OVERVIEW OF COMPLEX SYSTEMS IN SPORT

The complex systems approach offers an opportunity to replace the extant pre-dominant mechanistic view on sport-related phenomena.The emphasis on the environment-system relationship,the applications of complexity principles,and the use of nonlinear dynamics mathematical tools propose a deep change in sport science.Coordination dynamics,ecological dynamics,and network approaches have been successfully applied to the study of different sport-related behaviors,from movement patterns that emerge at different scales constrained by specific sport contexts to game dynamics.Sport benefit from the use of such approaches in the understanding of technical,tactical,or physical conditioning aspects which change their meaning and dilute their frontiers.The creation of new learning and training strategies for teams and individual athletes is a main practical consequence.Some challenges for the future are investigating the influence of key control parameters in the nonlinear behavior of athlete-environment systems and the possible relatedness of the dynamics and constraints acting at different spatio-temporal scales in team sports.Modelling sport-related phenomena can make useful contributions to a better understanding of complex systems and vice-versa.

CAPTURING COMPLEX,NON-LINEAR TEAM BEHAVIOURS DURING COMPETITIVE FOOTBALL PERFORMANCE

This study investigated changes in the complexity （magnitude and structure of variability） of the collective behaviours of association football teams during competitive performance. Raw positional data from an entire competitive match between two professional teams were obtained with the ProZone tracking system. Five compound positional variables were used to investigate the collective patterns of performance of each team including： surface and geometrical centre. Analyses involve the coefficient （ApEn）, as well as the linear association between both area, stretch index, team length, team width, of variation （%CV） and approximate entropy parameters. Collective measures successfully captured the idiosyncratic behaviours of each team and their variations across the six time periods of the match. Key events such as goals scored and game breaks （such as half time and full time） seemed to influence the collective patterns of performance. While ApEn values significantly decreased during each half, the %CV increased. Teams seem to become more regular and predictable, but with increased magnitudes of variation in their organisational shape over the natural course of a match.

SCIENCE OF WINNING SOCCER:EMERGENT PATTERN-FORMING DYNAMICS IN ASSOCIATION FOOTBALL

Quantitative analysis is increasingly being used in team sports to better understand performance in these stylized,delineated,complex social systems.Here,the authors provide a first step toward understanding the pattern-forming dynamics that emerge from collective offensive and defensive behavior in team sports.The authors propose a novel method of analysis that captures how teams occupy sub-areas of the field as the ball changes location.The authors use this method to analyze a game of association football(soccer) based upon a hypothesis that local player numerical dominance is key to defensive stability and offensive opportunity.The authors find that the teams consistently allocated more players than their opponents in sub-areas of play closer to their own goal.This is consistent with a predominantly defensive strategy intended to prevent yielding even a single goal.The authors also find differences between the two teams' strategies:while both adopted the same distribution of defensive,midfield,and attacking players(a 4:3:3 system of play),one team was significantly more effective in maintaining both defensive and offensive numerical dominance for defensive stability and offensive opportunity.That team indeed won the match with an advantage of one goal(2 to 1) but the analysis shows the advantage in play was more pervasive than the single goal victory would indicate.The proposed focus on the local dynamics of team collective behavior is distinct from the traditional focus on individual player capability.It supports a broader view in which specific player abilities contribute within the context of the dynamics of multiplayer team coordination and coaching strategy.By applying this complex system analysis to association football,the authors can understand how players' and teams' strategies result in successful and unsuccessful relationships between teammates and opponents in the area of play.