NFL schedule graph.jpg

A graph of the NFL's 2015 schedule shows how the league was divided into two separate clusters that rarely crossed paths in the regular season. (Courtesy of Steven Miller)

NEW BRUNSWICK -- A Rutgers University's mathematician says he has found a reason why the Carolina Panthers and New England Patriots did so well this regular season. And it doesn't have anything to do with their star quarterbacks.

A "flaw" in the 2015 National Football League schedule gave teams in the Panthers and Patriots divisions the rare opportunity to beat up on the same eight teams from the NFL's two weakest divisions, the AFC South and NFC East, said Stephen Miller, vice chair of Rutgers' mathematics department.

In other words: The NFL schedule usually does a good job of spreading around the lightweights, he said. In 2015, it didn't, Miller said.

"The idea that the schedule configuration is so different compared to other years is really weird," said Miller, whose graph of the NFL schedule is published in the Notices of the American Mathematical Society. "Think about how much money is at stake in the NFL -- players and their contracts and TV deals -- it's amazing there would be any room for a little mistake like this."

The NFL declined to comment on Miller's analysis.

But Mark Karwan, a sports scheduling expert at the University at Buffalo, said Miller's findings are fascinating.

The analysis shows that teams from the AFC East and NFC South, like the Patriots and Panthers, had a competitive advantage in building winning records and securing better playoff seeds, said Karwan, who has done his own studies on the fairness of NFL scheduling.

"You need to have two cream puff divisions for that (schedule) to have this impact," Karwan said. "And that happened in 2015."

While Karwans favorite team, the Buffalo Bills, didn't seize the opportunity, the Panthers and Patriots did, compiling a combined 15-1 against the NFL's worst divisions. They are two of the four teams competing Sunday for a spot in the Super Bowl.

Miller's analysis

Stephen Miller, vice chair of Rutgers' math department, says he discovered a flaw in the 2015 NFL schedule. (Andrew Miller | For NJ Advance Media)

Which NFL teams play each other in a season is determined by a rotation that ensures every team in the league's eight divisions play each of the 31 other teams during a four-year span.

Each season, every team plays six games against their three divisions rivals, four games against another division from their conference, four games against a division from the other conference and two games determined by their place in the standings the year before.

In nearly every season, the divisions that play each other are connected in a giant wheel, Miller said. Next year, every NFC East team will play every NFC North team, who play against every AFC South teams and so on until the cycle ties back around to the NFC East.

An illustration of how the 2016 NFL schedule will link teams from different divisions. Every team in each division plays against every team in the divisions next to theirs on the wheel. (Courtesy of Stephen Miller)

In 2015, however, the rotation that determined which divisions play one another aligned into two separate wheels, a cluster of teams from the North and West divisions and a cluster of teams from the East and South divisions. Those two clusters rarely crossed paths during the regular season.

The 2015 NFL schedule broke teams into two separate clusters that rarely crossed paths in the regular season. Only 12.5 percent of games featured teams from the North or West divisions against teams from the East or South divisions. (Courtesy of Stephen Miller)

Of the 256 regular season games, 87.5 percent (14 of every 16) were played between teams in the same cluster, Miller found.

Although unusual, the schedule likely wouldn't have created any significant competitive advantage if both clusters had an equal collection of strong and weak divisions, Miller said.

"One cluster had all the weak teams, basically, and the other cluster had all the strong teams," Miller said.

That scheduling oddity allowed the Panthers and Patriots to play eight common opponents outside of their own divisions: the Redskins, Eagles, Giants, Cowboys, Texans, Colts, Jaguars and Titans.

Those franchises ended the season with a combined .398 winning percentage.

Both Miller and Karwan acknowledged that teams can face an especially easy or difficult schedule any year. But the imbalance of the 2015 schedule led to an irregular concentration of bad teams almost entirely isolated to one half of the league's schedule, Miller contended.

To illustrate the schedule's imbalance, Miller made a graph of every schedule from 2010 to 2021. A look at the 2013-2016 seasons shows how different the 2015 schedule looks.

The 2015 NFL schedule saw less crossover between the different divisions. (Courtesy of Stephen Miller)

Miller found that the cluster-effect in 2015 happened before, in 2012, and will occur twice in every 12 seasons moving forward.

He suggests the league make a tweak to the divisional rotation in the 2019 schedule. The change will disrupt the league's four-year rotation during the 2019 and 2020 seasons but ensure what he calls the cluster flaw never happens again.

"If you want to make a system that is fair and equally competitive for everyone with good balance, you wouldn't set up two different clusters," Miller said.

Adam Clark may be reached at adam_clark@njadvancemedia.com. Follow him on twitter at @realAdamClark. Find NJ.com on Facebook.