J Syst Sci Complex (2012) : 1–13 SCIENCE OF WINNING SOCCER: EMERGENT PATTERN-FORMING DYNAMICS IN ASSOCIATION FOOTBALL * Lu´ ıs VILAR · Duarte ARA ´ UJO · Keith DAVIDS · Yaneer BAR-YAM DOI: Received: 27 December 2011/ Revised: 9 May 2012 c The Editorial Office of JSSC & Springer-Verlag Berlin Heidelberg 2010 Abstract Quantitative analysis is increasingly being used in team sports to better understand per- formance in these stylized, delineated, complex social systems. Here we provide a first step toward understanding the pattern-forming dynamics that emerge from collective offensive and defensive be- havior in team sports. We propose a novel method of analysis that captures how teams occupy sub-areas of the field as the ball changes location. We used 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. We found 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 de- fensive strategy intended to prevent yielding even a single goal. We 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 de- fensive 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. Our 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, we can understand how players’ and teams’ strategies result in successful and unsuccessful relationships between teammates and opponents in the area of play. Key words Team sports, collective behavior, performance analysis. Lu´ ıs VILAR Faculty of Physical Education and Sports, Lusofona University of Humanities and Technologies, Lis- bon, Portugal; Faculty of Human Kinetics, Technical University of Lisbon, Lisbon, Portugal. Email: luis.vilar@ulusofona.pt. Duarte ARA ´ UJO Faculty of Human Kinetics, Technical University of Lisbon, Lisbon, Portugal. Keith DAVIDS School of Human Movement Studies, Queensland University of Technologies, Brisbane, Queensland, Australia. Yaneer BAR-YAM New England Complex Systems Institute, Cambridge, Massachusetts, USA. ∗ The first author was supported by the Portuguese Foundation for Science and Technology (SFRH/BD/43251/2008). We thank Shlomiya Bar-Yam, Dominic Albino, Yavni Bar-Yam, and Karla Z. Bertrand for many helpful comments on the manuscript.