## Monday, June 24, 2013

### 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.

The four leagues have a striking amount of income equality between teams. Even the least equal of the group – the NHL, with Toronto, Montreal and New York on a different level – comes in at 0.14 while Norway, the country with the most equal distribution of income, has a coefficient of 0.24.

The numbers for the major European soccer leagues come out much more unequal. The Premier League has a clear upper class with Tottenham at £144m coming in 6th, more than 50% more than Newcastle United at £93m in 7th place. The £51m gap is greater than the distance between Newcastle and last place Wigan with £53m. The Bundesliga has a lower low end of the distribution, below even La Liga on the curve, but a stronger middle class relative to the few outliers at the high end. La Liga makes sense as the least equal of the group given their method of television revenue distribution (individual clubs negotiate deals rather than clubs collectively negotiating)[2]. Barcelona and Real Madrid together account for 43% of the revenue in the league.

Income distributions for individual players (sadly available only for the US leagues) skew even more unequal. Given the differences in distribution between owners and players it is likely that owners are more prone than players to share similar incentives in collective bargaining – played out in the form of big wins for NBA and NFL owners in the past few years.

Major League Baseball has the dubious honor of the greatest level of inequality, with rookie contracts and arbitration keeping salaries down on the low end and the Yankees and Angels keeping them up on the high end without a salary cap. Looking at MLB over time thanks to the invaluable Lahman database, the Gini was much lower in the 80s and early 90s before spiking to 0.68 in the mid-90s. The subsequent totals for MLB have settled into the 0.61 to 0.62 level – on par with a country like Botswana or South Africa.

Still, I don’t think any MLBPA members are getting too worked up over it – the minimum salary has gone from \$60,000 (roughly 2.5x the median US household income) to over \$400,000 (8x the median US household income) in the same period.

Data sources:
NBA Teams – http://www.forbes.com/nba-valuations/list/
NBA Players – http://www.draftexpress.com
NFL Teams – http://www.forbes.com/nfl-valuations/list/
NFL Players – http://www.usatoday.com
MLB Teams – http://www.forbes.com/mlb-valuations/list/
MLB Players – Lahman Database (
NHL Teams – http://www.forbes.com/nhl-valuations/list/
NHL Players – http://www.usatoday.com
Premier League – http://www guardian.co.uk/news/datablog/2013/apr/18/premier-league-club-accounts-debt
La Liga – http://monchismen.wordpress.com/2011/09/02/la-liga-tv-revenue-distribution-2011-12/

[1] When Canada wins a Stanley Cup again or the Blue Jays start trotting out Jimmy Key, Joe Carter and Robbie Alomar, I’ll update.

[2] I had to use television revenue only as a proxy for team revenue in La Liga. To be honest I’m not sure it makes them look any worse. The Premier League – with admittedly more equal TV sharing – has a Gini of only 0.16 when TV revenue alone is considered. The inequality that pushes the total up to 0.32 comes from gameday revenue (tickets and food) and sponsorships.

1. I'm interested in calculating the GINI index but for pure competing balance. Therefore, this is the stuff that always counts (regardless of money income/wealth).

Give me some ideas for this.

1. You can calculate a Gini coefficient for other metrics - wins, points etc. - by the same method as is used for income. Order the totals from lowest to highest and then compare the resulting cumulative curve with the line that would result from equal totals of that metric. The ratio of the area under the actual curve to the area under the theoretical "equal" line is the Gini coefficient. ماکان باند

2. Ernesto,

You can calculate a Gini coefficient for other metrics - wins, points etc. - by the same method as is used for income. Order the totals from lowest to highest and then compare the resulting cumulative curve with the line that would result from equal totals of that metric. The ratio of the area under the actual curve to the area under the theoretical "equal" line is the Gini coefficient.

3. Could you do an analysis to see if league inequality, perhaps at the individual level or at the team payroll level, is related to 'competitiveness.' What I mean is this: Do leagues with lower Gini coefficients see more variety in teams making the playoffs over a series of seasons?

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