Anthony Davis has permission to take plays off.

It’s not that Pelicans coach Alvin Gentry has given his star a pass to slack. It’s not that Gentry wants — or that New Orleans can afford — anything less than everything Davis has to give on any given night.

But sometimes — when a loose ball is bouncing out of bounds, for example, and Davis is in hot pursuit — Gentry would prefer the 6-foot-10 forward take a breather.

Davis hurdled into the stands in Thursday night’s win against the Detroit Pistons, two weeks after a similar stunt against the Indiana Pacers cost him almost three full games with a back contusion.

“I told him he doesn’t have to hustle that hard,” Gentry said. “We’ll let that one go. We’ll let that one ball go if he doesn’t run through the seats and fall again.”

The Pelicans need Davis giving his all-out best. But mostly they need him on the floor, as has become increasingly apparent in recent games.

Since Davis returned from that back injury, New Orleans has won four of five games, the lone loss coming by two points at Memphis. The Pelicans, who started an injury-ravaged season 1-11, entered Friday’s games four games out of the eighth and final playoff spot in the Western Conference.

In that five-game span, Davis is averaging 26.8 points per game on 51.1 percent shooting. The Pelicans’ offensive rating when he’s on the floor in that is 116.4 points per 100 possessions, up 12.4 from Davis’ season average.

And though Davis hasn’t to this point replicated his eye-popping statistical season of a year ago, he still ranks among the league’s most impactful players.

His Player Efficiency Rating — a league-leading 30.89 last season — has dropped to 24.99 this season, but that still ranks sixth in the NBA, behind only All-Star starters Stephen Curry, Russell Westbrook, Kevin Durant, LeBron James and Kawhi Leonard.

Of late, Davis is playing at an “MVP-type level,” Gentry said.

“That’s the Anthony I know,” Pelicans guard Jrue Holiday said. “I feel like he’s been playing like that all year. Obviously his shot is connecting a lot better. He’s getting to the free-throw line, doing a lot of everything. Anthony, that’s him.”

Over the past two games, Davis is shooting 12 for 20 (60 percent) on shots from 10-19 feet, a range from which he’s made 39.2 percent of his shots this season and made 43.5 percent a season ago.

“I was hesitating a lot (shooting),” Davis said. “Now I’m just catching it, shooting the ball with confidence and just letting it go. That’s been the main difference, and it’s been going in. Now I’ve just got to make reads off of it, know guys are going to try to close out.”

Those reads have been among the biggest offensive keys to New Orleans’ recent surge.

Over the past five games, Davis is averaging 2.2 assists, a half-assist higher than his season average. His assist-to-turnover ratio over that span is 1.83, up from 0.8 for the season. He’s creating 5.4 points per game off assists over that span, up from 4.3 over the course of the season.

On one sequence in Thursday’s win against Detroit, an open Davis animatedly called for the ball on the perimeter. Guard Tyreke Evans kicked it to Davis, the defense reacted, and Davis whipped a pass to Alonzo Gee, who had a clear path to dunk.

That’s “exactly” the sort of play Davis’ presence creates for the other Pelicans, Gentry said.

“He’s a very unselfish player, and he’s going to make the right play,” Gentry said. “And that doesn’t always mean him shooting the ball or trying to score.”

Davis’ willingness to move the ball has been “a little bit contagious,” Gentry said, and the Pelicans are seeing the results. They had 17 first-half assists against the Pistons, and over the past five games, New Orleans is creating 59 points per game off assists, about seven more than its season average.

It starts with Davis, who generates the most defensive attention and benefits the most from scoring opportunities for teammates that pull defenders away from him.

“I’ve got to make everybody better around me, giving them confidence,” Davis said. “When everybody else is making shots, it takes a lot of pressure off me and a lot of attention off me. That gives me a lot of room to roam and a lot of room to operate.”

Davis’ surge — and the Pelicans’ hot streak — comes just as he was snubbed by fans voting for All-Star Game starters. Davis finished ninth in voting among Western Conference frontcourt players, well outside the top three required for a starting nod.

Though Davis said wants to play in the game if NBA coaches select him as a reserve, he has other concerns.

“At the end of the day, I’m worried about what’s in this locker room,” Davis said. “That’s just a bonus in addition to players’ careers. Guys don’t come in like, ‘I’m coming in the league, I want to be a 10-time All-Star.’ They worry about rings and helping their team win.”

Lately, Davis is doing just that.

Davis pondered Gentry’s somewhat-facetious offer to stop diving into the stands for loose balls before turning it down. It’s an instinct, he said. He sees the ball and pursues it. He wants to chase a playoff bid with the same zeal.

“I like the fact that he says he needs to lift everybody else’s game up, because that’s what great players do,” Gentry said. “I think it’s something that he’ll continue to get better at as his career goes on. The one thing I do know about him, he’s a tremendous kid, and he really wants to win. That’s the most important thing to him.”