Competitive Balance in College Basketball, Based on the Final Four

A few days ago, I calculated competitive balance (CB) in NCAAB based on the champions of the NIT, looking at the marginally good teams right off of the cut line of the NCAA tournament.

A more accurate representation of overall CB in college basketball is obviously the finalists of the NCAA tournament, so I've updated the Herfindahl–Hirschman Index (HHI), which measures CB. In this case, it is the sum of the squares of the number of Final Four appearances by team i (f_i) during the designated period, over the number of possible Final Four finalists during the period (I'll be using the past 10 years). To account for the fact that there are 4 teams in the Final Four each year, we include a multiplier of 4 in the summation.

The closer HHI is to 1, the less CB there is in the league. Complete CB (4 different teams every single year) would be 0.1.

There have been 22 different Final Four finalists in the past decade (out of a possible 40), which indicates some saturation, far from complete CB. The HHI = 0.225, which supports this notion. The following teams (10 of them) account for 26 Final Fours in the past 10 years:

Team	Count
Kentucky	4
Florida	3
UCLA	3
Michigan State	3
Connecticut	3
North Carolina	2
Duke	2
Butler	2
Ohio State	2
Kansas	2
Sum	26