Competitive balance in the UEFA Champions League group stage: Novel measures show no evidence of decline
L\'aszl\'o Csat\'o, D\'ora Gr\'eta Petr\'oczy

TL;DR
This paper introduces new indices to measure competitive balance in UEFA Champions League group stages and finds no evidence of decline over two decades.
Contribution
It proposes novel ex ante and dynamic concentration indices to assess competitive balance, challenging previous claims of decline.
Findings
No long-term decline in competitive balance from 2003/04 to 2023/24.
New indices provide alternative measures of competitive balance.
Results suggest stability in tournament competitiveness over time.
Abstract
Competitive balance, which refers to the level of control teams have over a sports competition, is a crucial indicator for tournament organisers. According to previous studies, competitive balance has significantly declined in the UEFA Champions League group stage over the recent decades. Our paper introduces alternative indices to investigate this issue. Two ex ante measures are based on Elo ratings, and four dynamic concentration indicators compare the final group ranking to reasonable benchmarks. Using these indices, we find no evidence of any long-run trend in the competitive balance of the UEFA Champions League group stage between the 2003/04 and 2023/24 seasons.
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