Returns to inequality in the NHL

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

Sports + Numbers Prediction: "I am guessing that returns to inequality are strong here too, with relatively high leverage of the individual players resembling the NBA more than the NFL or MLB." 

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 0.00008) while the Gini coefficient comes in at a P-value of 0.21.

Payroll vs Points % (total points / potential points) - NHL 2009-10 to 2012-13

For every million dollars in team spending the expected increase in winning percentage is 0.00397. For a team that spends $10 million more than a comparable team – all else equal – we would expect them to win 3 additional games (or win 2 more with two additional overtime losses (or win 1 more with four additional overtime losses (or win the same number but have six additional overtime losses))).

Gini vs Points % (total points / potential points) - NHL 2009-10 to 2012-13

On inequality the - insignificant - coefficient is 0.19. Within the range of Gini coefficients in baseball (0.22 to 0.47) this would mean a difference of 8 points (4 wins but I’ll spare the rest) from the most equal to the least equal (more wins to the least equal). Not nothing but not exactly a huge impact. The gap in payroll ($30 million to $71 million) projects to a gap of nearly 27 points.

Payroll vs Gini (color-coded by points %) - NHL 2009-10 to 2012-13

Strength of the relationship over time

The relationship stays pretty consistent for each variable. For payroll the correlation from 2010-2013 runs 0.35, 0.56, 0.36, 0.37 with an overall correlation for the four years of 0.34. Looking just at the correlation between Gini and winning percentage, the values are 0.11, 0.13, -0.21, 0.15. The overall one-on-one correlation between Gini and winning percentage for the five year period (2010-2013) is 0.04.

Would you rather have one dollar or four quarters? You would rather have the dollar. The relationship is weak but directionally supports the notion that inequality benefits a team. As with other sports you’d rather have more money than worry too much about the distribution.

Sports + Numbers Predictive Accuracy: Medium – The NHL is certainly closer to the NBA than it is to MLB or NFL, but I got a bit overconfident using the word ‘strong’ to predict the relationship. Nothing here suggests that level of impact. 

Details  

As usual there were a few salaries that escaped the view of the data. The 2010 Atlanta Thrashers are for some reason not in the database I used (Spotrac.com) so they are excluded. They were a middle of the road team (51% points percentage) so I don’t expect their result would have moved the needle too much. Where teams had fewer than 20 players in the data set we use the minimum salary for that year to fill in the holes and complete the code. Now we can make a baby dinosaur.

