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Speaker: Leszek Szczecinski (INRS, University of Quebec, Montreal)
Room: B306
Day: 29/09/2026
Time: 14:00
Title: Sports ranking by points: the underlying model and where there is none
Abstract: Sport leagues rank the players, or the teams, by accumulating points awarded for the outcomes of their matches. Each possible outcome has a fixed value attached to it, for example two points for a win, one for a draw, and none for a loss, as football did for most of its history. Football now awards three points for a win. These values are set by convention, without a probabilistic model of the matches and without reference to the data. By treating the skills of the competitors as the parameters we want to estimate in a probabilistic model of the outcomes, we ask whether there is a model for which the accumulated points contain all the information the results provide about the skills. We show that the model is identified by requiring the point count to be a sufficient statistic for the skills. This holds if and only if the outcomes follow the adjacent-categories model, with the points themselves as its parameters, and the points rule is constant-sum, so that every match distributes the same total between the participants. Familiar rules fail this last condition. In the National Hockey League a match decided in regulation time distributes two points, and one decided in overtime distributes three. The two-point rule distributes two points in every match and satisfies the condition, while the three-point rule that replaced it distributes three in a decided match and only two in a draw. Sufficiency alone does not mean that the standings reproduce the ranking by estimated skills. We give the condition on the schedule under which the two orders agree, which also explains when the Elo rating produces the same order, and we measure how far they differ in nine leagues from football, ice hockey and volleyball. No background beyond basic probability is assumed.
References
Szczecinski, L. (2026). Ranking by points and ordinal models. arXiv preprint arXiv:2608.23859.
https://arxiv.org/abs/2608.23859
BIO: Leszek Szczecinski (M'98-SM'07) received the M.Eng. degree from the Technical University of Warsaw, Warsaw, Poland, in 1992, and the Ph.D. degree from INRS-Telecommunications, Montreal, QC, Canada, in 1997. From 1998 to 2001, he was Assistant Professor with the Electrical Engineering Department, University of Chile, Santiago, Chile. He is currently Professor with INRS, University of Quebec, Montreal. From 2009 to 2010, he was a Marie Curie Research Fellow with the Laboratory of Signals and Systems, CNRS, Gif-sur-Yvette, France. He co-authored the book Bit-Interleaved Coded Modulation: Fundamental, Analysis and Design (Wiley, 2015). His research interests are in the areas of mathematical modelling, estimation, and digital signal processing.
