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Open AccessArticle

Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective

1
Biomedical Engineering Department, Universidad de los Andes, 111711 Bogota, Colombia
2
Grupo Interdisciplinar de Sistemas Complejos (GISC), 28911 Madrid, Spain
3
Complex Systems Group, Rey Juan Carlos University, 28933 Madrid, Spain
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Laboratory of Biological Networks, Centre for Biomedical Technology (CTB-UPM), Universidad Politécnica de Madrid (UPM), 28223 Madrid, Spain
5
ICTP - South American Institute for Fundamental Research, 01140-070 Sao Paulo, Brazil
6
CeSiMo, Facultad de Ingeniería, Universidad de Los Andes, 5101 Merida, Venezuela
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Department of Operations, Innovation and Data Science, ESADE Business School, 08034 Barcelona, Spain
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Centro Universitario Los Lagos, Universidad de Guadalajara, 47463 Lagos de Moreno, Mexico
9
Institute of Unmanned System and Center for OPTical IMagery Analysis and Learning (OPTIMAL), Northwestern Polytechnical University, Xi’an 710072, China
*
Authors to whom correspondence should be addressed.
These authors contributed equally to this work.
Entropy 2020, 22(2), 172; https://doi.org/10.3390/e22020172
Received: 5 December 2019 / Revised: 27 January 2020 / Accepted: 31 January 2020 / Published: 2 February 2020
(This article belongs to the Special Issue Entropy, Nonlinear Dynamics and Complexity)
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’s 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. View Full-Text
Keywords: football; spatial entropy; network science; permutation entropy; statistical complexity; team performance football; spatial entropy; network science; permutation entropy; statistical complexity; team performance
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MDPI and ACS Style

Martínez, J.H.; Garrido, D.; Herrera-Diestra, J.L.; Busquets, J.; Sevilla-Escoboza, R.; Buldú, J.M. Spatial and Temporal Entropies in the Spanish Football League: A Network Science Perspective. Entropy 2020, 22, 172.

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