Competitive Balance Index

It means the observed spread of teams' win percentages is twice as large as the spread you would expect if every team were equally strong and results were determined by chance over the same schedule. A ratio of one is the idealized, perfectly balanced benchmark; values above one indicate that some teams are systematically better than others, with larger values indicating greater imbalance. Because the denominator adjusts for the number of games, the ratio is comparable across leagues that play schedules of different length.

The HHI, borrowed from industrial economics where it measures market concentration, treats each team's share of total wins like a firm's market share and sums the squared shares. It captures whether wins are spread evenly or concentrated among a few dominant clubs — a concentration perspective on balance distinct from win-percentage dispersion. Owen, Ryan, and Weatherston show that because the raw HHI's range depends on the number of teams, it should be normalized before leagues of different sizes are compared.

Because a league can look balanced within each season yet be dominated by the same team every year, or look imbalanced in a given season yet rotate its champions over time. Single-season dispersion captures only the snapshot, not the dynamics. Humphreys's Competitive Balance Ratio adds the time dimension by comparing within-team variation across seasons to overall variation, distinguishing leagues where standings reshuffle from those with an entrenched hierarchy — a distinction fans and policymakers care about.