A probabilistic match classification model for sports tournaments

TL;DR

This paper introduces a probabilistic model for classifying sports matches that accounts for simultaneous match effects and incentive differences, applied to UEFA tournaments, revealing insights into match competitiveness and collusion risks.

Contribution

It presents a novel probabilistic framework that classifies matches based on simulated qualifying probabilities, addressing limitations of previous models in tournament design.

Findings

Fewer stakeless matches in incomplete round-robin tournaments.

More matches with offensive incentives in incomplete tournaments.

Higher potential collusion risk identified in the new format.

Abstract

Existing match classification models in the tournament design literature have two major limitations: a contestant is considered indifferent only if uncertain future results do never affect its prize, and competitive matches are not distinguished with respect to the incentives of the contestants. We propose a probabilistic framework to address both issues. For each match, our approach relies on simulating all other matches played simultaneously or later to compute the qualifying probabilities under the three main outcomes (win, draw, loss), which allows the classification of each match into six different categories. The suggested model is applied to the previous group stage and the new incomplete round-robin league, introduced in the 2024/25 season of UEFA club competitions. An incomplete round-robin tournament is found to contain fewer stakeless matches where both contestants are indifferent, and substantially more matches where both contestants should play offensively. However, the robustly higher proportion of potentially collusive matches can threaten with serious scandals.