The NFL’s 12-team playoff field is sprinkled with very good coordinators who once were plenty bad enough to be fired as head coaches.

Packers defensive coordinator Mike Pettine was 10-22 in Cleveland. Texans defensive coordinator Romeo Crennel was 28-55 with the Browns and Chiefs. Eagles defensive coordinator Jim Schwartz was 28-51 with the Lions. And then there’s old friend Leslie Frazier, the Bills defensive coordinator who was 21-32-1 as head coach of the Vikings from 2010-13.

But perhaps the ultimate ongoing NFL image overhaul is happening in New Orleans, where defensive coordinator Dennis Allen is crafting a sturdy defense on a 13-win team as Sean Payton and Drew Brees continue making history on the other side of the ball.

In the NFL’s 100-year history, only two people have been head coaches in as many or more games while winning fewer of them than Allen did when he went 8-28 with the Raiders from 2012-14. They are Mike Nixon, who went 6-30-2 with Washington and Pittsburgh from 1959-65, and Phil Handler, who went 4-34 with the Chicago Cardinals from 1943-51.

And yet, as a coordinator, Allen heads into Sunday’s home wild-card playoff game against the Vikings with at least two particular strengths that could spell one-and-done for the underdog Vikings and their sputtering offense this postseason.

The first is a run defense that ranks fourth (91.3 yards per game). The second is a third-down defense that ranks sixth (34.76%).

“They’ve made a lot of progress [under Allen]; they’re much better,” Vikings coach Mike Zimmer said of Allen, who replaced the fired Rob Ryan during the 2015 season. “Part of it is personnel. But [Allen] has added a lot, package-wise, as far as different looks you’re going to get, especially on third down.”

The Vikings hope to counter Allen’s run defense with a finally healthy Dalvin Cook, whose dynamic skills have been muffled by injuries since the end of November. The last time he was healthy, he touched the ball 33 times for 183 yards and a touchdown in the 28-24 win at Dallas in Week 10.

“I definitely feel refreshed,” said Cook, who was rested the past two weeks. “I’ll be ready to go. I’ll be at full strength. I’m going to be me.”

Receiver Stefon Diggs was asked what that will mean to an offense that posted 139 yards, seven first downs and 10 points when Cook sat out the prime-time home loss to the Packers in Week 16.

“You been here all year,” Diggs told the reporter. “You seen the kind of football we played with him. He definitely changes the game, both in the running game and the passing game.”

The 47-year-old Allen got his NFL start as a defensive quality control coach with his hometown Falcons in 2002. He joined the Saints for the first time as assistant defensive line coach from 2006-07 and defensive backs coach from 2008-10.

The Broncos hired him as defensive coordinator in 2011. And despite Denver going 8-8 and giving up 45 points in a divisional playoff loss to the Patriots, the Raiders hired Allen as head coach.

After back-to-back 4-12 seasons, he was fired when the Raiders started 0-4 in 2014. He returned to New Orleans the following season as a defensive assistant but was an in-season replacement as Ryan’s defense was on its way to ranking last in points allowed and 31st in yards allowed.

This season, the Saints ranked 11th in yards allowed (333.1) and 13th in points allowed (21.3).

As far as run defense, they’ve been top-four two consecutive years after ranking second last year (80.2). The Vikings come in ranked fourth in rushing (144.9).

“They’re getting guys around the football, and guys aren’t really missing tackles,” Cook said. “But no matter what they did during the regular season, it’s a new season, a new start.”

As for third-down defense, the Saints haven’t been this good since 2011, when they ranked fifth (33.17%). The Vikings have the 13th-ranked third-down offense (38.43%).

“They’re very aggressive,” Zimmer said. “[End] Cam Jordan is an excellent player. They play a lot of under front where they get extra guys in there and are aggressive attacking the offensive line.

“On third downs they get an all-up look and do a lot of things out of the same look. They attack your protections and, overall, they’re about 40 percent man-to-man, so we’re going to have to defeat some man-to-man.”

In other words, Allen sounds a whole lot harder to beat in black and gold than silver and black.