Year	Team	W	L	OL	PTS	PTS%	Adj Payroll	Gini
2013	Chicago Blackhawks	36	7	5	77	0.802	$62,371,796	0.348054705
2013	Pittsburgh Penguins	36	12	0	72	0.750	$63,731,667	0.376968661
2013	Anaheim Ducks	30	12	6	66	0.688	$59,113,334	0.345757675
2013	Montreal Canadiens	29	14	5	63	0.656	$61,403,333	0.287509598
2013	Boston Bruins	28	14	6	62	0.646	$69,233,811	0.315963911
2013	St. Louis Blues	29	17	2	60	0.625	$59,238,334	0.264531352
2013	Vancouver Canucks	26	15	7	59	0.615	$60,013,333	0.363379564
2013	Los Angeles Kings	27	16	5	59	0.615	$62,259,394	0.351983601
2013	Toronto Maple Leafs	26	17	5	57	0.594	$56,654,167	0.34493953
2013	Washington Capitals	27	18	3	57	0.594	$58,634,296	0.4045806
2013	San Jose Sharks	25	16	7	57	0.594	$63,456,667	0.35357462
2013	New York Rangers	26	18	4	56	0.583	$59,341,667	0.348927718
2013	Ottawa Senators	25	17	6	56	0.583	$53,748,333	0.354110644
2013	Detroit Red Wings	24	16	8	56	0.583	$64,167,045	0.289981702
2013	New York Islanders	24	17	7	55	0.573	$46,697,143	0.314053889
2013	Columbus Blue Jackets	24	17	7	55	0.573	$63,725,476	0.31838205
2013	Minnesota Wild	26	19	3	55	0.573	$62,362,758	0.363378603
2013	Winnipeg Jets	24	21	3	51	0.531	$61,502,857	0.317271176
2013	Phoenix Coyotes	21	18	9	51	0.531	$57,466,667	0.335984977
2013	Philadelphia Flyers	23	22	3	49	0.510	$65,408,096	0.256791737
2013	New Jersey Devils	19	19	10	48	0.500	$55,666,667	0.328485884
2013	Buffalo Sabres	21	21	6	48	0.500	$54,267,024	0.363408846
2013	Dallas Stars	22	22	4	48	0.500	$60,972,778	0.33702567
2013	Edmonton Oilers	19	22	7	45	0.469	$60,175,000	0.289809484
2013	Carolina Hurricanes	19	25	4	42	0.438	$58,925,000	0.442915732
2013	Calgary Flames	19	25	4	42	0.438	$55,503,750	0.294764502
2013	Nashville Predators	16	23	9	41	0.427	$61,658,810	0.305226052
2013	Tampa Bay Lightning	18	26	4	40	0.417	$61,998,810	0.336756699
2013	Colorado Avalanche	16	25	7	39	0.406	$55,683,333	0.273128948
2013	Florida Panthers	15	27	6	36	0.375	$49,432,042	0.342643373
2012	Vancouver Canucks	51	22	9	111	0.677	$65,883,333	0.282714753
2012	New York Rangers	51	24	7	109	0.665	$58,947,501	0.349662086
2012	St. Louis Blues	49	22	11	109	0.665	$55,684,166	0.278597199
2012	Pittsburgh Penguins	51	25	6	108	0.659	$70,888,590	0.333146277
2012	Nashville Predators	48	26	8	104	0.634	$46,000,476	0.438093175
2012	Philadelphia Flyers	47	26	9	103	0.628	$55,316,667	0.342045074
2012	New Jersey Devils	48	28	6	102	0.622	$56,154,167	0.322033672
2012	Boston Bruins	49	29	4	102	0.622	$63,231,668	0.250188574
2012	Detroit Red Wings	48	28	6	102	0.622	$56,371,211	0.287557357
2012	Chicago Blackhawks	45	26	11	101	0.616	$62,597,559	0.333769345
2012	Phoenix Coyotes	42	27	13	97	0.591	$46,845,833	0.306107935
2012	San Jose Sharks	43	29	10	96	0.585	$54,379,167	0.408474448
2012	Los Angeles Kings	40	27	15	95	0.579	$57,774,393	0.363587615
2012	Florida Panthers	38	26	18	94	0.573	$47,695,334	0.348139939
2012	Ottawa Senators	41	31	10	92	0.561	$44,860,833	0.390296083
2012	Washington Capitals	42	32	8	92	0.561	$55,352,905	0.428427273
2012	Calgary Flames	37	29	16	90	0.549	$49,795,416	0.368689914
2012	Buffalo Sabres	39	32	11	89	0.543	$54,047,024	0.355335879
2012	Dallas Stars	42	35	5	89	0.543	$37,300,278	0.427864308
2012	Colorado Avalanche	41	35	6	88	0.537	$54,058,333	0.286485059
2012	Tampa Bay Lightning	38	36	8	84	0.512	$54,267,237	0.444438557
2012	Winnipeg Jets	37	35	10	84	0.512	$53,813,500	0.310916992
2012	Carolina Hurricanes	33	33	16	82	0.500	$42,744,167	0.471284014
2012	Minnesota Wild	35	36	11	81	0.494	$67,587,757	0.371230799
2012	Toronto Maple Leafs	35	37	10	80	0.488	$45,681,667	0.401814484
2012	Anaheim Ducks	34	36	12	80	0.488	$58,601,667	0.264100783
2012	New York Islanders	34	37	11	79	0.482	$52,252,500	0.318592636
2012	Montreal Canadiens	31	35	16	78	0.476	$58,378,333	0.304183032
2012	Edmonton Oilers	32	40	10	74	0.451	$52,008,333	0.28769047
