Misaligned incentives in sports: A mathematical analysis of the post-2024 UEFA Champions League qualification

TL;DR

This paper analyzes the unfair qualification rules of the post-2024 UEFA Champions League, demonstrating how misaligned incentives can lead to unfair outcomes, and proposes a mathematical model to address this issue.

Contribution

It introduces a mathematical model to identify and reduce incentives for losing in sports qualification systems, highlighting the need for better collaboration between sports governing bodies and scientists.

Findings

The current qualification system creates incentives for losing.

A mathematical model can help design fairer qualification rules.

UEFA's repeated mistakes suggest systemic issues in system design.

Abstract

UEFA declares that it is committed to respecting the fundamental values of sports. However, the qualification rules of the post-2024 UEFA Champions League are shown to be unfair: a game with misaligned incentives was narrowly avoided in the 2023/24 German Bundesliga. We develop a mathematical model to reveal how incentives for losing can be reduced or eliminated. Since UEFA repeatedly commits the same theoretical mistake in designing the qualification system of its competitions, governing bodies in sports are called to work more closely together with the scientific community.