Returns to inequality in the NBA

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

Sports + Numbers Prediction: "My 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.

Year	Team	W	L	W-L%	Top 12 $	GINI
2013	MIA	66	16	0.805	$79,995,141	0.44
2013	OKC	60	22	0.732	$65,929,729	0.47
2013	SAS	58	24	0.707	$67,332,396	0.40
2013	DEN	57	25	0.695	$61,650,463	0.38
2013	LAC	56	26	0.683	$68,272,745	0.41
2013	MEM	56	26	0.683	$62,131,353	0.44
2013	NYK	54	28	0.659	$76,586,215	0.48
2013	BKN	49	33	0.598	$82,388,869	0.49
2013	IND	49	32	0.605	$64,818,015	0.40
2013	GSW	47	35	0.573	$69,221,742	0.37
2013	CHI	45	37	0.549	$74,009,530	0.45
2013	LAL	45	37	0.549	$98,823,566	0.49
2013	HOU	45	37	0.549	$45,392,431	0.34
2013	ATL	44	38	0.537	$62,726,837	0.36
2013	UTA	43	39	0.524	$64,244,045	0.34
2013	BOS	41	40	0.506	$70,638,412	0.41
2013	DAL	41	41	0.5	$58,736,229	0.46
2013	MIL	38	44	0.463	$59,040,570	0.28
2013	PHL	34	48	0.415	$65,417,063	0.35
2013	TOR	34	48	0.415	$64,238,328	0.35
2013	POR	33	49	0.402	$52,809,379	0.38
2013	MIN	31	51	0.378	$59,396,624	0.31
2013	DET	29	53	0.354	$62,110,289	0.34
2013	WAS	29	53	0.354	$56,053,756	0.43
2013	SAC	28	54	0.341	$51,487,361	0.23
2013	NOL	27	55	0.329	$62,036,039	0.39
2013	PHX	25	57	0.305	$49,987,371	0.25
2013	CLE	24	58	0.293	$48,363,105	0.24
2013	CLT	21	61	0.256	$56,067,933	0.30
2013	ORL	20	62	0.244	$61,696,050	0.33
2012	SAS	50	16	0.758	$71,910,874	0.49
2012	CHI	50	16	0.758	$68,355,029	0.39
2012	OKC	47	19	0.712	$55,572,869	0.33
2012	MIA	46	20	0.697	$72,633,396	0.45
2012	IND	42	24	0.636	$43,148,483	0.38
2012	LAL	41	25	0.621	$86,973,025	0.49
2012	MEM	41	25	0.621	$68,750,720	0.44
2012	LAC	40	26	0.606	$65,469,102	0.39
2012	ATL	40	26	0.606	$71,000,383	0.45
2012	BOS	39	27	0.591	$77,542,411	0.46
2012	DEN	38	28	0.576	$56,716,901	0.33
2012	ORL	37	29	0.561	$66,331,867	0.42
2012	UTA	36	30	0.545	$56,404,430	0.37
2012	DAL	36	30	0.545	$73,674,537	0.43
2012	NYK	36	30	0.545	$62,298,721	0.54
2012	PHL	35	31	0.53	$65,892,972	0.43
2012	HOU	34	32	0.515	$54,745,206	0.32
2012	PHX	33	33	0.5	$76,711,464	0.30
2012	MIL	31	35	0.47	$58,472,900	0.31
2012	POR	28	38	0.424	$61,019,322	0.40
2012	MIN	26	40	0.394	$53,140,299	0.09
2012	DET	25	41	0.379	$68,929,375	0.31
2012	GSW	23	43	0.348	$56,227,417	0.40
2012	TOR	23	43	0.348	$51,651,613	0.34
2012	SAC	22	44	0.333	$47,714,437	0.28
2012	BKN	22	44	0.333	$58,422,668	0.41
2012	NOL	21	45	0.318	$64,179,540	0.38
2012	CLE	21	45	0.318	$49,098,799	0.42
2012	WAS	20	46	0.303	$53,521,874	0.46
2012	CLT	7	59	0.106	$55,285,831	0.30
2011	CHI	62	20	0.756	$54,329,812	0.41
2011	SAS	61	21	0.744	$68,538,122	0.49
2011	MIA	58	24	0.707	$62,638,433	0.47
2011	LAL	57	25	0.695	$90,480,932	0.45
2011	DAL	57	25	0.695	$83,491,745	0.37
2011	BOS	56	26	0.683	$80,993,506	0.38
2011	OKC	55	27	0.671	$53,518,288	0.32
2011	ORL	52	30	0.634	$88,513,149	0.40
2011	DEN	50	32	0.61	$66,322,520	0.38
2011	POR	48	34	0.585	$73,145,400	0.39
2011	NOL	46	36	0.561	$65,610,022	0.36
2011	MEM	46	36	0.561	$67,878,963	0.42
