Patriots most equal, thanks to Tom Brady

Tom Brady congratulates Peyton Manning after the Broncos defeated the Patriots during the AFC championship game on Jan. 19, 2014 in Denver.
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Tom Brady congratulates Peyton Manning after the Broncos defeated the Patriots during the AFC championship game on Jan. 19, 2014 in Denver.

The New England Patriots head to Denver this weekend for the AFC football championship game against the Broncos. The Pats are hoping to defend their title in next month's Super Bowl, and they might just have an ace up their sleeve: A well-distributed payroll.

It turns out the Patriots have the most evenly distributed payroll in the National Football League, according to a Big Crunch analysis. Another sports team that paid their players equally? The Kansas City Royals, who beat the New York Mets in five games to win the 2015 World Series.

We looked at average annual salaries based on current contracts for players on each football team. The NFL's salary cap — with a base of $150 million per team this year — makes the league unique in its distributions. With some wiggle room based on salary cap carryover, teams keep their payrolls under that figure, or risk massive fines and the loss of draft picks.

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The Gini coefficient is a 0-to-1 statistical measure of divergence that's normally used to describe income inequality in a country. In a nation with a Gini coefficient of 0, everyone would make the same amount of money while a nation with a coefficient of 1 would be purely unequal.

The Patriots have a Gini coefficient of 0.51, just a touch under the woeful Tennessee Titans — which only won three games in the 2015 regular season — at 0.52. The closer that figure is to 0, the more equal the payroll distribution.

There are some interesting patterns in the data. The New York Giants, for instance, have an Gini coefficient of 0.56, putting them solidly in the most equal quarter of the league. That's despite the fact that Super Bowl winning quarterback Eli Manning makes an average of $21 million a year, ranking him the fourth-highest-paid player in the league. His pay makes up 16 percent of the Giants' salary cap, and it's been reported that he wants even more.

The Patriots' low Gini coefficient is partly due to quarterback Tom Brady's (comparatively) modest contract. His $9 million annual average salary is far less than many star quarterbacks, like the Green Bay Packers' Aaron Rodgers ($22 million), the Seattle Seahawks' Russell Wilson ($21.9 million), the Pittsburgh Steelers' Ben Roethlisberger ($21.85 million) and the Carolina Panthers' Cam Newton ($20.8 million). The only Patriot that makes more than $10 million, on average, is offensive tackle Nate Solder — who hasn't actually played since tearing his bicep in a game against Dallas in October.

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Brady renegotiated his contract in 2013, and agreed to terms that lowered his average annual take home pay. That gave the team more space in its salary cap. As some observers have pointed out, it's not entirely altruism on Brady's part: He took a $30 million "signing bonus" in addition to the lower yearly salaries going forward.

The $9 million average annual salary that Brady is taking home now is for the first "out year" in which Brady has no guarantee. However, it's unlikely the Patriots would want to drop him considering how well he's been playing.

Still, that puts Brady in the lower half in terms of starting quarterback pay. That's especially surprising when you consider that he has four Super Bowl rings and finished the season fourth in quarterback ratings.

The teams in the NFL have the lowest GIni of major American sports, and one of the lowest worldwide. That's largely because of the league's salary cap that limits the total amount a team can put toward player salaries. Three teams are currently at risk of exceeding their salary caps in 2016, according to Over the Cap. That's the Miami Dolphins, Buffalo Bills and the New Orleans Saints, who are most in trouble with nearly $8 million already in the hole.

The idea is to increase competition, and not let any one team buy a ton of talent that may automatically create a dynasty (see: baseball's late '90s Yankees). However, there's little evidence that the salary cap in football did anything to equalize the competitive balance.

Research from Middlebury College — published in the Journal of Recreational Mathematics — found that the introduction of a salary cap in 1993 had no effect on a Gini measurement of winning percentage.

Yet massive payrolls supporting a few star players don't always pay off in baseball. The Los Angeles Dodgers had the biggest payroll in 2015, with more than $300 million. They still lost the divisional series to the Mets, and the eventual World Series champion Royals had a payroll of a comparatively cheaper $128 million.

If equality in pay really is a catalyst for sports teams, expect to see more teams moving in that direction in the coming years. In the shorter term, expect to see the Patriots in California for the Super Bowl, and Brady on the field for at least a few more Super Bowls to come.