Sunday, July 28, 2013

Returns to inequality in the NFL

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

Sports + Numbers Prediction: "I would think the returns to inequality are high here, but not exactly as a proxy for having stars. The NFL’s cap structure essentially forces teams to play rookies and younger, pre-contract extension players heavily and supplement them with selected veterans. The catch is that nearly all teams have a big young player population so the difference between one that works out and one that doesn’t might not be visible in the salary distribution."

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 0.07 with only salary spending being significant (P-value of 0.0007) while the Gini coefficient comes in at a P-value of 0.57.

Payroll and Winning %
For every million dollars in team spending the expected increase in winning percentage is 0.00417. For a team that spends $15 million more than a comparable team – all else equal – we would expect them to win an additional game.


Gini and Winning %

On inequality the coefficient is -0.17. Even though the P-value tells us this that Gini is insignificant, the fact that the variance from perfect equality to perfect inequality is slightly less than three wins should tell us all we need to know. 


Gini and Payroll, color coded by winning percentage


Strength of the relationship over time 

The relationship bounces around over time for both Gini and payroll. For payroll the correlation from 2008-2012 runs 0.08, 0.56, 0.34, 0.24, 0.14. Looking just at the correlation between Gini and winning percentage, the values are 0.16, 0.13, -0.02, -0.40, -0.21. The overall one-on-one correlation for the five year period (2008-2013) is 0.14.

Would you rather have one dollar or four quarters?

It doesn't matter - or, more accurately, we can't tell if it matters because the teams have a very narrow range of inequality. With the exception of a couple outliers every team/season is between 0.40 and 0.60 for a Gini coefficient.

Sports + Numbers Predictive Accuracy: Low-Medium – I predicted high returns to inequality but it turns out that is not the case. At the same time, I acknowledged that the NFL's salary cap structure (in particular the steeply increasing minimum salary but also the sheer number of roster spots) might make teams too similar for this analysis to work.

Details

Needed to deal with some inconsistencies in the data, but ended up going with a 45 player team up to the 2010 season and a 46 player team beyond that - the levels prescribed in the CBA for gameday roster. For any team with fewer than 45 or 46 players in their data set (sourced from USA Today and Spotrac.com) I filled in the gaps with rookie minimum salaries appropriate to that season. I don't think it's Jurassic Park-level hubris, but I'm sure someone will alert me if the gap-filling created a bias I haven't acknowledged.


