Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports |
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| Authors: | Fernando Martins Ricardo Gomes Vasco Lopes Frutuoso Silva Rui Mendes |
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| Institution: | 1.Instituto Politécnico de Coimbra, ESEC, UNICID-ASSERT, 3030-329 Coimbra, Portugal; (F.M.); (R.M.);2.Instituto de Telecomunicações, Delegação da Covilhã, 6201-001 Covilhã, Portugal;3.Instituto Politécnico de Coimbra, IIA, ROBOCORP, 3030-329 Coimbra, Portugal;4.CIDAF, FCDEF, Universidade de Coimbra, 3040-248 Coimbra, Portugal;5.Department of Informatics, Universidade da Beira Interior, 6201-001 Covilhã, Portugal; |
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| Abstract: | Pattern analysis is a widely researched topic in team sports performance analysis, using information theory as a conceptual framework. Bayesian methods are also used in this research field, but the association between these two is being developed. The aim of this paper is to present new mathematical concepts that are based on information and probability theory and can be applied to network analysis in Team Sports. These results are based on the transition matrices of the Markov chain, associated with the adjacency matrices of a network with n nodes and allowing for a more robust analysis of the variability of interactions in team sports. The proposed models refer to individual and collective rates and indexes of total variability between players and teams as well as the overall passing capacity of a network, all of which are demonstrated in the UEFA 2020/2021 Champions League Final. |
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| Keywords: | entropy football social network analysis Markov chain performance analysis dynamical systems |
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