A few years back I decided to try to calculate a simple version of MLS parity by: Calculating total points available across a regular season Calculating the amount of TPA taken by the league's best and worst teams for each season Calculating the difference and trends Normalizing (single table, standard 3/1/0 points awarded) as best as possible across seasons I updated that this morning with 2019 results. At a high level, what I found was: LAFC took the second-highest % of TPA all time (71%, following the 73% taken by 1998 LAG and just beating last season's NYRB, at 70%). The best-team average across all seasons is 65%, trending slightly upward. FCC took 24% of the TPA, below the all-time worst-team average of 29% (which has trended downward) and tied for fourth-worst all time. The worst team ever by this measure was 2013 DCU, at 16%. The spread between LAFC and FCC, 47 points, was a good bit larger than the 37-point historical average, and third-widest ever. This number has trended upward over time, generally suggesting a decline in parity according to this measure. Questions, corrections, suggestions, etc., do let me know. Data here: https://docs.google.com/spreadsheets/d/1sn-t6FExw6rCrJSyKirzebUL-49zxdTrUI7HT2MvR6o/edit?usp=sharing
You’re going to have less absolute parity with 24 teams than 16. The 24th worst team is going to normally be better than the 16th worst team. I wonder what the numbers would look like controlling for that.
This occurred to me this morning as I was updating the sheet. It feels right, though I haven't attempted to to quantify it. Probably it would be reasonable to test this for other expanding leagues over similar time periods. I also don't know how meaningful the increase over time actually is, so those trendlines might not be interesting in the first place. The year-to-year numbers are more fun anyway. Taking 70% or more of the available points has only happened three times, though we came close in 2017 too. If it becomes normal for the best team in the league to be that dominant, that seems noteworthy in some way.
With more teams it might be worth calculating a different measure of points disparity, like an HHI or Gini coefficient.
I only know enough about statistics to be dangerous, but your measure of using the best and worst in an expanding data set is not really going to measure parity. Even with absolute parity (coin flips), the more coins you flip, the larger the difference is going to be (on average) between the top head coin and the top tails coin in each flipping season. What you really want to do is break the standard deviation tools.
I don't think I've presented this as much more than a hack, which maybe produces a few interesting observations. With that said, I've done what I'm gonna do on this. I would welcome better efforts from smarter people!
Here are the standard deviations and gini coefficients of PPG for the 2004-2019 MLS seasons. On both graphs, a higher value indicates *less* parity. The standard deviation suggests a slight, totally non-significant decrease in parity, while the Gini shows a slight, even less significant increase in parity. Basically, even with LAFC's dominance this year, it was a below-average or below-trend year for disparity. I wonder if they would look significantly different if I had done total points rather than PPG. Also, measuring year-over-year PPG averages might show more disparity.
Good question. As an experiment, I re-ran the numbers, ranking teams in order of which one won the 2013 U.S. Open Cup. Turns out D.C. United tops that list.
I may be mistaken, but I see 4 teams with points earned percentage higher than LAFC's 71%. All from the shootout era. DC United '98 82%, DC United '99 78%, LA Galaxy '98 77% and Kansas City '97 73%.