SeasonAbbvTeamWLTW%SalaryGini
2012ATLAtlanta Falcons13300.813$116,402,511 0.514738721
2012DENDenver Broncos13300.813$113,287,666 0.571881361
2012NWENew England Patriots12400.75$92,364,848 0.521154508
2012HOUHouston Texans12400.75$97,351,637 0.543821195
2012SFOSan Francisco 49ers11410.719$126,583,805 0.491746891
2012SEASeattle Seahawks11500.688$90,741,771 0.513369361
2012GBPGreen Bay Packers11500.688$103,544,714 0.542784102
2012INDIndianapolis Colts11500.688$73,028,878 0.569385871
2012CINCincinnati Bengals10600.625$93,118,676 0.480068518
2012WASWashington Redskins10600.625$94,195,381 0.516259007
2012BALBaltimore Ravens10600.625$114,335,765 0.534004656
2012CHIChicago Bears10600.625$108,968,360 0.535175684
2012MINMinnesota Vikings10600.625$97,355,429 0.549985234
2012NYGNew York Giants9700.563$112,790,018 0.528370881
2012DALDallas Cowboys8800.5$93,026,340 0.485644402
2012PITPittsburgh Steelers8800.5$93,591,567 0.504570974
2012STLSt. Louis Rams7810.469$100,409,226 0.583828248
2012NOLNew Orleans Saints7900.438$102,760,641 0.463034194
2012MIAMiami Dolphins7900.438$86,245,856 0.493071779
2012SDGSan Diego Chargers7900.438$101,964,045 0.504575041
2012CARCarolina Panthers7900.438$89,788,875 0.561308904
2012TAMTampa Bay Buccaneers7900.438$108,457,218 0.588476417
2012BUFBuffalo Bills61000.375$88,301,554 0.473599438
2012TENTennessee Titans61000.375$89,244,843 0.516724483
2012NYJNew York Jets61000.375$119,479,123 0.546271004
2012ARIArizona Cardinals51100.313$103,494,516 0.488807417
2012CLECleveland Browns51100.313$94,890,118 0.535557105
2012DETDetroit Lions41200.25$115,542,993 0.480054871
2012OAKOakland Raiders41200.25$75,350,719 0.512867548
2012PHLPhiladelphia Eagles41200.25$90,771,742 0.535317206
2012JACJacksonville Jaguars21400.125$90,016,222 0.497013896
2012KANKansas City Chiefs21400.125$117,967,329 0.542708549
2011GBPGreen Bay Packers15100.938$98,721,322 0.517651285
2011SFOSan Francisco 49ers13300.813$113,086,631 0.436419722
2011NWENew England Patriots13300.813$96,686,743 0.484126159
2011NOLNew Orleans Saints13300.813$93,967,839 0.519117934
2011PITPittsburgh Steelers12400.750$108,796,294 0.476309884
2011BALBaltimore Ravens12400.750$119,119,865 0.529578754
2011DETDetroit Lions10600.625$115,163,524 0.450714324
2011ATLAtlanta Falcons10600.625$116,346,329 0.52013351
2011HOUHouston Texans10600.625$112,046,664 0.539587942
2011TENTennessee Titans9700.563$91,812,827 0.472658715
2011CINCincinnati Bengals9700.563$106,130,221 0.477609302
2011NYGNew York Giants9700.563$107,800,654 0.508865538
2011ARIArizona Cardinals8800.500$105,370,592 0.490605631
2011CHIChicago Bears8800.500$100,516,229 0.495191196
2011DALDallas Cowboys8800.500$89,773,364 0.499817128
2011SDGSan Diego Chargers8800.500$116,178,697 0.510889274
2011PHLPhiladelphia Eagles8800.500$110,604,800 0.524964555
2011DENDenver Broncos8800.500$99,063,772 0.555423572
2011NYJNew York Jets8800.500$108,252,231 0.589457617
2011OAKOakland Raiders8800.500$124,152,024 0.608148323
2011SEASeattle Seahawks7900.438$83,198,287 0.477357404
2011KANKansas City Chiefs7900.438$99,749,401 0.531227259
2011BUFBuffalo Bills61000.375$87,217,609 0.426841879
2011MIAMiami Dolphins61000.375$106,281,704 0.527877149
2011CARCarolina Panthers61000.375$108,447,151 0.556101307
2011JACJacksonville Jaguars51100.313$81,708,790 0.444561749
2011WASWashington Redskins51100.313$104,303,790 0.486349416
2011CLECleveland Browns41200.250$94,636,379 0.551086216
2011TAMTampa Bay Buccaneers41200.250$90,460,323 0.606441483
2011MINMinnesota Vikings31300.188$106,380,245 0.546191713
2011STLSt. Louis Rams21400.125$99,899,754 0.588592466
2011INDIndianapolis Colts21400.125$107,520,234 0.604144739
2010NWENew England Patriots14200.875$91,365,745 0.54722117
2010ATLAtlanta Falcons13300.813$117,331,778 0.502768158
2010BALBaltimore Ravens12400.750$105,532,857 0.479822121
2010PITPittsburgh Steelers12400.750$113,344,357 0.503911607
2010NYJNew York Jets11500.688$90,805,425 0.544672534
2010NOLNew Orleans Saints11500.688$98,322,894 0.560520956
2010CHIChicago Bears11500.688$102,532,239 0.576886075
2010PHLPhiladelphia Eagles10600.625$110,996,870 0.495578313
2010NYGNew York Giants10600.625$105,469,121 0.496178476
2010GBPGreen Bay Packers10600.625$111,649,687 0.5301165
2010KANKansas City Chiefs10600.625$75,710,016 0.552894929
2010TAMTampa Bay Buccaneers10600.625$84,965,923 0.577809189
2010INDIndianapolis Colts10600.625$116,380,990 0.641296236
2010SDGSan Diego Chargers9700.563$95,776,956 0.50631465
2010JACJacksonville Jaguars8800.500$73,432,499 0.461332401
2010OAKOakland Raiders8800.500$90,299,932 0.503781512
