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.
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| Payroll and Winning % |
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| 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.
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| 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.
| Season | Abbv | Team | W | L | T | W% | Salary | Gini |
|---|---|---|---|---|---|---|---|---|
| 2012 | ATL | Atlanta Falcons | 13 | 3 | 0 | 0.813 | $116,402,511 | 0.514738721 |
| 2012 | DEN | Denver Broncos | 13 | 3 | 0 | 0.813 | $113,287,666 | 0.571881361 |
| 2012 | NWE | New England Patriots | 12 | 4 | 0 | 0.75 | $92,364,848 | 0.521154508 |
| 2012 | HOU | Houston Texans | 12 | 4 | 0 | 0.75 | $97,351,637 | 0.543821195 |
| 2012 | SFO | San Francisco 49ers | 11 | 4 | 1 | 0.719 | $126,583,805 | 0.491746891 |
| 2012 | SEA | Seattle Seahawks | 11 | 5 | 0 | 0.688 | $90,741,771 | 0.513369361 |
| 2012 | GBP | Green Bay Packers | 11 | 5 | 0 | 0.688 | $103,544,714 | 0.542784102 |
| 2012 | IND | Indianapolis Colts | 11 | 5 | 0 | 0.688 | $73,028,878 | 0.569385871 |
| 2012 | CIN | Cincinnati Bengals | 10 | 6 | 0 | 0.625 | $93,118,676 | 0.480068518 |
| 2012 | WAS | Washington Redskins | 10 | 6 | 0 | 0.625 | $94,195,381 | 0.516259007 |
| 2012 | BAL | Baltimore Ravens | 10 | 6 | 0 | 0.625 | $114,335,765 | 0.534004656 |
| 2012 | CHI | Chicago Bears | 10 | 6 | 0 | 0.625 | $108,968,360 | 0.535175684 |
| 2012 | MIN | Minnesota Vikings | 10 | 6 | 0 | 0.625 | $97,355,429 | 0.549985234 |
| 2012 | NYG | New York Giants | 9 | 7 | 0 | 0.563 | $112,790,018 | 0.528370881 |
| 2012 | DAL | Dallas Cowboys | 8 | 8 | 0 | 0.5 | $93,026,340 | 0.485644402 |
| 2012 | PIT | Pittsburgh Steelers | 8 | 8 | 0 | 0.5 | $93,591,567 | 0.504570974 |
| 2012 | STL | St. Louis Rams | 7 | 8 | 1 | 0.469 | $100,409,226 | 0.583828248 |
| 2012 | NOL | New Orleans Saints | 7 | 9 | 0 | 0.438 | $102,760,641 | 0.463034194 |
| 2012 | MIA | Miami Dolphins | 7 | 9 | 0 | 0.438 | $86,245,856 | 0.493071779 |
| 2012 | SDG | San Diego Chargers | 7 | 9 | 0 | 0.438 | $101,964,045 | 0.504575041 |
| 2012 | CAR | Carolina Panthers | 7 | 9 | 0 | 0.438 | $89,788,875 | 0.561308904 |
| 2012 | TAM | Tampa Bay Buccaneers | 7 | 9 | 0 | 0.438 | $108,457,218 | 0.588476417 |
| 2012 | BUF | Buffalo Bills | 6 | 10 | 0 | 0.375 | $88,301,554 | 0.473599438 |
| 2012 | TEN | Tennessee Titans | 6 | 10 | 0 | 0.375 | $89,244,843 | 0.516724483 |
| 2012 | NYJ | New York Jets | 6 | 10 | 0 | 0.375 | $119,479,123 | 0.546271004 |
| 2012 | ARI | Arizona Cardinals | 5 | 11 | 0 | 0.313 | $103,494,516 | 0.488807417 |
| 2012 | CLE | Cleveland Browns | 5 | 11 | 0 | 0.313 | $94,890,118 | 0.535557105 |
| 2012 | DET | Detroit Lions | 4 | 12 | 0 | 0.25 | $115,542,993 | 0.480054871 |
