Take a look over here if you want to get the background for this series, otherwise read on.





Sports + Numbers Prediction: "M

y guess is the NBA will have the biggest returns to inequality as a proxy for teams having stars. With those stars they are not able to afford middling salaries for role players and drop quickly down to minimum salary or exception-level players."





The data





To see the impact of inequality we will look at each team’s Gini coefficient against their winning percentage, controlling for team spending. The resulting equation gives us an r-squared value of 0.32 with both terms being significant (P-values of 0.000008 for spending and 0.00004 for Gini coefficient).

Payroll and Winning %

For every million dollars in team spending the expected increase in winning percentage is 0.005. For a team that spends $20 million more than a comparable team – all else equal – we would expect them to win an additional eight games.

Gini and Winning %

On inequality the coefficient is 0.67. In theory this would tell us that a team with a single superstar making all of the money (stay with me, I understand this is not possible under the NBA CBA) would have 55 more wins than a team with all players making exactly the same salary. In practice we have variation within a much smaller band ranging from 0.09 to 0.56 (see table below for details) so the projected difference if those two teams had the same salary would be 25 games.

Gini and Payroll, color coded by winning percentage

Strength of the relationship over time

The relationship holds up pretty well. Looking just at the correlation between Gini and winning percentage, 2011-12 and 2010-11 come in at 0.37 on the low end and 2012-13 is 0.66. The overall one-on-one correlation for the five year period (2008-2013) is 0.47.

Would you rather have one dollar or four quarters?

One dollar. The NBA has significant (statistically and practically) returns to concentrating spending in a fewer, more talented players over building a team of equals.

Sports + Numbers Predictive Accuracy: High – I went out on a limb predicting that NBA teams need superstars to win (basically what we’re measuring here) and was vindicated by the data.

Details

Because there is some variation between the number of players on each team ranging from 12 (Utah, 2009-10) all the way to 23 (Houston, 2012-13) we need to standardize so that a team with a bunch of minimum salary guys way down the bench doesn’t look more unequal simply by virtue of a bigger team. Since the smallest team in the set is also the max number of players the NBA allows to dress for a game we’ll go with that and highlight only the 12 highest salaries on each team. As a further correction, we will also go through and remove the players who have been amnestied. They do represent an allocation decision by team management, but they do not count against the salary cap so they will not be counted here.