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Mathematical Models to Measure the Variability of Nodes and Networks in Team Sports

Martins, F. ; Gomes, RG ; Lopes, V. ; Silva, F. ; Mendes, R.

Entropy Vol. 23, Nº 8, pp. 1072 - 1072, August, 2021.

ISSN (print): 1099-4300
ISSN (online):

Journal Impact Factor: 1,564 (in 2013)

Digital Object Identifier: 10.3390/e23081072

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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.
Keywords: entropy; football; social network analysis; Markov chain; performance analysis;
dynamical systems