Sports Gini: Inequality within major sports leagues

The Gini coefficient is a way to measure the level of income equality in a country. It is calculated by plotting cumulative incomes in ascending order and measuring the gap between the resulting curve and the straight line that results from taking the average income in each instance. This sounds much more complicated than it is (but you can read more about it here).

Here is an example where total income is 100. The red area is the cumulative income. The blue area represents the gap between cumulative income and perfect equality of income.

A country with a Gini coefficient of 0 would have no blue area visible, as the income for each individual is the same so the cumulative income function looks the same as the straight line average income function. Perfect inequality, on the other hand, would have virtually no red visible as all but one of the people earns nothing and the other person earns something.

In the real world, countries tend to fall between 0.25 or so on the low (equal) side and 0.6-0.7 on the high (unequal) side. The lower countries tend to be Scandanavian or Eastern European while the highest are often African or Latin American countries.

Let’s take a look at the Gini for team revenue in the Big 4 US sports leagues[1]: NFL, MLB, NBA and NHL.

Small Ball - Do lighter and/or shorter NBA teams have different winning percentages?

After watching the Pacers hang with the Heat through seven games on the strength of Roy Hibbert and David West pushing the smaller Miami defenders around – and having significant concerns about Nerlens Noel and his 206 lbs. coming to Cleveland with the number one pick – I want to look at the impact of weight on team performance.

I will weight the player weights by minutes played to put an average size on the lineups being rolled out by each team throughout the season and limit myself to the past five seasons so I don’t have to steal too much data from www.basketball-reference.com

Promisingly for Nerlens Noel’s prospects, the weight of the average lineup appears to have almost no correlation with winning percentage (0.05), ORtg (0.08) or DRtg (0.002). Statistics related to playing inside, as you would expect for a heavier team, show bulkier, more substantial correlations: turnover percentage (0.36), ORB% (0.25) and FT/FGA (0.23). The fatter huskier teams also failed to distinguish themselves in attendance with a negative correlation coming in at -0.10.

The distribution of teams is about as close to the textbook definition of random data as you can get. In fact, here is the distribution of random normal data recentered to the mean/standard deviation of the NBA data.

On the other easy-to-visualize metric of team physical appearance – height – there is a similar lack of relationship with the key metrics. Correlation with winning percentage (0.01), ORtg (0.11) and DRtg (0.09) is in the vicinity of perfectly unrelated – the mild improvement in offensive performance of taller teams is offset by an equally mild decrease in defensive performance (lower DRtg is better). Height has a hefty correlation with ORB% (0.28) similar to weight’s correlation with that metric, but the TOV% (0.11) and FT/FGA (0.12) correlations are much slimmer than those for weight.

In the current NBA Finals matchup between the Spurs and the Heat, the season-average lineups for the two teams have the Spurs outweighing the Heat 217.5 to 215.9 pounds (about 0.4 standard deviations) while San Antonio's height advantage is 78.76 with Miami averaging 78.43 inches (a difference of 0.75 standard deviations).

All in all this analysis doesn’t deliver the big insights I was hoping for, but does allow me to unload a small number of weight-related puns. For that I am grateful.