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Node and Network Entropy—A Novel Mathematical Model for Pattern Analysis of Team Sports Behavior

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

Mathematics Vol. 8, Nº 9, pp. 1543 - 1543, September, 2020.

ISSN (print): 2227-7390
ISSN (online):

Journal Impact Factor: 1,747 (in 2019)

Digital Object Identifier: 10.3390/math8091543

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Abstract
Pattern analysis is a well-established topic in team sports performance analysis, and is
usually centered on the analysis of passing sequences. Taking a Bayesian approach to the study of
these interactions, this work presents novel entropy mathematical models for Markov chain-based
pattern analysis in team sports networks, with Relative Transition Entropy and Network Transition
Entropy applied to both passing and reception patterns. To demonstrate their applicability, these
mathematical models were used in a case study in football—the 2016/2017 Champions League Final,
where both teams were analyzed. The results show that the winning team, Real Madrid, presented
greater values for both individual and team transition entropies, which indicate that greater levels
of unpredictability may bring teams closer to victory. In conclusion, these metrics may provide
information to game analysts, allowing them to provide coaches with accurate and timely
information about the key players of the game.
Keywords: social network analysis; entropy; Markov chain; football