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Entropy 2014, 16(2), 645-674;

Dynamical Stability and Predictability of Football Players: The Study of One Match

RoboCorp, Polytechnic Institute of Coimbra, Engineering Institute of Coimbra (ISEC), Department of Electrical Engineering (DEE), Rua Pedro Nunes-Quinta da Nora, 3030-199 Coimbra, Portugal
Ingeniarius, Lda., Rua da Vacariça, nº 37, 3050-381, Mealhada, Portugal
Polytechnic Institute of Coimbra, Coimbra College of Education (ESEC), Department of Education (DE), Rua Dom João III Solum, 3030-329 Coimbra, Portugal
Faculty of Sport Sciences and Physical Education, University of Coimbra, Estádio Universitário de Coimbra, Pavilhão 3, 3040-156 Coimbra, Portugal
Instituto de Telecomunicações, Delegação da Covilhã, Convento Santo António, 6201-001 Covilhã, Portugal
Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. António Bernardino de Almeida, 431, 4200-072 Porto, Portugal
Author to whom correspondence should be addressed.
Received: 2 August 2013 / Revised: 11 January 2014 / Accepted: 14 January 2014 / Published: 23 January 2014
(This article belongs to the Special Issue Dynamical Systems)
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The game of football demands new computational approaches to measure individual and collective performance. Understanding the phenomena involved in the game may foster the identification of strengths and weaknesses, not only of each player, but also of the whole team. The development of assertive quantitative methodologies constitutes a key element in sports training. In football, the predictability and stability inherent in the motion of a given player may be seen as one of the most important concepts to fully characterise the variability of the whole team. This paper characterises the predictability and stability levels of players during an official football match. A Fractional Calculus (FC) approach to define a player’s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player’s predictability and stability. This paper also formulates the concept of attraction domain, related to the tactical region of each player, inspired by stability theory principles. To compare the variability inherent in the player’s process variables (e.g., distance covered) and to assess his predictability and stability, entropy measures are considered. Experimental results suggest that the most predictable player is the goalkeeper while, conversely, the most unpredictable players are the midfielders. We also conclude that, despite his predictability, the goalkeeper is the most unstable player, while lateral defenders are the most stable during the match. View Full-Text
Keywords: fractional calculus; entropy; stability; predictability; dynamic systems; football; performance analysis; variability fractional calculus; entropy; stability; predictability; dynamic systems; football; performance analysis; variability

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This is an open access article distributed under the Creative Commons Attribution License (CC BY 3.0).
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Couceiro, M.S.; Clemente, F.M.; Martins, F.M.L.; Machado, J.A.T. Dynamical Stability and Predictability of Football Players: The Study of One Match. Entropy 2014, 16, 645-674.

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