Entropy 2014, 16(2), 645-674; doi:10.3390/e16020645
Article

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

1,2email, 3,4,* email, 3,5email and 6email
Received: 2 August 2013; in revised form: 11 January 2014 / Accepted: 14 January 2014 / Published: 23 January 2014
(This article belongs to the Special Issue Dynamical Systems)
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract: 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.
Keywords: fractional calculus; entropy; stability; predictability; dynamic systems; football; performance analysis; variability
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MDPI and ACS Style

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.

AMA Style

Couceiro MS, Clemente FM, Martins FML, Machado JAT. Dynamical Stability and Predictability of Football Players: The Study of One Match. Entropy. 2014; 16(2):645-674.

Chicago/Turabian Style

Couceiro, Micael S.; Clemente, Filipe M.; Martins, Fernando M.L.; Machado, José A.T. 2014. "Dynamical Stability and Predictability of Football Players: The Study of One Match." Entropy 16, no. 2: 645-674.


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