Did the UEFA Champions League winners start in an easy group?

Abstract

<p class="MsoNormal" style="margin-top: 12.0pt;"><span lang="EN-US" style="font-family: 'times new roman', times, serif; font-size: 14pt;">Competitive balance indicates the degree of control participating teams have over a sports competition. Supporters look for excuses to justify their team’s defeat and the triumph of their rivals. If the competition has required a preliminary qualifying group stage, they will argue that the winning team was in an "easy group" from the start, and their team was unlucky to be in a "difficult group". It is therefore of interest to determine what is an "easy group" and what is a "difficult group". This is directly related to the concept of competitive balance. We have a wide range of indices to measure competitive balance. We will use the Distance to Competitive Balance, a standardized index that complies cardinality property. The perfectly unbalanced distribution is the truncated cascade, which allows the maximum value of concentration to be obtained. We focus our attention on the UEFA Champions League, before and after competition, and we measure the competitive balance of the qualifying stage groups between the 1999/2000 and 2022/2023 seasons. The composition of the UEFA Champions League groups seems to be balanced and has no influence on which team will be the champion. A highly competitive group will be more "difficult" in terms of qualifying than a highly concentrated one. Supporters say that their team was unlucky to be in a “difficult” group, but the data does not prove them right.</span></p>