We argue for the application of bibliometric indices to quantify the long-term uncertainty of outcome in sports. The Euclidean index is proposed to reward quality over quantity, while the rectangle index can be an appropriate measure of core performance. Their differences are highlighted through an axiomatic analysis and several examples. Our approach also requires a weighting scheme to compare different achievements. The methodology is illustrated by studying the knockout stage of the UEFA Champions League in the 20 seasons played between 2003 and 2023: club and country performances as well as three types of competitive balance are considered. Measuring competition at the level of national associations is a novelty. All results are remarkably robust concerning the bibliometric index and the assigned weights. Since the performances of national associations are more stable than the results of individual clubs, it would be better to build the seeding in the UEFA Champions League group stage upon association coefficients adjusted for league finishing positions rather than club coefficients.

翻译：本文论证了将文献计量指标应用于体育赛事长期结果不确定性量化的可行性。我们提出用欧几里得指数以质量胜数量，而矩形指数则可作为核心绩效的恰当度量方式。通过公理化分析与若干案例，两种指标的差异得以凸显。本研究还要求建立权重体系以实现不同成就的比较。以2003至2023年间二十个赛季的欧冠联赛淘汰赛阶段为实证对象，我们从俱乐部表现、国家表现及三类竞争平衡维度展开分析。在国家协会层面衡量竞争平衡系本文的创新点。所有结果均显示出对文献计量指标及权重分配的高度稳健性。鉴于国家协会表现较个体俱乐部更具稳定性，建议欧冠小组赛种子队分配应基于经联赛最终排名调整的协会系数，而非俱乐部系数。