Small-world networks in professional football: conceptual model and data
The aim of this study was to verify whether interactions taking place between professional football players are compatible with the concept of small world networks. We observed 30 matches and analysed 7.583 collective offensive actions, since the beginning of possession of the ball to their loss, including: passes completed, passes received and crosses, involving a total of 22.518 intra-team interactions in the Portuguese Premier League, corresponding to all 2010/2011 season. The players were classified based on their tactical intervention region and movements, through four sectors: 1) goalkeepers; 2) defenders; 3) midfielders, and 4) forwards. Performance data was analysed using the Match Analysis Software Amisco® (version 184.108.40.206). We analysed the relevant actions typically used during offensive phases, including: passes to teammates, crosses into the penalty box and ball receptions. The results suggest that players’ interactive behaviours within a football match support the existence of a scale free network. Defenders and midfielders are the athletes presenting the highest level of connectivity with their teammates. It was concluded that network analysis might be useful to shed some light on the individual contributions to the collective team performance and provide insights on how creative and organizing individuals might act to orchestrate team strategies. This suggests that the proposed methodology can be used to characterize the collective behaviours that emerge through cooperation and competition between players during football matches.
Albert, R., Jeong, H., & Barabási, A.L. (2000). Error and attack tolerance in complex system. Nature, 406, 378. Doi: 10.1038/35019019.
Balague N., Torrents C., Hristovski R., Davids K., & Araújo D. (2013). Overview of complex systems in sport. Journal of System Science and Complexity, 26, 4-13. Doi: 10.1007/s11424-013-2285-0.
Balkundi, P., & Harrison, D. (2006). Ties, leaders, and time in teams: strong inference about network structure’s effects on team viability and perdormance. Academy of Management Journal, 49-68. Doi: 10.5465/AMJ.2006.20785500.
Barabasi, A.L., & Oltvai, Z.N. (2004), Network biology: understanding the cell’s functional organization, Nature Reviews Genetics, 5(2), 101-113. Doi: 10.1038/nrg1272.
Bartlett, R., Button, C., Robins, M., Dutt-Mazumder, A., & Kennedy, G. (2012). Analysing Team Coordination Patterns from Player Movement Trajectories in Football: Methodological Considerations. International Journal of Performance Analysis in Sport, 12(2), 398-424.
Belli, R., Dias, G., Gama, J., Couceiro, M.S., & Vaz, V. (In Press). Análise multidimensional dos indicadores de rendimento desportivo de equipas profissionais de futebol. Revista Portuguesa de Ciências do Desporto.
Carling, C., Williams, A.M., & Reilly, T. (2005), Handbook of soccer match analysis: a systematic approach to improving performance. London: Routledge.
Carling, C. (2010), Analysis of physical activity profiles when running with the ball in a professional soccer team, Journal of Sports Sciences, 28, 319-326. Doi: 10.1080/02640410903473851.
Castellano, J., Alvarez-Pastor, D., & Bradley, P.S. (2014). Evaluation of research using computerised tracking systems (Amisco® and Prozone®) to analyse physical performance in elite soccer: A systematic review. Sports Medicine, 44(5), 701-712. Doi: 10.1007/s40279-014-0144-3.
Clemente, F.M., Couceiro, M.S, Martins, F.M.L., Dias, G., & Mendes, R. (2013). Interpersonal Dynamics: 1v1 Sub-Phase at Sub-18 Football Players’. Journal of Human Kinetics, 36(1), 179-189. Doi: 10.2478/hukin-2013-0018.
Clemente, F., Couceiro, M.S, Martins, F., & Mendes, R. (2014). Using network metrics to investigate football team players’ connections: A pilot study. Motriz, 20, 3, 262-271. Doi: dx.doi.org/10.1590/S1980-65742014000300004.
Clemente, F., Couceiro, M.S, Martins, F., & Mendes, R. (2015). Using Network Metrics in Soccer. Journal of Human Kinetics, 45, 123-134. Doi: 10.1515/hukin-2015-0013.
Clemente, F., Couceiro, M.S, Martins, F., Mendes, R., & Figueiredo, A. (2014). Intelligent systems for analyzing soccer games: The weighted centroid. Ingeniería e Investigación, 34, 3, 70-75.
Couceiro, M.S, Clemente, F., & Martins, F.M. (2014). Toward the Evaluation of
Research Groups based on Scientific Co-authorship Networks: The
Robocorp Case Study. Arab Gulf Journal of Scientific Research, 31(1), 36-52.
Di Salvo, V., Baron, R., Tschan, H., Calderon Montero, F.J., Bachl, N., & Pigozzi, F. (2007). Performance characteristics according to playing position in elite soccer. International Journal of Sports Medicine, 28, 222-227. Doi:10.1055/s-2006-924294.
Duarte, R., Araújo, D., Correia, V., & Davids, K. (2012). Sports Teams as Superorganisms: Implications of Sociobiological Models of Behaviour for Research and Practice in Team Sports Performance Analysis. Sports Medicine, 42(8), 633-642. Doi: 10.2165/11632450-000000000-00000.
Duch, J., Waitzman, J.S., & Amaral, L.A.N. (2010). Quantifying the performance of individual players in a team activity. PLoS ONE, 5, 6: e10937. Doi: 10.1371/journal.pone.0010937.
Folgado H, Lemmink, K.A.P.M., Frencken, W., & Sampaio, J. (2014) Length, width and centroid distance as measures of teams tactical performance in youth football. European Journal of Sport Science, 14(1), 487-492. Doi: 10.1080/17461391.2012.730060.
Freeman, C. L. (1978). Centrality in social networks conceptual clarification. Social Networks, 1(3), 215-239.
