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The Vikings’ considerable accomplishments in their first 4½ seasons under Mike Zimmer — a 45-30-1 record, a pair of NFC North titles and a trip to the NFC Championship Game last season — were built on the bedrock of principles the coach considers to be foundational: football intelligence, a paucity of mistakes and a level of mental grit that has often allowed them to shake off early mistakes and prevail in the fourth quarter.

There’s another key ingredient to the formula the team has divined under Zimmer: home-field advantage. And if the 2018 Vikings are to make the kind of deep playoff run many had predicted for them, it’s very possible they will have to do it without that potent piece of the recipe.

If these Vikings, who are 27-11 at home under Zimmer, are going to capitalize on their considerable potential and make a run to Super Bowl LIII, only two paths still seem available to them. They can beat Seattle on Monday to keep their division title hopes in decent standing, or attempt to do three times in as many weeks what they have done only twice in Zimmer’s tenure: win a road game over a playoff team.

Since Zimmer took over as Vikings coach in 2014, they are 2-8 on the road against playoff teams in the regular season. They lost their only road playoff game, 38-7 in the NFC Championship Game in Philadelphia last year. This season, the Vikings are 0-1 on the road against a team that’s already qualified for the playoffs (the Rams), and 0-2 against two teams that would be in the playoffs if the season ended today (the Patriots and Bears).

In Zimmer’s tenure, the Vikings have only won four of their 17 games on the road against teams with a winning record; their .235 winning percentage in such games is 17th in the NFL in that time. While their struggles to beat good teams on the road are far from unique, they’re also flailing in an area that’s been fairly essential to the résumé of recent teams that have made deep playoff runs. Of the 32 teams that have played in conference championship games since 2010, only six have gotten that far without a road victory over a team without a winning record.

It’s been a different story at home. Under Zimmer, the Vikings are 7-7 against playoff teams at home, and 1-1 in the actual home playoff games they’ve hosted. Since 2016, they’re 5-2 against playoff teams in the regular season, though the mark will drop to 5-3 once the Saints — who beat the Vikings at home on Oct. 28 — officially qualify for the 2018 playoffs.

“That’s why they give you three points in the points spread when you’re playing on the road,” Zimmer said. “It’s a combination of travel. It’s staying in different beds. Somebody told me once, it’s not just the crowd noise, but everybody there is rooting for them. So, the aura or whatever it is.

“You always try to maintain the same consistency on the road as you do [at home], but there’s a lot of factors that go on.”

It was striking to hear the coach — usually one to exhort his team to overcome adversity through its own fortitude — talk about things such as travel schedules and crowd noise in such stark terms. And yet, he’s right to do so: the data suggests those things have a real effect on the kind of home-field advantage the Seahawks will enjoy on Monday night.

Teams traveling two or more time zones west are 14-32 in Pacific coast night games since 2006. Seattle is 18-4 at home at night in that time, with only New Orleans (in 2007) and Atlanta (last year) winning at the deafening CenturyLink Field after traveling at least two time zones west.

The Vikings, as a whole, have been an above-average road team under Zimmer: their .487 winning percentage away from home ranks 11th in the league since 2014, in a time where road teams leaguewide have an average percentage of .429.

But no matter what happens to the Bears against the Rams on Sunday night, a loss to the Seahawks would leave the Vikings at least 1½ games back in the division with three to play. They would essentially need to win out, and hope the Bears drop one of their two games — at home against the 4-7-1 Packers or on the road against the 2-10 49ers — before the two teams meet at U.S. Bank Stadium on Dec. 30.

In other words, their best chance to win a division title and play at least one playoff game at home lies with their ability to topple a fellow contender in a daunting environment on Monday night.

Getting in only as a wild card would require a sudden answer to a problem that has vexed them for the better part of Zimmer’s tenure.

“It has that [playoff] vibe,” defensive end Stephen Weatherly said. “This is that type of game, and that’s how we must treat it.”