{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,3]],"date-time":"2026-05-03T07:20:05Z","timestamp":1777792805527,"version":"3.51.4"},"reference-count":43,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2020,2,2]],"date-time":"2020-02-02T00:00:00Z","timestamp":1580601600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003141","name":"Consejo Nacional de Ciencia y Tecnolog\u00eda","doi-asserted-by":"publisher","award":["SEP-CONACYT\/CB-2016-01, grant number 285909"],"award-info":[{"award-number":["SEP-CONACYT\/CB-2016-01, grant number 285909"]}],"id":[{"id":"10.13039\/501100003141","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>We quantified the spatial and temporal entropy related to football teams and their players by means of a pass-based interaction. First, we calculated the spatial entropy associated to the positions of all passes made by a football team during a match, obtaining a spatial entropy ranking of Spanish teams during the 2017\/2018 season. Second, we investigated how the player\u2019s average location in the field is related to the amount of entropy of his passes. Next, we constructed the temporal passing networks of each team and computed the deviation of their network parameters along the match. For each network parameter, we obtained the permutation entropy and the statistical complexity of its temporal fluctuations. Finally, we investigated how the permutation entropy (and statistical complexity) of the network parameters was related to the total number of passes made by a football team. Our results show that (i) spatial entropy changes according to the position of players in the field, and (ii) the organization of passing networks change during a match and its evolution can be captured measuring the permutation entropy and statistical complexity of the network parameters, allowing to identify what parameters evolve more randomly.<\/jats:p>","DOI":"10.3390\/e22020172","type":"journal-article","created":{"date-parts":[[2020,2,3]],"date-time":"2020-02-03T11:28:31Z","timestamp":1580729311000},"page":"172","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":33,"title":["Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3365-8189","authenticated-orcid":false,"given":"Johann H.","family":"Mart\u00ednez","sequence":"first","affiliation":[{"name":"Biomedical Engineering Department, Universidad de los Andes, 111711 Bogota, Colombia"},{"name":"Grupo Interdisciplinar de Sistemas Complejos (GISC), 28911 Madrid, Spain"}]},{"given":"David","family":"Garrido","sequence":"additional","affiliation":[{"name":"Grupo Interdisciplinar de Sistemas Complejos (GISC), 28911 Madrid, Spain"},{"name":"Complex Systems Group, Rey Juan Carlos University, 28933 Madrid, Spain"},{"name":"Laboratory of Biological Networks, Centre for Biomedical Technology (CTB-UPM), Universidad Polit\u00e9cnica de Madrid (UPM), 28223 Madrid, Spain"}]},{"given":"Jos\u00e9 L","family":"Herrera-Diestra","sequence":"additional","affiliation":[{"name":"ICTP - South American Institute for Fundamental Research, 01140-070 Sao Paulo, Brazil"},{"name":"CeSiMo, Facultad de Ingenier\u00eda, Universidad de Los Andes, 5101 Merida, Venezuela"}]},{"given":"Javier","family":"Busquets","sequence":"additional","affiliation":[{"name":"Department of Operations, Innovation and Data Science, ESADE Business School, 08034 Barcelona, Spain"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-3664-978X","authenticated-orcid":false,"given":"Ricardo","family":"Sevilla-Escoboza","sequence":"additional","affiliation":[{"name":"Centro Universitario Los Lagos, Universidad de Guadalajara, 47463 Lagos de Moreno, Mexico"}]},{"given":"Javier M.","family":"Buld\u00fa","sequence":"additional","affiliation":[{"name":"Grupo Interdisciplinar de Sistemas Complejos (GISC), 28911 Madrid, Spain"},{"name":"Complex Systems Group, Rey Juan Carlos University, 28933 Madrid, Spain"},{"name":"Laboratory of Biological Networks, Centre for Biomedical Technology (CTB-UPM), Universidad Polit\u00e9cnica de Madrid (UPM), 28223 Madrid, Spain"},{"name":"Institute of Unmanned System and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi\u2019an 710072, China"}]}],"member":"1968","published-online":{"date-parts":[[2020,2,2]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","unstructured":"Duch, J., Waitzman, J.S., and Amaral, L.A.N. (2010). Quantifying the Performance of Individual Players in a Team Activity. PLoS ONE, 5.","DOI":"10.1371\/journal.pone.0010937"},{"key":"ref_2","unstructured":"Cintia, P., Rinzivillo, S., and Pappalardo, L. (2015, January 9). A network-based approach to evaluate the performance of football teams. Proceedings of the Machine Learning and Data Mining for Sports Analytics Workshop, Porto, Portugal."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"1173","DOI":"10.3389\/fpsyg.2017.01173","article-title":"Network Characteristics of Successful Performance in Association Football. A Study on the UEFA Champions League","volume":"8","author":"Pina","year":"2017","journal-title":"Front. Psychol."