NEW ORLEANS — There’s hope.

To be sure, as thrilling as Sunday’s 31-27 victory against previously unbeaten Atlanta may have been, one game into the second half of the season, the Saints are still only 4-5, with more teams ahead of them than behind them in the NFC.

But those four victories have come in the last five games following that execrable 0-4 start.

And, as the NFL so helpfully pointed out Sunday, since 2000, 29 teams have reached the halfway point of the season with a .500-or- below record and still made the playoffs, including at least one each year.

Winning the NFC South probably is out of reach. Despite Sunday’s loss, the Falcons are still four games ahead of the Saints with seven to go, including a rematch 17 days from now in Atlanta.

And they don’t have the look of a team about to fold.

You also can probably slot one of the two wild-card spots to either Chicago or Green Bay. That missed opportunity in Lambeau Field may come back to haunt the Saints even more than the home collapse against Kansas City.

Of the other NFC playoff contenders, Seattle, 6-4 after a 28-7 victory against the New York Jets on Sunday, look to be the hardest team to catch. And since the Saints don’t play them, there’s no opportunity to gain a head-to-head advantage.

Still, it’s fun to speculate.

But it would have been moot point, had not the Saints defense made a goal line stand for the ages. Giving up 454 yards isn’t so bad when No. 455 would have meant the difference between victory and defeat.

And even after that stop, the Falcons nearly pulled it out when Matt Ryan’s long pass went just over a backpedaling Roddy White’s head.

Everyone of a certain age in the Superdome had to be thinking “Big Ben.”

“Is that Ben Roethlisberger?” guessed second-year cornerback Isa Abdul-Quddus, whom White had gotten behind on the play, when asked he if had ever heard of it.

Abdul-Quddus can be forgiven for not knowing about the other Big Ben. It occurred in 1978, 11 years before he was born.

What would have been unforgivable was if White had caught the ball, although he fallen before reaching the end zone.

“If he’d caught it, I would have tackled him,” Abdul-Quddus said. “No way he’s getting in.”

Such is the confidence of youth.

And such is the growing confidence of the Saints.

This is a team that still gives up yards in bunches. But it’s getting better in the red zone. Out of six times inside Saints 20 Sunday, the Falcons twice had to settle for field goals in addition to the fourth-quarter stand.

And the running game, which produced 140 yards last week, topped that with 148 on Sunday, including Chris Ivory’s 56-yard TD that brought the team and the crowd to life after the Falcons had jumped to a 10-0 lead.

This is also a team that shuts out distractions.

Sean Payton’s contract status seemed of little interest to the players last week.

“I truly believe our best football is yet to come,” quarterback Drew Bees said in the afterglow of victory.

Yep, there’s hope.