Competitive balance with unbalanced schedules

초록

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. © 2019 Walter de Gruyter GmbH, Berlin/Boston.

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