{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,7]],"date-time":"2026-04-07T10:05:12Z","timestamp":1775556312099,"version":"3.50.1"},"reference-count":32,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2023,6,19]],"date-time":"2023-06-19T00:00:00Z","timestamp":1687132800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>It seems that one cannot find many papers relating entropy to sport competitions. Thus, in this paper, I use (i) the Shannon intrinsic entropy (S) as an indicator of \u201cteams sporting value\u201d (or \u201ccompetition performance\u201d) and (ii) the Herfindahl-Hirschman index (HHi) as a \u201cteams competitive balance\u201d indicator, in the case of (professional) cyclist multi-stage races. The 2022 Tour de France and 2023 Tour of Oman are used for numerical illustrations and discussion. The numerical values are obtained from classical and and new ranking indices which measure the teams \u201cfinal time\u201d, on one hand, and \u201cfinal place\u201d, on the other hand, based on the \u201cbest three\u201d riders in each stage, but also the corresponding times and places throughout the race, for these finishing riders. The analysis data demonstrate that the constraint, \u201conly the finishing riders count\u201d, makes much sense for obtaining a more objective measure of \u201cteam value\u201d and team performance\u201d, at the end of a multi-stage race. A graphical analysis allows us to distinguish various team levels, each exhibiting a Feller-Pareto distribution, thereby indicating self-organized processes. In so doing, one hopefully better relates objective scientific measures to sport team competitions. Moreover, this analysis proposes some paths to elaborate on forecasting through standard probability concepts.<\/jats:p>","DOI":"10.3390\/e25060955","type":"journal-article","created":{"date-parts":[[2023,6,20]],"date-time":"2023-06-20T02:26:56Z","timestamp":1687228016000},"page":"955","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Shannon Entropy and Herfindahl-Hirschman Index as Team\u2019s Performance and Competitive Balance Indicators in Cyclist Multi-Stage Races"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9973-0019","authenticated-orcid":false,"given":"Marcel","family":"Ausloos","sequence":"first","affiliation":[{"name":"School of Business, University of Leicester, Brookfield, Leicester LE2 1RQ, UK"},{"name":"Group of Researchers Applying Physics in Economy and Sociology (GRAPES), Beauvallon, Rue de la Belle Jardini\u00e8re, 483\/0021 Sart Tilman, Angleur, B-4031 Li\u00e8ge, Belgium"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,6,19]]},"reference":[{"key":"ref_1","unstructured":"De Condorcet, N. 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