Frencken, W., & Lemmink, K. (2008). Team kinematics of small-sided football games: A systematic approach. In T. Reilly, & F. Korkusuz (Eds.), Science and Football VI (pp. 161-166). Oxon: Routledge Taylor & Francis Group.
Fencken, W., Lemmink, K., Delleman, N., & Visscher, C. (2011). Oscillations of centroid position and surface area of football teams in small-sided games. European Journal of Sport Science, 11(4), 215-223. Doi: 10.1080/17461391.2010.499967.
Gama, J., Passos, P., Davids, K., Relvas, H., Ribeiro, J., Vaz, V., & Dias, G. (2014). Network analysis and intra-team activity in attacking phases of professional football. International Journal of Performance Analysis in Sport, 14, 692-708. E-ISSN:1474-8185.
Grund, T.U. (2012), Network structure and team performance: The case of English Premier League soccer teams, Social Networks, 34(4), 682-690.
Horvath S. (2011). Weighted Network Analysis: Applications in Genomics and Systems Biology. London: Springer.
Lames, M., Erdmann, J., & Walter, F. (2010). Oscillations in football – Order and disorder in spatial interactions between the two teams. International Journal of Sport Psychology, 41(4), 85-86.
Malta, P., & Travassos, B. (2014). Characterization of the defense-attack transition of a soccer team. Motricidade, 10, 1, 27-37.Doi: 10.6063/motricidade. 10(1).1544
Mitchell, M. (2009). Complexity. A guided tour. New York: Oxford University Press.
Moura, F. A., Martins, L. E., Anido, R. O., Barros, R. M., & Cunha, S.A. (2012). Quantitative analysis of Brazilian football players’ organization on the pitch. Sports Biomechanics, 11(1),85-96. Doi: 10.1080/14763141.2011.637123.
Passos, P., Davids, K., Araújo, D., Paz, N., Minguéns, J., & Mendes, J. (2011). Network as a novel tool for studying team ball sports as complex social system. Journal of Science and Medicine in Sport, 14, 170-176. Doi:10.1016/j.jsams.2010.10.459.
Peña, J.P., & Touchette, H. (2013). A network theory analysis of football strategies, In C. Clanet (Eds), Sports Physics: Proceedings Euromech Physics of Sports Conference Proc. Éditions de l'École Polytechnique: Palaiseau, 517-528.
Perl, J., & Dauscher, P. (2006). Dynamic pattern recognition in sport by means of artificial neural networks. In R. Begg & M. Palaniswami (Eds.), Computational Intelligence for Movement Science (pp. 299-318). Hershey London-Melbourne-Singapore: Idea Group Publishing.
Perl, J., & Weber, K. (2004). A neural network approach to pattern learning in sport. International Journal of Computer Science in Sport, 3(1), 67-70.
Randers, M.B., Mujika, I., Hewitt, A., Satiesteban, J., Bischoff, R., & Solano R. (2010). Application of four different football match analysis systems: A comparative study. Journal of Sports Sciences, 28(2), 171-182. Doi: 10.1080/02640410903428525.
Ravasz, E., & Barabási, A.L. (2002). Hierarchical Organization in Complex Networks. Physical Review. E, 67, 026122. Doi: 10.1103/PhysRevE.67.026112.
Sargent, J., & Bedford, A. (2013). Evaluating Australian Football League Player Contributions Using Interactive Network Simulation. Journal of Sports Science and Medicine, 12, 116-121.
Travassos, B., Araújo, D., Vilar, L., & McGarry, T. (2011) Interpersonal coordination and ball dynamics in futsal (indoor football). Human Movement Science, 30, 1245-1259. Doi: 10.1016/ j.humov.2011.04.003.
Vaz, V., Gama, G., Valente dos Santos, J., Figueiredo. A., & Dias, G. (2014). Network – Análise da Interação e Dinâmica do Jogo de Futebol. Revista Portuguesa de Ciências do Desporto, 14(1), 12-25.
Vilar, L., Araújo, D., Davids, K., & Travassos, B. (2012). Constraints on competitive performance of attacker-defender dyads in team sports. Journal of Sports Sciences, 30(5), 459-469. Doi: 10.1080/02640414.2011.627942.
Watts, D. J. (2002). A simple model of information cascades on random networks. Proceedings of the National Academy of Science, U.S.A. 99, 5766-5771. Doi: 10.1073/pnas.082090499.
Watts, D. J., & Strogatz, S. H. (1998). Collective dynamics of 'small-world' networks. Nature, 393(6684), 440-442. Doi: doi: 10.1038/30918.
Yamamoto, Y. (2010). Scale-free Property of the Passing Behavior. International Journal of Sport and Health Science, 7, 86-95. Doi: 10.5432/ijshs.IJSHS20090014.
Yamamoto, Y., & Yokoyama, K. (2011). Common and unique network dynamics in football games, PloS ONE, 6, e29638. Doi:10.1371/journal.pone.0029638.
Yamamoto, Y., Yokohama, K., Okumura, M., Kijima, A., Kadota, K., & Gohara, K. (2013). Joint Action Syntax in Japanese Martial Arts, PLoS ONE, 8(9), e72436. Doi: 10.1371/journal.pone.0072436.
Zhang, Z., & Zhang, J. (2009). A Big World Inside Small-World Networks. PLoS ONE 4(5): e5686. Doi: 10.1371/journal.pone.0005686.
Zubillaga, A., Gorospe, G., Hernandez, A., & Blanco, A. (2009). Comparative analysis of the high-intensity activity of soccer players in top level competition. In: T. Reilly, F. Korkusuz (Eds.) Science and Football VI (pp. 182-185). London: Routledge.