Returns to inequality in MLB

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

Sports + Numbers Prediction: "This is anyone’s guess. The returns to inequality – after controlling for the wide distribution in overall team salary – might be strong or they might not. I don’t have a good feel for it so this will be more of a fact finding mission."

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 0.13 with only salary spending being significant (P-value of 0.00001) while the Gini coefficient comes in at a P-value of 0.18.

Payroll vs Winning % - MLB 2008-2012

For every million dollars in team spending the expected increase in winning percentage is 0.000654. For a team that spends $10 million more than a comparable team – all else equal – we would expect them to win an additional game.

Gini vs Winning % - MLB 2008-2012

On inequality the - insignificant - coefficient is -0.14. Within the range of Gini coefficients in baseball (0.35 to 0.66) this would mean a difference of 7 wins from the most equal to the least equal (more wins to the most equal). Not nothing but not exactly a huge impact. The gap in payroll ($19 million to $206 million) projects to a gap of nearly 20 wins.

Payroll vs Gini (color-coded by winning %) - MLB 2008-2012

Strength of the relationship over time 

The relationship stays pretty consistent for each variable. For payroll the correlation from 2008-2012 runs 0.32, 0.47, 0.37, 0.40, 0.19. Looking just at the correlation between Gini and winning percentage, the values are -0.17, 0.24, -0.04, -0.18, -0.27. The overall one-on-one correlation between Gini and winning percentage for the five year period (2008-2012) is -0.09.

Would you rather have one dollar or four quarters?

As with football it doesn't appear to matter. The graph of Gini alone looks a lot like random, normally distributed data. You'd rather have lots and lots of both. Nothing here to get my hopes up about the Indians scrappy band of equals overcoming Detroit's bloated juggernaut of Hot-N-Ready stars supported by scrap heap players.

Sports + Numbers Predictive Accuracy: High – I predicted that I didn't know where this would go and the numbers don't know it either. This turns out to be something of a known - or at least predicted - unknown.

Details

As usual there were a few salaries that escaped the view of the data. For any team with fewer than 25 players in their data set (sourced from the Lahman database) I filled in the gaps with league minimum salaries appropriate to that season. This splicing continues to upset the game warden, but he's a bit of an alarmist.