2012	Columbus Blue Jackets	29	46	7	65	0.396	$48,869,643	0.392118071
2011	Vancouver Canucks	54	19	9	117	0.713	$64,033,333	0.275935151
2011	Washington Capitals	48	23	11	107	0.652	$62,109,128	0.378680725
2011	Philadelphia Flyers	47	23	12	106	0.646	$65,917,928	0.25314506
2011	Pittsburgh Penguins	49	25	8	106	0.646	$61,884,000	0.375394876
2011	San Jose Sharks	48	25	9	105	0.640	$58,325,001	0.364956894
2011	Detroit Red Wings	47	25	10	104	0.634	$56,171,211	0.325578364
2011	Boston Bruins	46	25	11	103	0.628	$53,704,167	0.343227335
2011	Tampa Bay Lightning	46	25	11	103	0.628	$59,697,713	0.348575613
2011	Nashville Predators	44	27	11	99	0.604	$52,849,821	0.306848322
2011	Anaheim Ducks	47	30	5	99	0.604	$51,510,000	0.340562628
2011	Phoenix Coyotes	43	26	13	99	0.604	$51,775,000	0.236439723
2011	Los Angeles Kings	46	30	6	98	0.598	$62,816,537	0.330196152
2011	Chicago Blackhawks	44	29	9	97	0.591	$59,789,295	0.338951562
2011	Montreal Canadiens	44	30	8	96	0.585	$50,311,342	0.37742872
2011	Buffalo Sabres	43	29	10	96	0.585	$59,662,024	0.330974235
2011	Dallas Stars	42	29	11	95	0.579	$42,312,500	0.284246551
2011	Calgary Flames	41	29	12	94	0.573	$57,484,916	0.370531086
2011	New York Rangers	44	33	5	93	0.567	$63,404,167	0.342952902
2011	Carolina Hurricanes	40	31	11	91	0.555	$52,095,833	0.374732923
2011	St. Louis Blues	38	33	11	87	0.530	$49,295,833	0.238119378
2011	Minnesota Wild	39	35	8	86	0.524	$49,771,667	0.40657414
2011	Toronto Maple Leafs	37	34	11	85	0.518	$54,974,167	0.307722452
2011	New Jersey Devils	38	39	5	81	0.494	$51,006,667	0.372547016
2011	Columbus Blue Jackets	34	35	13	81	0.494	$50,087,250	0.373563766
2011	Atlanta Thrashers	34	36	12	80	0.488	$47,472,126	0.289268357
2011	Ottawa Senators	32	40	10	74	0.451	$47,374,166	0.369072119
2011	New York Islanders	30	39	13	73	0.445	$43,240,000	0.267983778
2011	Florida Panthers	30	40	12	72	0.439	$50,817,875	0.310670235
2011	Colorado Avalanche	30	44	8	68	0.415	$44,641,666	0.29438119
2011	Edmonton Oilers	25	45	12	62	0.378	$61,233,333	0.26907225
2010	Washington Capitals	54	15	13	121	0.738	$54,800,795	0.418919414
2010	San Jose Sharks	51	20	11	113	0.689	$62,471,668	0.374850555
2010	Chicago Blackhawks	52	22	8	112	0.683	$60,112,170	0.36448695
2010	Phoenix Coyotes	50	25	7	107	0.652	$46,533,333	0.224024423
2010	New Jersey Devils	48	27	7	103	0.628	$60,178,333	0.299460485
2010	Vancouver Canucks	49	28	5	103	0.628	$55,450,000	0.34043253
2010	Detroit Red Wings	44	24	14	102	0.622	$44,609,544	0.380383237
2010	Pittsburgh Penguins	47	28	7	101	0.616	$64,617,333	0.372043525
2010	Los Angeles Kings	46	27	9	101	0.616	$53,361,666	0.326286495
2010	Buffalo Sabres	45	27	10	100	0.610	$47,117,024	0.422005774
2010	Nashville Predators	47	29	6	100	0.610	$48,901,078	0.287900147
2010	Colorado Avalanche	43	30	9	95	0.579	$41,234,999	0.379460762
2010	Ottawa Senators	44	32	6	94	0.573	$48,008,333	0.379084317
2010	Boston Bruins	39	30	13	91	0.555	$61,239,643	0.289111495
2010	St. Louis Blues	40	32	10	90	0.549	$39,233,331	0.311633735
2010	Calgary Flames	40	32	10	90	0.549	$56,951,160	0.357879059
2010	Anaheim Ducks	39	32	11	89	0.543	$57,650,000	0.353116095
2010	Philadelphia Flyers	41	35	6	88	0.537	$58,907,928	0.343890069
2010	Montreal Canadiens	39	33	10	88	0.537	$54,137,976	0.398357421
2010	Dallas Stars	37	31	14	88	0.537	$40,884,167	0.400833358
2010	New York Rangers	38	33	11	87	0.530	$55,767,500	0.376595431
2010	Minnesota Wild	38	36	8	84	0.512	$47,088,325	0.296034451
2010	Carolina Hurricanes	35	37	10	80	0.488	$47,131,166	0.400046175
2010	Tampa Bay Lightning	34	36	12	80	0.488	$58,281,046	0.330163885
2010	New York Islanders	34	37	11	79	0.482	$33,625,000	0.359065333
2010	Columbus Blue Jackets	32	35	15	79	0.482	$44,348,083	0.371995553
2010	Florida Panthers	32	37	13	77	0.470	$29,788,334	0.333535803
2010	Toronto Maple Leafs	30	38	14	74	0.451	$50,528,333	0.357252029
2010	Edmonton Oilers	27	47	8	62	0.378	$53,783,333	0.293136783