Measuring Competitive Balance in Sports

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 pre-
dictability 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.