yearID	lgID	teamID	W	L	W%	Payroll	Gini
2008	AL	BAL	68	93	0.422	$64,466,246	0.52
2008	AL	BOS	95	67	0.586	$132,190,785	0.52
2008	AL	CHA	89	74	0.546	$120,401,832	0.52
2008	AL	CLE	81	81	0.500	$78,579,666	0.50
2008	AL	DET	74	88	0.457	$135,717,696	0.47
2008	AL	KC	75	87	0.463	$57,855,500	0.54
2008	AL	LAA	100	62	0.617	$117,628,333	0.55
2008	AL	MIN	88	75	0.540	$56,932,766	0.50
2008	AL	NYA	89	73	0.549	$205,938,839	0.52
2008	AL	OAK	75	86	0.466	$46,792,126	0.55
2008	AL	SEA	61	101	0.377	$117,276,482	0.55
2008	AL	TBA	97	65	0.599	$41,850,597	0.47
2008	AL	TEX	79	83	0.488	$66,147,326	0.54
2008	AL	TOR	86	76	0.531	$97,009,600	0.55
2008	NL	ARI	82	80	0.506	$65,026,712	0.58
2008	NL	ATL	72	90	0.444	$100,415,683	0.62
2008	NL	CHN	97	64	0.602	$117,561,833	0.53
2008	NL	CIN	74	88	0.457	$72,945,195	0.52
2008	NL	COL	74	88	0.457	$68,265,500	0.55
2008	NL	MIA	84	77	0.522	$18,691,500	0.35
2008	NL	HOU	86	75	0.534	$88,150,414	0.59
2008	NL	LAN	84	78	0.519	$117,027,536	0.56
2008	NL	MIL	90	72	0.556	$79,359,999	0.48
2008	NL	NYN	89	73	0.549	$135,782,876	0.49
2008	NL	PHI	92	70	0.568	$96,702,380	0.50
2008	NL	PIT	67	95	0.414	$48,299,783	0.57
2008	NL	SDN	63	99	0.389	$71,335,166	0.54
2008	NL	SFN	72	90	0.444	$75,034,500	0.58
2008	NL	SLN	86	76	0.531	$96,484,949	0.50
2008	NL	WAS	59	102	0.366	$53,366,500	0.45
2009	AL	BAL	64	98	0.395	$66,701,666	0.50
2009	AL	BOS	95	67	0.586	$119,731,999	0.48
2009	AL	CHA	79	83	0.488	$95,668,500	0.58
2009	AL	CLE	65	97	0.401	$80,775,366	0.51
2009	AL	DET	86	77	0.528	$113,885,145	0.52
2009	AL	KC	65	97	0.401	$70,114,333	0.50
2009	AL	LAA	97	65	0.599	$112,505,000	0.53
2009	AL	MIN	87	76	0.534	$63,664,766	0.59
2009	AL	NYA	103	59	0.636	$201,049,189	0.53
2009	AL	OAK	75	87	0.463	$61,110,000	0.59
2009	AL	SEA	85	77	0.525	$97,704,166	0.60
2009	AL	TBA	84	78	0.519	$61,670,034	0.47
2009	AL	TEX	87	75	0.537	$66,572,068	0.62
2009	AL	TOR	75	87	0.463	$79,334,600	0.58
2009	NL	ARI	70	92	0.432	$72,715,666	0.51
2009	NL	ATL	86	76	0.531	$95,121,166	0.56
2009	NL	CHN	83	78	0.516	$134,809,000	0.56
2009	NL	CIN	78	84	0.481	$74,358,500	0.60
2009	NL	COL	92	70	0.568	$74,399,000	0.58
2009	NL	MIA	87	75	0.537	$35,634,000	0.48
2009	NL	HOU	74	88	0.457	$102,143,914	0.58
2009	NL	LAN	95	67	0.586	$100,414,592	0.62
2009	NL	MIL	80	82	0.494	$79,782,502	0.51
2009	NL	NYN	70	92	0.432	$148,166,987	0.48
2009	NL	PHI	93	69	0.574	$112,199,046	0.48
2009	NL	PIT	62	99	0.385	$48,293,000	0.49
2009	NL	SDN	75	87	0.463	$42,533,700	0.58
2009	NL	SFN	88	74	0.543	$81,825,450	0.60
2009	NL	SLN	91	71	0.562	$87,728,409	0.57
2009	NL	WAS	59	103	0.364	$58,728,000	0.52
2010	AL	BAL	66	96	0.407	$81,212,500	0.52
2010	AL	BOS	89	73	0.549	$160,734,833	0.41
2010	AL	CHA	88	74	0.543	$105,130,000	0.51
2010	AL	CLE	69	93	0.426	$59,601,266	0.62
2010	AL	DET	81	81	0.500	$122,064,928	0.57
2010	AL	KC	67	95	0.414	$70,598,500	0.51
2010	AL	LAA	80	82	0.494	$103,359,666	0.48
2010	AL	MIN	94	68	0.580	$96,346,666	0.51
2010	AL	NYA	95	67	0.586	$206,333,389	0.56
2010	AL	OAK	81	81	0.500	$52,424,900	0.60
2010	AL	SEA	61	101	0.377	$85,309,000	0.57
2010	AL	TBA	96	66	0.593	$71,117,071	0.49
2010	AL	TEX	90	72	0.556	$53,640,814	0.56
2010	AL	TOR	85	77	0.525	$60,214,200	0.54
2010	NL	ARI	65	97	0.401	$60,318,166	0.48
