Their franchise player is out. The playoffs are out of reach.

For the New Orleans Pelicans, these are the very definition of the dog days.

But that doesn’t mean they’re dogging it.

“We got pride,” point guard Tim Frazier said after New Orleans cut a 22-point lead to five before losing 113-99 to the Miami Heat on Tuesday at the Smoothie King Center. “Everybody wants to come out here and win. Nobody wants to just lay down. We’re going to go out there and fight until the buzzer sounds.”

It wasn’t enough Tuesday as the Heat got 25 points from Dwyane Wade, 24 points and 14 rebounds from Hasaan Whiteside and 21 points from Goran Dragic.

And there’s a case to be made that the Pelicans would be best served by losing.

They’ll be mathematically eliminated from playoff contention soon — any combination of New Orleans losses and Houston wins totaling four will do it — and they’ve been out of the picture practically speaking for some time.

With the league’s sixth-worst record, the Pelicans might be wise to focus on maximizing their chance to land a higher pick in the NBA draft lottery.

But even with Anthony Davis shut down for the season with knee and shoulder injuries, New Orleans’ goals haven’t changed, coach Alvin Gentry insisted.

“We’re going to try to win every game,” Gentry said. “We’ve got a competitive group in there.”

That showed Tuesday, when New Orleans shot 30.6 percent in the first half, trailed 59-40 at halftime and fell behind by 22 points early in the third quarter, when the Heat took a 65-43 lead on Dragic’s layup with 10:31 to play

“We dug ourselves a hole, and I think that was kind of the difference,” said Luke Babbitt, who scored a season-high 23 points for the Pelicans. “We played hard in the second half, corrected some mistakes. But we just can’t dig ourselves a hole like that.”

Still, even in a season that’s flailing to the finish, the Pelicans worked to dig their way out of that deficit. They cut Miami’s lead to 11 points early in the fourth quarter, then rallied again after a Heat run extended the spread by to 18.

A jumper from Jrue Holiday — who led the Pelicans with 24 points — cut the lead to single digits at 96-87 with 6:51 to play. Holiday engineered a four-point possession, making a free throw defensive-three-seconds technical foul, then finding Alonzo Gee for a layup-and-foul three-point play that cut the margin to 96-91 with 6:15 to play.

Wade’s jumper with 3:15 to play stretched the Miami lead back to 105-95, and from there the floodgates opened. He made another with 1:55 to play that put the Heat in front 109-97.

“He wasn’t hitting those shots in the beginning,” Holiday said. “He was really getting to the basket, getting to the free-throw line and his turnaround fadeaways were missing. But he hit some big ones down the stretch. It’s D-Wade. That’s what he does.”

What the Pelicans want to do is keep putting themselves in position to win down the stretch, no matter how bleak the stretch run looks.

“(Miami) made some good plays down the stretch and had some things in transition, but defensively I think we’ve been playing really well and we play really hard,” Holiday said. “I feel like that’s the fun part about it. I know my teammates have my back, and ... even though people are out and the season might not have gone the way we wanted to, we’re still playing hard. That’s really encouraging.”