论文标题
在欧洲冠军联赛的淘汰赛阶段，文献计量指数是衡量表现和竞争平衡的衡量标准
Bibliometric indices as a measure of performance and competitive balance in the knockout stage of the UEFA Champions League
论文作者
论文摘要
我们主张应用文献计量指数来量化运动中结果的长期不确定性。提出了欧几里得指数以奖励质量而不是数量，而矩形指数可以是核心性能的适当度量。通过公理分析和几个示例，强调了它们的差异。我们的方法还需要一个加权方案来比较不同的成就。通过研究2003年至2023年赛季欧洲冠军联赛的淘汰赛阶段来说明该方法：俱乐部和国家表演以及三种类型的竞争平衡。在国家协会级别的衡量竞争是一种新颖性。关于文献计量指数和分配的权重，所有结果都非常强大。由于国家协会的表演比单个俱乐部的结果更稳定，因此最好是在欧洲冠军联赛小组舞台上建立播种，该协会系数已针对联赛终结职位而不是俱乐部系数进行调整。
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.