| 2012 | OAK | Oakland Raiders | 4 | 12 | 0 | 0.25 | $75,350,719 | 0.512867548 |
| 2012 | PHL | Philadelphia Eagles | 4 | 12 | 0 | 0.25 | $90,771,742 | 0.535317206 |
| 2012 | JAC | Jacksonville Jaguars | 2 | 14 | 0 | 0.125 | $90,016,222 | 0.497013896 |
| 2012 | KAN | Kansas City Chiefs | 2 | 14 | 0 | 0.125 | $117,967,329 | 0.542708549 |
| 2011 | GBP | Green Bay Packers | 15 | 1 | 0 | 0.938 | $98,721,322 | 0.517651285 |
| 2011 | SFO | San Francisco 49ers | 13 | 3 | 0 | 0.813 | $113,086,631 | 0.436419722 |
| 2011 | NWE | New England Patriots | 13 | 3 | 0 | 0.813 | $96,686,743 | 0.484126159 |
| 2011 | NOL | New Orleans Saints | 13 | 3 | 0 | 0.813 | $93,967,839 | 0.519117934 |
| 2011 | PIT | Pittsburgh Steelers | 12 | 4 | 0 | 0.750 | $108,796,294 | 0.476309884 |
| 2011 | BAL | Baltimore Ravens | 12 | 4 | 0 | 0.750 | $119,119,865 | 0.529578754 |
| 2011 | DET | Detroit Lions | 10 | 6 | 0 | 0.625 | $115,163,524 | 0.450714324 |
| 2011 | ATL | Atlanta Falcons | 10 | 6 | 0 | 0.625 | $116,346,329 | 0.52013351 |
| 2011 | HOU | Houston Texans | 10 | 6 | 0 | 0.625 | $112,046,664 | 0.539587942 |
| 2011 | TEN | Tennessee Titans | 9 | 7 | 0 | 0.563 | $91,812,827 | 0.472658715 |
| 2011 | CIN | Cincinnati Bengals | 9 | 7 | 0 | 0.563 | $106,130,221 | 0.477609302 |
| 2011 | NYG | New York Giants | 9 | 7 | 0 | 0.563 | $107,800,654 | 0.508865538 |
| 2011 | ARI | Arizona Cardinals | 8 | 8 | 0 | 0.500 | $105,370,592 | 0.490605631 |
| 2011 | CHI | Chicago Bears | 8 | 8 | 0 | 0.500 | $100,516,229 | 0.495191196 |
| 2011 | DAL | Dallas Cowboys | 8 | 8 | 0 | 0.500 | $89,773,364 | 0.499817128 |
| 2011 | SDG | San Diego Chargers | 8 | 8 | 0 | 0.500 | $116,178,697 | 0.510889274 |
| 2011 | PHL | Philadelphia Eagles | 8 | 8 | 0 | 0.500 | $110,604,800 | 0.524964555 |
| 2011 | DEN | Denver Broncos | 8 | 8 | 0 | 0.500 | $99,063,772 | 0.555423572 |
| 2011 | NYJ | New York Jets | 8 | 8 | 0 | 0.500 | $108,252,231 | 0.589457617 |
| 2011 | OAK | Oakland Raiders | 8 | 8 | 0 | 0.500 | $124,152,024 | 0.608148323 |
| 2011 | SEA | Seattle Seahawks | 7 | 9 | 0 | 0.438 | $83,198,287 | 0.477357404 |
| 2011 | KAN | Kansas City Chiefs | 7 | 9 | 0 | 0.438 | $99,749,401 | 0.531227259 |
| 2011 | BUF | Buffalo Bills | 6 | 10 | 0 | 0.375 | $87,217,609 | 0.426841879 |
| 2011 | MIA | Miami Dolphins | 6 | 10 | 0 | 0.375 | $106,281,704 | 0.527877149 |
| 2011 | CAR | Carolina Panthers | 6 | 10 | 0 | 0.375 | $108,447,151 | 0.556101307 |
| 2011 | JAC | Jacksonville Jaguars | 5 | 11 | 0 | 0.313 | $81,708,790 | 0.444561749 |
| 2011 | WAS | Washington Redskins | 5 | 11 | 0 | 0.313 | $104,303,790 | 0.486349416 |
| 2011 | CLE | Cleveland Browns | 4 | 12 | 0 | 0.250 | $94,636,379 | 0.551086216 |
| 2011 | TAM | Tampa Bay Buccaneers | 4 | 12 | 0 | 0.250 | $90,460,323 | 0.606441483 |
