# Is it appropriate to compare sports with different-length seasons using Gini?

I made this plot to try and compare the competitiveness of the major US sports (NHL/NBA/MLB/NFL):

Each point of a given color represents, for a given season, the Gini coefficient of the win percentages in that league. So for example, the rightmost red circle is the Gini for the 2015-16 NBA season (as of yesterday). I calculate the win-loss percentage for each team in the league and feed this as data to ineq::Gini in R, which should be calculating the Gini as explained on Wikipedia.

There may be many criticisms for using the Gini as a measure of inequality, but my concern here stems from something more specific:

The NFL season has 16 games; the NHL & NBA seasons have 82 games; and the MLB season has 162 games. The curves (which, by the way, are 5-year moving averages of the Ginis) seem to match season length in levels, which has led me to wonder:

Is there something mechanical about a longer season leading to a lower level of the Gini coefficient in this context?

If this is indeed the case, is there any sort of bias correction that can be done to level the playing field and allow for fairer comparison across the sports?

• You can try to augment the graph with a confidence band around each curve? – kjetil b halvorsen Apr 12 '16 at 18:00
• Also, could you make the data available? – kjetil b halvorsen Apr 12 '16 at 18:03

Not sure---you could try to get at a data-based answer to your question, by taking the league with shortest season, and calculate the gini coefficient by pooling more and more seasons, and plotting the resulting gini coefficients against "pooled season length".

• thanks for the suggestion. in fact, after posting this Q I tried the reverse -- using pseudo-sub-seasons for baseball (instead of pooling seasons for football). and the correlation is obvious -- season length mechanically depresses Gini. intuitively, an 0-16 season is rare but possible, but anything like an 0-162 season is impossible, even while teams regularly go on 16-game winning/losing streaks; regression to the mean breeds equality. When I get around to it, I'm going to post a new question about how we can account for this. – MichaelChirico Apr 12 '16 at 20:10
• Posted here, and included the code. I'll delete this question. – MichaelChirico Apr 13 '16 at 1:15
• Please, there is no reason for you to delete the question. It is a good question. Question should normally not be deleted, only in very special circumstances. – kjetil b halvorsen Apr 13 '16 at 6:50