AI 中文总结
研究一级方程式赛车竞争平衡，提出用加权距离衡量，应用两种加权方案与标准凯梅尼距离比较，发现竞争平衡演变对权重稳健，过去二十年更不利，还揭示与监管变化相关的三个结构断点。
AI 中文摘要
赛车运动中的竞争力可通过比较比赛内的起跑和完赛排名以及赛季中各场比赛的起跑和完赛排名来衡量。由于位置变化的重要性不一致，排名靠前的差异比靠后的更受关注，我们为此提议使用加权距离。应用了两种加权方案并与标准凯梅尼距离进行比较，以分析1950年至2024年的一级方程式赛车。竞争平衡的演变对权重意外地具有稳健性，但关注靠前位置时竞争更激烈。过去二十年的竞争平衡比以往任何时候都更不利。统计测试揭示了竞争平衡中的三个结构断点，它们与监管变化密切相关，凸显了决策者在竞争力演变中的作用。
英文摘要
Competitiveness in racing sports can be measured by comparing the start and finish rankings within races, as well as the start and finish rankings across races in a season. Since the importance of position changes is non-uniform and variance at the top of the ranking is more interesting than at the bottom of the ranking, we propose using weighted distances for this purpose. Therefore, two weighting schemes are applied and compared to the standard Kemeny distance to analyse the Formula One between 1950 and 2024. The evolution of competitive balance is unexpectedly robust to the weights, but competition is more intense if one focuses on the top positions. Competitive balance has been more unfavourable in the last two decades than ever before. Statistical tests uncover three structural breaks in competitive balance that are closely related to regulatory changes, highlighting the role of decision-makers in the evolution of competitiveness.
Comments16 pages, 7 figures, 2 tables