| 2011 | MIN | Minnesota Vikings | 3 | 13 | 0 | 0.188 | $106,380,245 | 0.546191713 |
| 2011 | STL | St. Louis Rams | 2 | 14 | 0 | 0.125 | $99,899,754 | 0.588592466 |
| 2011 | IND | Indianapolis Colts | 2 | 14 | 0 | 0.125 | $107,520,234 | 0.604144739 |
| 2010 | NWE | New England Patriots | 14 | 2 | 0 | 0.875 | $91,365,745 | 0.54722117 |
| 2010 | ATL | Atlanta Falcons | 13 | 3 | 0 | 0.813 | $117,331,778 | 0.502768158 |
| 2010 | BAL | Baltimore Ravens | 12 | 4 | 0 | 0.750 | $105,532,857 | 0.479822121 |
| 2010 | PIT | Pittsburgh Steelers | 12 | 4 | 0 | 0.750 | $113,344,357 | 0.503911607 |
| 2010 | NYJ | New York Jets | 11 | 5 | 0 | 0.688 | $90,805,425 | 0.544672534 |
| 2010 | NOL | New Orleans Saints | 11 | 5 | 0 | 0.688 | $98,322,894 | 0.560520956 |
| 2010 | CHI | Chicago Bears | 11 | 5 | 0 | 0.688 | $102,532,239 | 0.576886075 |
| 2010 | PHL | Philadelphia Eagles | 10 | 6 | 0 | 0.625 | $110,996,870 | 0.495578313 |
| 2010 | NYG | New York Giants | 10 | 6 | 0 | 0.625 | $105,469,121 | 0.496178476 |
| 2010 | GBP | Green Bay Packers | 10 | 6 | 0 | 0.625 | $111,649,687 | 0.5301165 |
| 2010 | KAN | Kansas City Chiefs | 10 | 6 | 0 | 0.625 | $75,710,016 | 0.552894929 |
| 2010 | TAM | Tampa Bay Buccaneers | 10 | 6 | 0 | 0.625 | $84,965,923 | 0.577809189 |
| 2010 | IND | Indianapolis Colts | 10 | 6 | 0 | 0.625 | $116,380,990 | 0.641296236 |
| 2010 | SDG | San Diego Chargers | 9 | 7 | 0 | 0.563 | $95,776,956 | 0.50631465 |
| 2010 | JAC | Jacksonville Jaguars | 8 | 8 | 0 | 0.500 | $73,432,499 | 0.461332401 |
| 2010 | OAK | Oakland Raiders | 8 | 8 | 0 | 0.500 | $90,299,932 | 0.503781512 |
| 2010 | SEA | Seattle Seahawks | 7 | 9 | 0 | 0.438 | $77,009,612 | 0.528152786 |
| 2010 | MIA | Miami Dolphins | 7 | 9 | 0 | 0.438 | $93,403,361 | 0.539524351 |
| 2010 | STL | St. Louis Rams | 7 | 9 | 0 | 0.438 | $80,314,537 | 0.552466806 |
| 2010 | SFO | San Francisco 49ers | 6 | 10 | 0 | 0.375 | $95,872,378 | 0.486611973 |
| 2010 | DET | Detroit Lions | 6 | 10 | 0 | 0.375 | $94,972,505 | 0.522357588 |
| 2010 | HOU | Houston Texans | 6 | 10 | 0 | 0.375 | $105,389,279 | 0.527209521 |
| 2010 | TEN | Tennessee Titans | 6 | 10 | 0 | 0.375 | $79,001,894 | 0.56637778 |
| 2010 | DAL | Dallas Cowboys | 6 | 10 | 0 | 0.375 | $116,918,515 | 0.599744828 |
| 2010 | MIN | Minnesota Vikings | 6 | 10 | 0 | 0.375 | $106,267,142 | 0.605239727 |
| 2010 | WAS | Washington Redskins | 6 | 10 | 0 | 0.375 | $135,509,024 | 0.633499691 |
| 2010 | ARI | Arizona Cardinals | 5 | 11 | 0 | 0.313 | $93,565,874 | 0.489663554 |
| 2010 | CLE | Cleveland Browns | 5 | 11 | 0 | 0.313 | $80,914,238 | 0.555798132 |
| 2010 | BUF | Buffalo Bills | 4 | 12 | 0 | 0.250 | $78,278,893 | 0.474524417 |
| 2010 | CIN | Cincinnati Bengals | 4 | 12 | 0 | 0.250 | $83,915,560 | 0.530727526 |