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1689","DOI":"10.1007\/s40279-017-0695-1","article-title":"Team sports performance analysed through the lens of social network theory: Implications for research and practice","volume":"47","author":"Ribeiro","year":"2017","journal-title":"Sports Med."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"1900","DOI":"10.3389\/fpsyg.2018.01900","article-title":"Using network science to analyse football passing networks: Dynamics, space, time, and the multilayer nature of the game","volume":"9","author":"Busquets","year":"2018","journal-title":"Front. Psychol."},{"key":"ref_6","first-page":"22","article-title":"Spatio-temporal analysis of team sports","volume":"50","author":"Gudmundsson","year":"2017","journal-title":"ACM Comput. Surv."},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Felipe, J.L., Garcia-Unanue, J., Viejo-Romero, D., Navandar, A., and S\u00e1nchez-S\u00e1nchez, J. (2019). Validation of a Video-Based Performance Analysis System (Mediacoach) to Analyze the Physical Demands during Matches in LaLiga. Sensors, 19.","DOI":"10.3390\/s19194113"},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"645","DOI":"10.3390\/e16020645","article-title":"Dynamical stability and predictability of football players: The study of one match","volume":"16","author":"Couceiro","year":"2014","journal-title":"Entropy"},{"key":"ref_9","doi-asserted-by":"crossref","unstructured":"Rossi, A., Pappalardo, L., Cintia, P., Iaia, F.M., Fern\u00e1ndez, J., and Medina, D. (2018). Effective injury forecasting in soccer with GPS training data and machine learning. PLoS ONE, 13.","DOI":"10.1371\/journal.pone.0201264"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"395","DOI":"10.1055\/s-0031-1301320","article-title":"Measuring tactical behaviour in football","volume":"33","author":"Sampaio","year":"2012","journal-title":"Int. J. Sports Med."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"1723","DOI":"10.1080\/02640414.2015.1136068","article-title":"Timescales for exploratory tactical behaviour in football small-sided games","volume":"34","author":"Ric","year":"2016","journal-title":"J. Sports Sci."},{"key":"ref_12","unstructured":"Newman, M.E.J. (2010). Networks: An Introduction, Oxford University Press. [1st ed.]."},{"key":"ref_13","first-page":"1","article-title":"Defining a historic football team: Using Network Science to analyze Guardiola\u2019s FC Barcelona","volume":"9","author":"Busquets","year":"2019","journal-title":"Sci. Rep."},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"21","DOI":"10.1007\/s11424-013-2291-2","article-title":"A network analysis of the 2010 FIFA world cup champion team play","volume":"26","author":"Cotta","year":"2013","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1016\/j.physa.2014.06.037","article-title":"Statistical properties of position-dependent ball-passing networks in football games","volume":"412","author":"Narizuka","year":"2014","journal-title":"Physica A"},{"key":"ref_16","unstructured":"Gyarmati, L., Kwak, H., and Rodr\u00edguez, P. (2014, January 24\u201327). Searching for a Unique Style in Soccer. Proceedings of the ACM International Conference on Knowledge Discovery and Data Mining (KDD) Workshop on Large-Scale Sports Analytics, New York, NY, USA."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"123","DOI":"10.1515\/hukin-2015-0013","article-title":"Using Network Metrics in Soccer: A Macro-Analysis","volume":"45","author":"Clemente","year":"2015","journal-title":"J. Hum. Kinet."},{"key":"ref_18","unstructured":"L\u00f3pez Pe\u00f1a, J., and S\u00e1nchez Navarro, R. (2015). Who can replace Xavi? A passing motif analysis of football players. arXiv."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Gon\u00e7alves, B., Coutinho, D., Santos, S., Lago-Penas, C., Jim\u00e9nez, S., and Sampaio, J. (2017). Exploring team passing networks and player movement dynamics in youth association football. PLoS ONE, 12.","DOI":"10.1371\/journal.pone.0171156"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"193","DOI":"10.2307\/1912537","article-title":"Inequality decomposition by factor components","volume":"50","author":"Shorrocks","year":"1982","journal-title":"Econometrica"},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1093","DOI":"10.1080\/00036846.2010.537638","article-title":"Measuring competitive balance in sports using generalized entropy with an application to English premier league football","volume":"44","author":"Borooah","year":"2012","journal-title":"Appl. Econ."},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"2297","DOI":"10.1073\/pnas.88.6.2297","article-title":"Approximate entropy as a measure of system complexity","volume":"88","author":"Pincus","year":"1991","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"62","DOI":"10.1007\/s11424-013-2290-3","article-title":"Capturing complex, non-linear team behaviours during competitive football performance","volume":"26","author":"Duarte","year":"2013","journal-title":"J. Syst. Sci. Complex."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1016\/0034-4877(76)90050-1","article-title":"Basic properties of the generalized Boltzmann-Gibbs-Shannon entropy","volume":"9","author":"Ochs","year":"1976","journal-title":"Rep. Math. