If you’re a Vikings fan, there’s a good chance you’ve spent at least some time this week examining the 2019 schedule released Wednesday for pluses and minuses as they relate to the purple.

There’s a better chance, though, that Mark Karwan was looking even more closely at it.

Karwan, a professor of operations research at the University of Buffalo, is part of a team of researchers that has partnered with the NFL in an attempt to make the league schedule as fair as possible for every team.

The group earned a three-year grant in November, and while their work didn’t impact this year’s schedule Karwan is studying it with great interest as he looks for ways to improve things next season and beyond. His conclusion for 2019? Vikings fans should be happy.

“In terms of things the NFL tries to avoid, you did really well,” Karwan said in a phone interview Thursday.

For example, the NFL tries to avoid giving teams three consecutive road games. Because the Vikings had a stretch like that in 2017, the league tried particularly hard to avoid it last year and this year — and it did. The Vikings don’t have any three-game road stretches and have just two sets of back-to-back road games.

The league also works to avoid sending teams on the road a week after playing a Monday night road game. The Vikings are in the clear there, too. The NFL likes to maximize division matchups late in the year. The Vikings have three of those in the final four weeks – all at home.

And there is an attempt made to minimize the number of games a team plays after an opponent’s bye week because research shows such games favor the fresher team. The Vikings have just one such game (Week 11 against the Broncos, who are idle the previous week).

Arriving at a schedule that is fair, however, is an arduous task. Factoring in days of the week and opponents, the Vikings alone have about 60 trillion different possible schedule combinations. For the entire league?

“There are more combinations than the number of atoms in the universe,” Karwan said.

He was dead serious.

Add in the fact that TV partners need to be accounted for and that about 40 percent of all possible home dates are blocked because of things such as team requests or stadium conflicts, and it becomes impossible even for a group of supercomputers working around the clock.

“If you try to use math to solve all of it, it won’t solve during our lifetime,” Karwan said.

To get a handle on all those combinations, the league locks in about 50 games before filling in the rest of the 256-game regular-season schedule. Some of those are coveted primetime matchups, but others are less obvious.

Karwan’s team is studying ways to more carefully consider those 50 games to maximize fairness across the whole schedule. The group can also spend more dedicated time on schedule questions during the long stretches of the year when the NFL is focused on other things.

It’ll never be perfect. But in the future, the schedule could improve with their help.

As for now? Maybe you’re grumbling about the Vikings playing five of their final nine games at night, especially given Kirk Cousins’ woeful record in primetime games.

Speaking non-mathematically, Karwan says: “Obviously great things are expected from Minnesota this year.”

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