In order to make comparisons of competitive balance across sports leagues, we need to take into account how different season lengths influence observed measures of balance. We develop the first measures of competitive balance that are invariant to season length. The most commonly used measure, the ASD/ISD or Noll-Scully ratio, is biased. It artificially inflates the imbalance for leagues with long seasons (e.g., MLB) compared to those with short seasons (e.g., NFL). We provide a general model of competition that leads to unbiased variance estimates. The result is a new ordering across leagues: the NFL goes from having the most balance to being tied for the least, while MLB becomes the sport with the most balance. Our model also provides insight into competitive balance at the game level. We shift attention from team-level to game-level measures as these are more directly related to the predictability of a representative contest. Finally, we measure competitive balance at the season level. We do so by looking at the predictability of the final rankings as seen from the start of the season. Here the NBA stands out for having the most predictable results and hence the lowest full-season competitive balance.

中文翻译：

---

衡量运动中的竞争平衡

为了比较各个体育联盟的竞争平衡，我们需要考虑不同的赛季时长如何影响观察到的平衡度。我们开发了第一个衡量竞争平衡的方法，该方法不随季节的长短而变化。最常用的衡量标准是ASD / ISD或Noll-Scully比率。与淡季（例如NFL）相比，长赛季（例如MLB）的联赛会人为地加剧失衡。我们提供了导致无偏方差估计的一般竞争模型。结果是各联盟之间有了新的秩序：NFL从拥有最多平衡的人变为最少并列的领带，而MLB则成为拥有最多平衡的运动。我们的模型还可以洞察游戏水平上的竞争平衡。我们将注意力从团队级别转移到游戏级别，因为这些都与代表比赛的可预测性直接相关。最后，我们在季节水平上衡量竞争平衡。我们通过从赛季开始时查看最终排名的可预测性来做到这一点。在这里，NBA以最可预测的结果而出众，因此全季比赛平衡最低。