{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,13]],"date-time":"2026-03-13T15:04:28Z","timestamp":1773414268635,"version":"3.50.1"},"reference-count":49,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2014,1,23]],"date-time":"2014-01-23T00:00:00Z","timestamp":1390435200000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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\u2019s trajectory. By applying FC, one can benefit from newly considered modeling perspectives, such as the fractional coefficient, to estimate a player\u2019s 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\u2019s 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.<\/jats:p>","DOI":"10.3390\/e16020645","type":"journal-article","created":{"date-parts":[[2014,1,24]],"date-time":"2014-01-24T02:42:04Z","timestamp":1390531324000},"page":"645-674","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":41,"title":["Dynamical Stability and Predictability of Football Players: The Study of One Match"],"prefix":"10.3390","volume":"16","author":[{"given":"Micael","family":"Couceiro","sequence":"first","affiliation":[{"name":"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"},{"name":"Ingeniarius, Lda., Rua da Vacari\u00e7a, n\u00ba 37, 3050-381, Mealhada, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9813-2842","authenticated-orcid":false,"given":"Filipe","family":"Clemente","sequence":"additional","affiliation":[{"name":"Polytechnic Institute of Coimbra, Coimbra College of Education (ESEC), Department of Education (DE), Rua Dom Jo\u00e3o III Solum, 3030-329 Coimbra, Portugal"},{"name":"Faculty of Sport Sciences and Physical Education, University of Coimbra, Est\u00e1dio Universit\u00e1rio de Coimbra, Pavilh\u00e3o 3, 3040-156 Coimbra, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-1812-2300","authenticated-orcid":false,"given":"Fernando","family":"Martins","sequence":"additional","affiliation":[{"name":"Polytechnic Institute of Coimbra, Coimbra College of Education (ESEC), Department of Education (DE), Rua Dom Jo\u00e3o III Solum, 3030-329 Coimbra, Portugal"},{"name":"Instituto de Telecomunica\u00e7\u00f5es, Delega\u00e7\u00e3o da Covilh\u00e3, Convento Santo Ant\u00f3nio, 6201-001 Covilh\u00e3, Portugal"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-4274-4879","authenticated-orcid":false,"given":"Jos\u00e9","family":"Machado","sequence":"additional","affiliation":[{"name":"Department of Electrical Engineering, Institute of Engineering, Polytechnic of Porto, Rua Dr. Ant\u00f3nio Bernardino de Almeida, 431, 4200-072 Porto, Portugal"}]}],"member":"1968","published-online":{"date-parts":[[2014,1,23]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"739","DOI":"10.1080\/026404102320675602","article-title":"The use of performance indicators in performance analysis","volume":"20","author":"Hughes","year":"2002","journal-title":"J. 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