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"753","DOI":"10.1080\/24748668.2016.11868921","article-title":"Application of entropy measures to analysis of performance in team sports","volume":"16","author":"Silva","year":"2016","journal-title":"Int. J. Perform. Anal. Sport"},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1553","DOI":"10.3390\/e14081553","article-title":"Permutation entropy and its main biomedical and econophysics applications: A review","volume":"14","author":"Zanin","year":"2012","journal-title":"Entropy"},{"key":"ref_27","unstructured":"(2020, February 01). Football. Available online: https:\/\/www.optasports.com\/sports\/football."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"445","DOI":"10.2307\/1931034","article-title":"Distance to nearest neighbor as a measure of spatial relationships in populations","volume":"35","author":"Clark","year":"1954","journal-title":"Ecology"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"230","DOI":"10.1038\/nphys2556","article-title":"Successful strategies for competing networks","volume":"9","author":"Aguirre","year":"2013","journal-title":"Nat. Phys."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"174102","DOI":"10.1103\/PhysRevLett.88.174102","article-title":"Permutation entropy: A natural complexity measure for time series","volume":"88","author":"Bandt","year":"2002","journal-title":"Phys. Rev. Lett."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"439","DOI":"10.1016\/j.physa.2005.11.053","article-title":"Generalized statistical complexity measures: Geometrical and analytical properties","volume":"369","author":"Plastino","year":"2006","journal-title":"Physica A"},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"775","DOI":"10.1142\/S021812741002606X","article-title":"Generalized statistical complexity measure","volume":"20","author":"Rosso","year":"2010","journal-title":"Int. J. Bifurc Chaos"},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"154102","DOI":"10.1103\/PhysRevLett.99.154102","article-title":"Distinguish noise from chaos","volume":"99","author":"Rosso","year":"2007","journal-title":"Phys. Rev. Lett."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"755","DOI":"10.1111\/j.1461-0248.2004.00629.x","article-title":"Symbolic dynamics for identifying similarity between rhythms of ecological time series","volume":"7","author":"Cazelles","year":"2004","journal-title":"Ecol. Lett."},{"key":"ref_35","doi-asserted-by":"crossref","first-page":"013819","DOI":"10.1103\/PhysRevA.82.013819","article-title":"Quantifying the statistical complexity of low-frequency fluctuations in semiconductor lasers with optical feedback","volume":"82","author":"Torrent","year":"2010","journal-title":"Phys. Rev. A"},{"key":"ref_36","first-page":"535","article-title":"Ordinal pattern and statistical complexity analysis of daily stream flow time series","volume":"222","author":"Lange","year":"2013","journal-title":"Eur. Phys. J."},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"123111","DOI":"10.1063\/1.5055855","article-title":"Detection of time reversibility in time series by ordinal patterns analysis","volume":"28","author":"Chavez","year":"2018","journal-title":"Chaos"},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1016\/j.physrep.2014.07.001","article-title":"The structure and dynamics of multilayer networks","volume":"544","author":"Boccaletti","year":"2014","journal-title":"Phys. Rep."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"203","DOI":"10.1093\/comnet\/cnu016","article-title":"Multilayer networks","volume":"2","author":"Arenas","year":"2014","journal-title":"J. Complex Netw."},{"key":"ref_40","doi-asserted-by":"crossref","first-page":"016101","DOI":"10.1103\/PhysRevE.76.016101","article-title":"Ensemble approach to the analysis of weighted networks","volume":"76","author":"Ahnert","year":"2007","journal-title":"Phys. Rev. E"},{"key":"ref_41","doi-asserted-by":"crossref","first-page":"440","DOI":"10.1038\/30918","article-title":"Collective dynamics of small-world networks","volume":"393","author":"Watts","year":"1998","journal-title":"Nature"},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"269","DOI":"10.1007\/BF01386390","article-title":"A note on two problems in connection with graphs","volume":"1","author":"Dijkstra","year":"1959","journal-title":"Numer. Math."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Van Mieghem, P. (2011). Graph Spectra for Complex Networks, Cambridge University Press. [1st ed.].","DOI":"10.1017\/CBO9780511921681"}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/172\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,11]],"date-time":"2025-10-11T08:54:02Z","timestamp":1760172842000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/22\/2\/172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2020,2,2]]},"references-count":43,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2020,2]]}},"alternative-id":["e22020172"],"URL":"https:\/\/doi.org\/10.3390\/e22020172","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2020,2,2]]}}}