{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,24]],"date-time":"2026-03-24T11:48:50Z","timestamp":1774352930787,"version":"3.50.1"},"reference-count":27,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T00:00:00Z","timestamp":1651536000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"European Commission","award":["739574"],"award-info":[{"award-number":["739574"]}]},{"name":"European Commission","award":["N2-0171"],"award-info":[{"award-number":["N2-0171"]}]},{"name":"European Commission","award":["SNN-135643"],"award-info":[{"award-number":["SNN-135643"]}]},{"name":"Republic of Slovenia (Investment funding of the Republic of Slovenia and the European Union of the European Regional Development Fund)","award":["739574"],"award-info":[{"award-number":["739574"]}]},{"name":"Republic of Slovenia (Investment funding of the Republic of Slovenia and the European Union of the European Regional Development Fund)","award":["N2-0171"],"award-info":[{"award-number":["N2-0171"]}]},{"name":"Republic of Slovenia (Investment funding of the Republic of Slovenia and the European Union of the European Regional Development Fund)","award":["SNN-135643"],"award-info":[{"award-number":["SNN-135643"]}]},{"DOI":"10.13039\/100005393","name":"Slovenian Research Agency (ARRS)","doi-asserted-by":"publisher","award":["739574"],"award-info":[{"award-number":["739574"]}],"id":[{"id":"10.13039\/100005393","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005393","name":"Slovenian Research Agency (ARRS)","doi-asserted-by":"publisher","award":["N2-0171"],"award-info":[{"award-number":["N2-0171"]}],"id":[{"id":"10.13039\/100005393","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100005393","name":"Slovenian Research Agency (ARRS)","doi-asserted-by":"publisher","award":["SNN-135643"],"award-info":[{"award-number":["SNN-135643"]}],"id":[{"id":"10.13039\/100005393","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Research, Development and Innovation Office","award":["739574"],"award-info":[{"award-number":["739574"]}]},{"name":"National Research, Development and Innovation Office","award":["N2-0171"],"award-info":[{"award-number":["N2-0171"]}]},{"name":"National Research, Development and Innovation Office","award":["SNN-135643"],"award-info":[{"award-number":["SNN-135643"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Information"],"abstract":"<jats:p>In this paper, we provide a simple forward-looking approach to compare rating methods with respect to their stability over time. Given a rating vector of entities involved in the comparison and a ranking indicated by the rating, the stability of the methods is measured by the change in rating vector and ranks of the entities over time from a forward-looking perspective. We investigate various linear algebraic rating methods and use the Euclidean distance and Kendall tau rank correlation to measure their stability in rating and ranking, respectively. The investigations are based on both rolling and expanding window approaches. We apply the methodology to sports as a widely known ranking and rating environment. The results suggest that PageRank and Massey rating methods provide better rating and ranking stability than simple methods, such as winning percentage, and more advanced ones, such as Colley\u2019s least square and Keener\u2019s eigenvector-based method. Finally, a simple way to examine the potential predictive power of the rating methods is also provided.<\/jats:p>","DOI":"10.3390\/info13050232","type":"journal-article","created":{"date-parts":[[2022,5,3]],"date-time":"2022-05-03T08:26:35Z","timestamp":1651566395000},"page":"232","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":7,"title":["A Forward-Looking Approach to Compare Ranking Methods for Sports"],"prefix":"10.3390","volume":"13","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6497-6481","authenticated-orcid":false,"given":"Peter Juma","family":"Ochieng","sequence":"first","affiliation":[{"name":"Institute of Informatics, University of Szeged, 2 \u00c1rp\u00e1d t\u00e9r, H-6720 Szeged, Hungary"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1957-5368","authenticated-orcid":false,"given":"Andr\u00e1s","family":"London","sequence":"additional","affiliation":[{"name":"Institute of Informatics, University of Szeged, 2 \u00c1rp\u00e1d t\u00e9r, H-6720 Szeged, Hungary"},{"name":"Department of Operations Research and Mathematical Economics, Institute of Informatics and Quantitative Economics, Pozna\u0144 University of Economics and Business, 61-875 Pozna\u0144, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7547-1128","authenticated-orcid":false,"given":"Mikl\u00f3s","family":"Kr\u00e9sz","sequence":"additional","affiliation":[{"name":"InnoRenew CoE, Livade 6, 6310 Izola, Slovenia"},{"name":"Andrej Maru\u0161i\u010d Institute, University of Primorska, Muzejski trg 2, 6000 Koper, Slovenia"},{"name":"Department of Applied Informatics, University of Szeged, Boldogasszony sgt. 6, H-6725 Szeged, Hungary"}]}],"member":"1968","published-online":{"date-parts":[[2022,5,3]]},"reference":[{"key":"ref_1","unstructured":"Langville, A.N., and Meyer, C.D. 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