2011	ATL	44	38	0.537	$70,247,583	0.42
2011	HOU	43	39	0.524	$69,040,343	0.37
2011	NYK	42	40	0.512	$65,088,569	0.50
2011	PHL	41	41	0.5	$66,846,131	0.37
2011	PHX	40	42	0.488	$65,015,978	0.38
2011	UTA	39	43	0.476	$74,294,192	0.41
2011	IND	37	45	0.451	$61,330,275	0.34
2011	GSW	36	46	0.439	$67,221,950	0.37
2011	MIL	35	47	0.427	$66,895,761	0.43
2011	CLT	34	48	0.415	$61,322,647	0.26
2011	LAC	32	50	0.39	$50,618,617	0.34
2011	DET	30	52	0.366	$63,519,827	0.36
2011	SAC	24	58	0.293	$42,521,358	0.43
2011	BKN	24	58	0.293	$56,977,639	0.34
2011	WAS	23	59	0.28	$55,546,676	0.40
2011	TOR	22	60	0.268	$65,808,297	0.33
2011	CLE	19	63	0.232	$51,767,822	0.47
2011	MIN	17	65	0.207	$51,040,432	0.23
2010	CLE	61	21	0.744	$81,102,376	0.42
2010	ORL	59	23	0.72	$80,894,461	0.43
2010	LAL	57	25	0.695	$90,418,953	0.39
2010	DAL	55	27	0.671	$86,840,635	0.34
2010	PHX	54	28	0.659	$63,523,901	0.47
2010	DEN	53	29	0.646	$73,165,776	0.44
2010	UTA	53	29	0.646	$71,905,244	0.47
2010	ATL	53	29	0.646	$65,129,338	0.40
2010	POR	50	32	0.61	$55,433,023	0.30
2010	OKC	50	32	0.61	$53,608,643	0.23
2010	SAS	50	32	0.61	$77,776,392	0.48
2010	BOS	50	32	0.61	$82,900,784	0.45
2010	MIA	47	35	0.573	$72,426,326	0.51
2010	MIL	46	36	0.561	$64,017,352	0.37
2010	CLT	44	38	0.537	$67,339,289	0.30
2010	HOU	42	40	0.512	$64,377,923	0.35
2010	CHI	41	41	0.5	$64,616,705	0.33
2010	MEM	40	42	0.488	$53,220,617	0.35
2010	TOR	40	42	0.488	$65,210,061	0.34
2010	NOL	37	45	0.451	$69,636,421	0.41
2010	IND	32	50	0.39	$62,989,931	0.34
2010	LAC	29	53	0.354	$57,420,102	0.29
2010	NYK	29	53	0.354	$83,176,055	0.40
2010	PHL	27	55	0.329	$63,378,259	0.43
2010	DET	27	55	0.329	$58,445,160	0.38
2010	GSW	26	56	0.317	$61,955,545	0.30
2010	WAS	26	56	0.317	$70,105,075	0.41
2010	SAC	25	57	0.305	$62,507,868	0.33
2010	MIN	15	67	0.183	$57,181,660	0.29
2010	BKN	12	70	0.146	$52,625,187	0.28
2009	CLE	66	16	0.805	$89,618,931	0.33
2009	LAL	65	17	0.793	$77,006,098	0.46
2009	BOS	62	20	0.756	$78,646,859	0.56
2009	ORL	59	23	0.72	$68,961,462	0.40
2009	DEN	54	28	0.659	$68,700,235	0.43
2009	POR	54	28	0.659	$75,118,432	0.32
2009	SAS	54	28	0.659	$66,192,427	0.44
2009	HOU	53	29	0.646	$68,655,932	0.44
2009	DAL	50	32	0.61	$90,638,805	0.43
2009	NOL	49	33	0.598	$65,508,005	0.35
2009	UTA	48	34	0.585	$63,152,386	0.40
2009	ATL	47	35	0.573	$66,303,693	0.42
2009	PHX	46	36	0.561	$75,891,350	0.50
2009	MIA	43	39	0.524	$67,731,911	0.49
2009	PHL	41	41	0.5	$66,519,372	0.41
2009	CHI	41	41	0.5	$67,327,364	0.30
2009	DET	39	43	0.476	$70,992,060	0.49
2009	IND	36	46	0.439	$65,045,632	0.29
2009	CLT	35	47	0.427	$61,944,466	0.30
2009	BKN	34	48	0.415	$59,969,552	0.38
2009	MIL	34	48	0.415	$67,666,341	0.36
2009	TOR	33	49	0.402	$72,178,703	0.37
2009	NYK	32	50	0.39	$95,470,166	0.31
2009	GSW	29	53	0.354	$65,171,702	0.32
2009	MIN	24	58	0.293	$60,784,995	0.27
2009	MEM	24	58	0.293	$49,218,385	0.24
2009	OKC	23	59	0.28	$59,106,433	0.14
2009	LAC	19	63	0.232	$58,956,998	0.46
2009	WAS	19	63	0.232	$67,467,685	0.35
2009	SAC	17	65	0.207	$61,770,109	0.26