| 2010 | DEN | Denver Broncos | 4 | 12 | 0 | 0.250 | $92,139,914 | 0.561059831 |
| 2010 | CAR | Carolina Panthers | 2 | 14 | 0 | 0.125 | $74,828,293 | 0.51161398 |
| 2009 | IND | Indianapolis Colts | 14 | 2 | 0 | 0.875 | $112,046,913 | 0.604378024 |
| 2009 | SDG | San Diego Chargers | 13 | 3 | 0 | 0.813 | $108,336,478 | 0.473416893 |
| 2009 | NOL | New Orleans Saints | 13 | 3 | 0 | 0.813 | $113,070,030 | 0.476819209 |
| 2009 | MIN | Minnesota Vikings | 12 | 4 | 0 | 0.750 | $125,660,249 | 0.484507003 |
| 2009 | DAL | Dallas Cowboys | 11 | 5 | 0 | 0.688 | $91,959,385 | 0.388781666 |
| 2009 | PHL | Philadelphia Eagles | 11 | 5 | 0 | 0.688 | $129,490,714 | 0.476215351 |
| 2009 | GBP | Green Bay Packers | 11 | 5 | 0 | 0.688 | $111,331,013 | 0.493502022 |
| 2009 | NWE | New England Patriots | 10 | 6 | 0 | 0.625 | $106,649,396 | 0.482710786 |
| 2009 | CIN | Cincinnati Bengals | 10 | 6 | 0 | 0.625 | $93,509,595 | 0.537605751 |
| 2009 | ARI | Arizona Cardinals | 10 | 6 | 0 | 0.625 | $107,015,288 | 0.549513199 |
| 2009 | BAL | Baltimore Ravens | 9 | 7 | 0 | 0.563 | $99,344,492 | 0.443037456 |
| 2009 | ATL | Atlanta Falcons | 9 | 7 | 0 | 0.563 | $95,555,443 | 0.482378844 |
| 2009 | PIT | Pittsburgh Steelers | 9 | 7 | 0 | 0.563 | $109,227,619 | 0.490124964 |
| 2009 | HOU | Houston Texans | 9 | 7 | 0 | 0.563 | $102,497,704 | 0.502996939 |
| 2009 | NYJ | New York Jets | 9 | 7 | 0 | 0.563 | $113,187,006 | 0.505387954 |
| 2009 | SFO | San Francisco 49ers | 8 | 8 | 0 | 0.500 | $114,583,550 | 0.452341525 |
| 2009 | TEN | Tennessee Titans | 8 | 8 | 0 | 0.500 | $112,889,896 | 0.456394581 |
| 2009 | NYG | New York Giants | 8 | 8 | 0 | 0.500 | $116,251,144 | 0.495780592 |
| 2009 | DEN | Denver Broncos | 8 | 8 | 0 | 0.500 | $87,645,146 | 0.498371223 |
| 2009 | CAR | Carolina Panthers | 8 | 8 | 0 | 0.500 | $99,465,157 | 0.543775815 |
| 2009 | JAC | Jacksonville Jaguars | 7 | 9 | 0 | 0.438 | $95,509,950 | 0.474754181 |
| 2009 | MIA | Miami Dolphins | 7 | 9 | 0 | 0.438 | $104,970,549 | 0.476998646 |
| 2009 | CHI | Chicago Bears | 7 | 9 | 0 | 0.438 | $116,436,322 | 0.509504646 |
| 2009 | BUF | Buffalo Bills | 6 | 10 | 0 | 0.375 | $97,949,368 | 0.442274865 |
| 2009 | CLE | Cleveland Browns | 5 | 11 | 0 | 0.313 | $95,408,685 | 0.468675144 |
| 2009 | OAK | Oakland Raiders | 5 | 11 | 0 | 0.313 | $93,696,393 | 0.49001838 |
| 2009 | SEA | Seattle Seahawks | 5 | 11 | 0 | 0.313 | $106,263,156 | 0.494565776 |
| 2009 | WAS | Washington Redskins | 4 | 12 | 0 | 0.250 | $102,423,196 | 0.465466658 |
| 2009 | KAN | Kansas City Chiefs | 4 | 12 | 0 | 0.250 | $74,596,962 | 0.524442539 |
| 2009 | TAM | Tampa Bay Buccaneers | 3 | 13 | 0 | 0.188 | $90,385,079 | 0.464772086 |
| 2009 | DET | Detroit Lions | 2 | 14 | 0 | 0.125 | $93,945,478 | 0.456114577 |
