A Forward-Looking Approach to Compare Ranking Methods for Sports
- 1. Institute of Informatics, University of Szeged, 2 Árpád tér, H-6720 Szeged, Hungary
- 2. Institute of Informatics, University of Szeged, 2 Árpád tér, H-6720 Szeged, Hungary ; Department of Operations Research and Mathematical Economics, Institute of Informatics and Quantitative Economics, Poznań University of Economics and Business, 61-875 Poznań, Poland
- 3. InnoRenew CoE, Livade 6, 6310 Izola, Slovenia ; Andrej Marušič Institute, University of Primorska, Muzejski trg 2, 6000 Koper, Slovenia ; Department of Applied Informatics, University of Szeged, Boldogasszony sgt. 6, H-6725 Szeged, Hungary
Description
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’s least square and Keener’s eigenvector-based method. Finally, a simple way to examine the potential predictive power of the rating methods is also provided.
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