文献计量指数作为 UEFA 冠军联赛淘汰赛阶段表现与竞争平衡的衡量指标
Bibliometric indices as a measure of performance and competitive balance in the knockout stage of the UEFA Champions League
AI总结：
提出用 Euclidean 与 rectangle 文献计量指数及权重方案衡量足球长期结果不确定性，并基于 2003–2023 年欧冠数据验证其稳健性，建议按协会系数设定种子队。
摘要：
我们主张应用文献计量指数来量化体育赛事结果的长期不确定性。文中提出 Euclidean index（欧几里得指数）以奖励质量而非数量，而 rectangle index（矩形指数）可作为核心表现的适当衡量指标。通过公理化分析和若干示例，突出了二者差异。我们的方法还需要一种权重方案来比较不同成就。该方法通过研究 2003 年至 2023 年间进行的 20 个赛季的 UEFA 冠军联赛淘汰赛阶段得到说明：研究考察了俱乐部和国家层面的表现，以及三种类型的竞争平衡。在国家协会层面衡量竞争是一项创新。所有结果关于文献计量指数和所分配权重都表现出显著稳健性。由于国家协会的表现比单个俱乐部的结果更稳定，因此 UEFA 冠军联赛小组赛阶段的种子排位最好基于根据联赛最终排名调整后的协会系数，而不是俱乐部系数。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
