In light of the end of this year's NBA and NHL postseasons, both Finals in each sport had a team that seems to be there almost every year (Golden State in NBA and Boston in NHL). Which begs the question: are both sports devoid of competitive balance (CB)? Especially in relation to the other 2 major pro sports leagues in North America, MLB and NFL?
I've measured CB before in NCAAB and the NBA, but haven't compared the leagues against eachother. So I've compiled all semifinalists over the past 10 years in each league, and calculated the Herfindahl–Hirschman Index (HHI), which measures CB. In this case, it is the sum of the squares of the number of semifinal (conference championship) appearances by team i (f_i) during the designated period, over the number of possible semifinalists during the period. To account for the fact that there are 4 teams that are semifinalists 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.
NHL has the most competitive balance over the last decade! At least in the conference finals. NBA and NFL are actually both tied for the least amount of CB. The NFL is very much weighed down by the Patriots, who have made 8 of the last 10 conference title games.
What if we just look at the final round of each league?
NHL and MLB are tied, and unsurprisingly, the NBA is by FAR the least balanced (Warriors/Cavs/Heat/Spurs account for 75% (!!!) of the Finals appearances over the last 10 years). Similarly, the Patriots account for half of the Super Bowl appearances over the last decade.
This raises another question: is there any correlation in CB and the salary cap structure of each league? NFL and NHL are hard caps (you literally can't go over the cap), and that appears to exhibit mixed results (primarily due to the Patriots). MLB and NBA have soft caps (you can go over the cap, but you get penalized via escalating taxes for doing so), but MLB has a much softer cap than NBA (less severe penalties). So the CB between the two appears to be more influenced by the structure of their respective playoff rounds and the games themselves (baseball has shorter series and more volatility game-to-game).
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