| 2009 | STL | St. Louis Rams | 1 | 15 | 0 | 0.063 | $91,955,433 | 0.529708514 |
| 2008 | TEN | Tennessee Titans | 13 | 3 | 0 | 0.813 | $97,258,310 | 0.443805238 |
| 2008 | PIT | Pittsburgh Steelers | 12 | 4 | 0 | 0.750 | $102,872,395 | 0.465079082 |
| 2008 | NYG | New York Giants | 12 | 4 | 0 | 0.750 | $91,428,041 | 0.468937358 |
| 2008 | CAR | Carolina Panthers | 12 | 4 | 0 | 0.750 | $87,849,189 | 0.505626239 |
| 2008 | IND | Indianapolis Colts | 12 | 4 | 0 | 0.750 | $106,251,977 | 0.610158374 |
| 2008 | ATL | Atlanta Falcons | 11 | 5 | 0 | 0.688 | $70,590,651 | 0.446269963 |
| 2008 | MIA | Miami Dolphins | 11 | 5 | 0 | 0.688 | $78,036,678 | 0.447985099 |
| 2008 | NWE | New England Patriots | 11 | 5 | 0 | 0.688 | $100,536,554 | 0.478324332 |
| 2008 | BAL | Baltimore Ravens | 11 | 5 | 0 | 0.688 | $98,915,180 | 0.502840182 |
| 2008 | MIN | Minnesota Vikings | 10 | 6 | 0 | 0.625 | $119,082,602 | 0.460686197 |
| 2008 | PHL | Philadelphia Eagles | 9 | 6 | 1 | 0.594 | $108,876,033 | 0.47437581 |
| 2008 | TAM | Tampa Bay Buccaneers | 9 | 7 | 0 | 0.563 | $89,164,352 | 0.360053618 |
| 2008 | DAL | Dallas Cowboys | 9 | 7 | 0 | 0.563 | $93,610,366 | 0.422449909 |
| 2008 | ARI | Arizona Cardinals | 9 | 7 | 0 | 0.563 | $105,149,491 | 0.477134243 |
| 2008 | CHI | Chicago Bears | 9 | 7 | 0 | 0.563 | $100,115,226 | 0.483588262 |
| 2008 | NYJ | New York Jets | 9 | 7 | 0 | 0.563 | $100,763,674 | 0.490567487 |
| 2008 | NOL | New Orleans Saints | 8 | 8 | 0 | 0.500 | $97,280,431 | 0.391458567 |
| 2008 | SDG | San Diego Chargers | 8 | 8 | 0 | 0.500 | $105,695,579 | 0.418737727 |
| 2008 | HOU | Houston Texans | 8 | 8 | 0 | 0.500 | $92,055,101 | 0.464834876 |
| 2008 | WAS | Washington Redskins | 8 | 8 | 0 | 0.500 | $100,554,829 | 0.470041596 |
| 2008 | DEN | Denver Broncos | 8 | 8 | 0 | 0.500 | $75,801,186 | 0.476332436 |
| 2008 | SFO | San Francisco 49ers | 7 | 9 | 0 | 0.438 | $100,137,791 | 0.417411613 |
| 2008 | BUF | Buffalo Bills | 7 | 9 | 0 | 0.438 | $108,193,773 | 0.474746009 |
| 2008 | GBP | Green Bay Packers | 6 | 10 | 0 | 0.375 | $94,785,701 | 0.499982522 |
| 2008 | OAK | Oakland Raiders | 5 | 11 | 0 | 0.313 | $90,074,793 | 0.418856663 |
| 2008 | JAC | Jacksonville Jaguars | 5 | 11 | 0 | 0.313 | $106,673,857 | 0.420964118 |
| 2008 | CIN | Cincinnati Bengals | 4 | 11 | 1 | 0.281 | $91,656,013 | 0.525841289 |
| 2008 | CLE | Cleveland Browns | 4 | 12 | 0 | 0.250 | $111,738,289 | 0.446048194 |
| 2008 | SEA | Seattle Seahawks | 4 | 12 | 0 | 0.250 | $94,436,096 | 0.49044353 |
| 2008 | STL | St. Louis Rams | 2 | 14 | 0 | 0.125 | $100,642,742 | 0.496167006 |
| 2008 | KAN | Kansas City Chiefs | 2 | 14 | 0 | 0.125 | $73,628,451 | 0.519413408 |
| 2008 | DET | Detroit Lions | 0 | 16 | 0 | 0.000 | $87,631,618 | 0.377494237 |
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