2010SEASeattle Seahawks7900.438$77,009,612 0.528152786
2010MIAMiami Dolphins7900.438$93,403,361 0.539524351
2010STLSt. Louis Rams7900.438$80,314,537 0.552466806
2010SFOSan Francisco 49ers61000.375$95,872,378 0.486611973
2010DETDetroit Lions61000.375$94,972,505 0.522357588
2010HOUHouston Texans61000.375$105,389,279 0.527209521
2010TENTennessee Titans61000.375$79,001,894 0.56637778
2010DALDallas Cowboys61000.375$116,918,515 0.599744828
2010MINMinnesota Vikings61000.375$106,267,142 0.605239727
2010WASWashington Redskins61000.375$135,509,024 0.633499691
2010ARIArizona Cardinals51100.313$93,565,874 0.489663554
2010CLECleveland Browns51100.313$80,914,238 0.555798132
2010BUFBuffalo Bills41200.250$78,278,893 0.474524417
2010CINCincinnati Bengals41200.250$83,915,560 0.530727526
2010DENDenver Broncos41200.250$92,139,914 0.561059831
2010CARCarolina Panthers21400.125$74,828,293 0.51161398
2009INDIndianapolis Colts14200.875$112,046,913 0.604378024
2009SDGSan Diego Chargers13300.813$108,336,478 0.473416893
2009NOLNew Orleans Saints13300.813$113,070,030 0.476819209
2009MINMinnesota Vikings12400.750$125,660,249 0.484507003
2009DALDallas Cowboys11500.688$91,959,385 0.388781666
2009PHLPhiladelphia Eagles11500.688$129,490,714 0.476215351
2009GBPGreen Bay Packers11500.688$111,331,013 0.493502022
2009NWENew England Patriots10600.625$106,649,396 0.482710786
2009CINCincinnati Bengals10600.625$93,509,595 0.537605751
2009ARIArizona Cardinals10600.625$107,015,288 0.549513199
2009BALBaltimore Ravens9700.563$99,344,492 0.443037456
2009ATLAtlanta Falcons9700.563$95,555,443 0.482378844
2009PITPittsburgh Steelers9700.563$109,227,619 0.490124964
2009HOUHouston Texans9700.563$102,497,704 0.502996939
2009NYJNew York Jets9700.563$113,187,006 0.505387954
2009SFOSan Francisco 49ers8800.500$114,583,550 0.452341525
2009TENTennessee Titans8800.500$112,889,896 0.456394581
2009NYGNew York Giants8800.500$116,251,144 0.495780592
2009DENDenver Broncos8800.500$87,645,146 0.498371223
2009CARCarolina Panthers8800.500$99,465,157 0.543775815
2009JACJacksonville Jaguars7900.438$95,509,950 0.474754181
2009MIAMiami Dolphins7900.438$104,970,549 0.476998646
2009CHIChicago Bears7900.438$116,436,322 0.509504646
2009BUFBuffalo Bills61000.375$97,949,368 0.442274865
2009CLECleveland Browns51100.313$95,408,685 0.468675144
2009OAKOakland Raiders51100.313$93,696,393 0.49001838
2009SEASeattle Seahawks51100.313$106,263,156 0.494565776
2009WASWashington Redskins41200.250$102,423,196 0.465466658
2009KANKansas City Chiefs41200.250$74,596,962 0.524442539
2009TAMTampa Bay Buccaneers31300.188$90,385,079 0.464772086
2009DETDetroit Lions21400.125$93,945,478 0.456114577
2009STLSt. Louis Rams11500.063$91,955,433 0.529708514
2008TENTennessee Titans13300.813$97,258,310 0.443805238
2008PITPittsburgh Steelers12400.750$102,872,395 0.465079082
2008NYGNew York Giants12400.750$91,428,041 0.468937358
2008CARCarolina Panthers12400.750$87,849,189 0.505626239
2008INDIndianapolis Colts12400.750$106,251,977 0.610158374
2008ATLAtlanta Falcons11500.688$70,590,651 0.446269963
2008MIAMiami Dolphins11500.688$78,036,678 0.447985099
2008NWENew England Patriots11500.688$100,536,554 0.478324332
2008BALBaltimore Ravens11500.688$98,915,180 0.502840182
2008MINMinnesota Vikings10600.625$119,082,602 0.460686197
2008PHLPhiladelphia Eagles9610.594$108,876,033 0.47437581
2008TAMTampa Bay Buccaneers9700.563$89,164,352 0.360053618
2008DALDallas Cowboys9700.563$93,610,366 0.422449909
2008ARIArizona Cardinals9700.563$105,149,491 0.477134243
2008CHIChicago Bears9700.563$100,115,226 0.483588262
2008NYJNew York Jets9700.563$100,763,674 0.490567487
2008NOLNew Orleans Saints8800.500$97,280,431 0.391458567
2008SDGSan Diego Chargers8800.500$105,695,579 0.418737727
2008HOUHouston Texans8800.500$92,055,101 0.464834876
2008WASWashington Redskins8800.500$100,554,829 0.470041596
2008DENDenver Broncos8800.500$75,801,186 0.476332436
2008SFOSan Francisco 49ers7900.438$100,137,791 0.417411613
2008BUFBuffalo Bills7900.438$108,193,773 0.474746009
2008GBPGreen Bay Packers61000.375$94,785,701 0.499982522
2008OAKOakland Raiders51100.313$90,074,793 0.418856663
2008JACJacksonville Jaguars51100.313$106,673,857 0.420964118
2008CINCincinnati Bengals41110.281$91,656,013 0.525841289
2008CLECleveland Browns41200.250$111,738,289 0.446048194
2008SEASeattle Seahawks41200.250$94,436,096 0.49044353
2008STLSt. Louis Rams21400.125$100,642,742 0.496167006
2008KANKansas City Chiefs21400.125$73,628,451 0.519413408
2008DETDetroit Lions01600.000$87,631,618 0.377494237


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