2010	NL	ATL	91	71	0.562	$83,623,666	0.57
2010	NL	CHN	75	87	0.463	$145,808,000	0.56
2010	NL	CIN	91	71	0.562	$71,361,542	0.61
2010	NL	COL	83	79	0.512	$82,613,000	0.52
2010	NL	MIA	80	82	0.494	$56,225,219	0.56
2010	NL	HOU	76	86	0.469	$91,155,500	0.58
2010	NL	LAN	80	82	0.494	$94,553,516	0.55
2010	NL	MIL	77	85	0.475	$79,489,778	0.51
2010	NL	NYN	79	83	0.488	$133,206,942	0.54
2010	NL	PHI	97	65	0.599	$140,722,379	0.48
2010	NL	PIT	57	105	0.352	$34,141,500	0.49
2010	NL	SDN	90	72	0.556	$37,398,000	0.52
2010	NL	SFN	92	70	0.568	$97,435,333	0.56
2010	NL	SLN	86	76	0.531	$93,540,751	0.61
2010	NL	WAS	69	93	0.426	$59,399,000	0.56
2011	AL	BAL	69	93	0.426	$84,887,038	0.49
2011	AL	BOS	90	72	0.556	$160,895,475	0.45
2011	AL	CHA	79	83	0.488	$126,950,000	0.48
2011	AL	CLE	80	82	0.494	$47,114,466	0.59
2011	AL	DET	95	67	0.586	$104,868,231	0.59
2011	AL	KC	71	91	0.438	$35,298,000	0.41
2011	AL	LAA	86	76	0.531	$136,059,166	0.54
2011	AL	MIN	63	99	0.389	$112,737,000	0.56
2011	AL	NYA	97	65	0.599	$200,547,428	0.54
2011	AL	OAK	74	88	0.457	$65,282,500	0.42
2011	AL	SEA	67	95	0.414	$84,454,100	0.60
2011	AL	TBA	91	71	0.562	$40,638,671	0.47
2011	AL	TEX	96	66	0.593	$90,628,264	0.53
2011	AL	TOR	81	81	0.500	$60,010,300	0.41
2011	NL	ARI	94	68	0.580	$52,808,833	0.45
2011	NL	ATL	89	73	0.549	$86,588,692	0.58
2011	NL	CHN	71	91	0.438	$125,047,329	0.59
2011	NL	CIN	79	83	0.488	$73,869,634	0.55
2011	NL	COL	73	89	0.451	$87,733,071	0.54
2011	NL	MIA	72	90	0.444	$56,530,000	0.57
2011	NL	HOU	56	106	0.346	$69,027,000	0.61
2011	NL	LAN	82	79	0.509	$102,093,499	0.46
2011	NL	MIL	96	66	0.593	$83,394,333	0.54
2011	NL	NYN	77	85	0.475	$118,019,309	0.64
2011	NL	PHI	102	60	0.630	$170,906,379	0.48
2011	NL	PIT	72	90	0.444	$43,388,500	0.52
2011	NL	SDN	71	91	0.438	$43,379,300	0.51
2011	NL	SFN	86	76	0.531	$117,365,833	0.51
2011	NL	SLN	90	72	0.556	$104,605,572	0.58
2011	NL	WAS	80	81	0.497	$62,198,928	0.52
2012	AL	BAL	93	69	0.574	$75,907,999	0.52
2012	AL	BOS	69	93	0.426	$168,475,117	0.49
2012	AL	CHA	85	77	0.525	$96,919,500	0.59
2012	AL	CLE	68	94	0.420	$76,503,200	0.55
2012	AL	DET	88	74	0.543	$130,375,000	0.59
2012	AL	KC	72	90	0.444	$58,499,300	0.49
2012	AL	LAA	89	73	0.549	$152,555,166	0.51
2012	AL	MIN	66	96	0.407	$93,125,000	0.60
2012	AL	NYA	95	67	0.586	$194,548,864	0.53
2012	AL	OAK	94	68	0.580	$52,972,500	0.51
2012	AL	SEA	75	87	0.463	$80,537,400	0.64
2012	AL	TBA	90	72	0.556	$62,731,300	0.47
2012	AL	TEX	93	69	0.574	$120,030,974	0.48
2012	AL	TOR	73	89	0.451	$74,045,000	0.45
2012	NL	ARI	81	81	0.500	$72,841,833	0.46
2012	NL	ATL	94	68	0.580	$80,909,942	0.59
2012	NL	CHN	61	101	0.377	$87,717,033	0.58
2012	NL	CIN	97	65	0.599	$80,763,616	0.52
2012	NL	COL	64	98	0.395	$76,149,571	0.54
2012	NL	HOU	55	107	0.340	$60,171,000	0.66
2012	NL	LAN	86	76	0.531	$92,736,575	0.51
2012	NL	MIA	69	93	0.426	$117,118,000	0.55
2012	NL	MIL	83	79	0.512	$97,172,944	0.51
2012	NL	NYN	74	88	0.457	$92,393,103	0.64
2012	NL	PHI	81	81	0.500	$172,127,438	0.52
2012	NL	PIT	79	83	0.488	$61,507,999	0.51
2012	NL	SDN	76	86	0.469	$53,797,000	0.46
2012	NL	SFN	94	68	0.580	$115,219,683	0.56
2012	NL	SLN	88	74	0.543	$108,860,862	0.56
2012	NL	WAS	98	64	0.605	$78,442,143	0.55