It’s getting so I hate the New Orleans Saints the way I used to hate the Dallas Cowboys. Well, maybe not the same way. I root for whoever’s playing the Cowboys, but I don’t have anything against the Saints — I just don’t want to hear any more about them.

Well, no, that’s not exactly right, either. I don’t actually mind hearing about the Saints, who have gotten increasingly interesting as the season goes on. What I’m sick of is the obligatory “The Saints represent the hopes and struggles of a Katrina-ravaged populace” paragraph that sportswriters tack onto their Saints story as if to admit that sports isn’t a big enough subject to write about.As if a tenuous if not utterly bogus connection between football and the alleviation of human misery somehow makes what they’re writing about more meaningful.

As if the Saints’ coldblooded owner, Tom Benson, wouldn’t move the team in a heartbeat to Los Angeles or San Antonio or anywhere else that offered him a better deal — which in fact he was plotting to do before the deluge.

See? I’m doing it myself. It’s hard to get out of this sports-as-metaphor syndrome, even when trying to reject it. I suppose what I’m really tired of is this synthetic feel-good attitude the early success of the Saints this year is supposed to have inspired in us all, fostering an attitude that by watching them on TV and cheering along with their fans, we’ve done something to help restore New Orleans. Or as Will Forte’s President Bush said in a “Saturday Night Live” sketch, “Well, the Saints are winning, so I guess New Orleans is back.”

New Orleans isn’t back, and I’m dubious about the Saints. I’m forced to admit, though, that the fourth quarter of their 27–24 win over the Eagles last Sunday, in which they held onto the ball for more than eight minutes, was probably the most impressive drive in the team’s history. Granted, that isn’t saying much for a team with the Saints’ history, and enthusiasm over the team’s fine start this year should be tempered somewhat by the knowledge that their opponents in their four victories before the Philadelphia game were, aside from their games with the Saints, a collective 6–11. Still, those are precisely the kind of teams the Saints have lost to many times in the past, so change, ushered in by energetic head coach Sean Payton, seems to have arrived in New Orleans at last.

I say “seems” because three times since the Saints were born 40 years ago, they have started the season by winning five of their six games and wound up with nothing to show for it.This coming Sunday they have a bye, after which they play Baltimore, Tampa Bay, Pittsburgh, and Cincinnati in successive weeks — a four-game stretch that should determine the course of their season. Should they manage to win three of four, they will be regarded as one of the NFC’s elite teams, along with the Bears, the Eagles, and the Seahawks. Even if they stumble, they’ll be in a good position to make a run at the playoffs. This looks awfully good after going 3–13 last year, when they failed to excel in any area of the game except punting — and that, probably, was because they had so much practice.

This year, under Payton (whose credits include going to the Super Bowl as offensive coordinator with an undistinguished 2000 New York Giants team) and defensive coordinator Gary Gibbs (who, like Payton, was an assistant to Bill Parcells at Dallas), the Saints have improved in every area of the game. The defense, so far, has gone from yielding an average of 25 points a game (28th worst in the league last year) to 18.3 (10th best this year). The biggest improvement has been the offense. Thanks largely to the acquisition of quarterback Drew Brees, they’ve gone from 14.7 points scored a game (31st in the league) last year to better than 24 points in six games this year (seventh best).

Last year, with quarterback Aaron Brooks, the Saints were averaging just 6.7 yards a throw and had fewer TD passes (13) than interceptions (17). This season, with Brees, they’re averaging 7.3 yards a throw and two TDs per pick, 8–4. The revamped offensive line, thought to be the Saints’ weakest spot last season, is providing superb protection: Brees has been sacked on just 2.8% of his attempts, compared with 7.1% for Brooks.

One reason the Saints are not winning this year is the much celebrated Reggie Bush, who, if he had been playing for a losing team, would be regarded as yet another Heisman Trophy winner-turned-NFL bust. Bush did come up big with a 65-yard punt return to help beat Tampa Bay two weeks ago, but that’s been his only tangible contribution so far. He has gained just 195 yards rushing for a dismal 3.0 average; the Saints, amazingly, actually average 1.2 yards better when someone else runs the ball. My guess is that the disparity between Bush’s yards per rush and his teammates, is caused by the opposition constantly keying on him, which may also explain why Brees has been so effective throwing the ball. But whatever the reason, it’s doubtful that the Saints are going to win anything with Reggie Bush averaging just 3.0 yards a carry.

Contrary to popular opinion, the Saints have gone to one Super Bowl, but that was in a very bad movie, “Number One” (1969), and their quarterback was Charlton Heston. Brees isn’t as good a quarterback in real life as Heston was in the movie, but he may be the best passer in the Saints’ real-life history. If Reggie Bush starts to play anywhere near the level of his press clippings, we’re all going to be deluged with stories about how the Saints saved the city.Who knows? If the Saints make it to the Super Bowl, the stories might even be true.

Mr. Barra is the author of “The Last Coach: A Life of Paul ‘Bear’ Bryant.”