a key element of play strategy/ tactics in elite football matches, analysis of the non-linear evolution and transitions of passing sequences of teams may yield information about their play organization. Therefore this study tried to identify sequential passing patterns and transitions between these patterns by RPA in the World Championship 2006.

METHODS A one dimensional time series of passing sequences (total 650) was constructed by counting the number of successive passes of one team (France) until ball loss. The time series was embedded in M-dimensional phase space by construction of state vectors using lagged values of the scalar counts. Recurrence plots were constructed by calculating the Euclidean distances between all pairs of vectors (Grehaigne et al., 1997).

RESULTS Means (p, 0.05, one-way ANOVA), standard deviations and maximum pass counts for successive passing sequences of France in five games are shown (Table 1). The recurrence plot constructed by appending all passing sequences of the five games shows stationary periods (white squares) and sharp transitions (dark black lines) in the system dynamics, which correspond to variable periods in the games.

DISCUSSION By application of RPA to time series of passing sequences in football we were able to identify variable periods of ball possession with stationary system dynamics. Sharp transitions in successive passing dynamics were also detected. Thus, this study implied that RPA was able to identify -historical epochs and events' of team dynamics in football, which could be scrutinized by detailed expert analysis.

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Recurrence plot analysis of successive passing sequences in 2006 World Championship