Abstract Many empirical studies on competitive balance (CB) use the ratio of the actual standard deviation to the idealized standard deviation of win percentages (RSD). This paper suggests that empirical studies that use RSD to compare CB among different leagues are invalid, but that RSD may be used for time-series analysis on CB in a league if there are no changes in season length. When schedules are unbalanced and/or include interleague games, the final winning percentage is a biased estimator of the true win probability. This paper takes a mathematical statistical approach to derive an unbiased estimator of within-season CB that can be applied to not only balanced but also unbalanced schedules. Simulations and empirical applications are also presented, which confirm that the debiasing strategy to obtain the unbiased estimator of within-season CB is still effective for unbalanced schedules.

中文翻译：

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日程不平衡的竞争平衡

摘要许多关于竞争平衡（CB）的经验研究都使用实际标准偏差与理想赢率百分比标准偏差（RSD）的比率。本文认为，使用RSD比较不同联赛中CB的经验研究是无效的，但如果赛季长度没有变化，则RSD可以用于联赛中CB的时间序列分析。当日程安排不平衡和/或包括同业比赛时，最终获胜百分比是真实获胜概率的有偏估计。本文采用数学统计方法来得出季节内CB的无偏估计量，该估计量不仅可用于均衡计划，而且还可用于不均衡计划。还介绍了仿真和经验应用，