Think of the Saints, and you envision Drew Brees receiving a snap, peering down the field as he takes his drop, settling in to deliver a deep pass down the field to one of his many weapons.

This vision has been true for nearly a decade. Since 2007, Brees has attempted 490 passes that have traveled 20 or more yards through the air, or 4.4 per game. This year, however, he’s only attempted seven such passes, according to Pro Football Focus, obliterating that vision.

A more accurate depiction of the Saints offense this season would be one of Brees throwing an intermediate pass to tight end Jimmy Graham down the seam or of a running back hitting a hole opened by the offensive line for a gain of 10 yards.

Is this who the Saints have become? Is there a change in philosophy ordering Brees to attempt higher-percentage passes, or is the prohibition on big plays being governed by stingy defenses?

“At times,” coach Sean Payton said, “the ball comes down to underneath coverages.”

In other words, the lack of deep attempts is not necessarily by design. The Saints are always looking to put the defense on the ropes as quickly and easily as possible. The best way to do so is often by taking a shot down the field and picking up big yards. The issue is that those defenses know New Orleans’ method of operation and try to make the Saints win in other ways.

That happened several times in Sunday’s 20-9 win over the Minnesota Vikings. The Saints were running the same plays out of the same formations they’ve used for years, which often times result in Brees connecting with a receiver deep down the field. The difference was the Vikings were taking away the deep third of the field, which forced Brees to throw to his second or third read.

One instance of this occurred with 6:07 remaining in the first quarter of Sunday’s game. The Saints ran a play where they created their three-level concept, with three players running a deep, intermediate and short route that ended on the left side of the field.

The goal was to get the ball to Graham, who was split out wide and ran a deep route down the sideline. But the Vikings bracketed him with a cornerback and safety. This left rookie receiver Brandin Cooks, who ran a slant over the middle, open in the intermediate level of the field. Brees was forced to throw to the open man for a gain of 16 yards.

“There’s a deeper throw on top of that,” Payton said. “Sometimes the progression takes you to an underneath throw.”

And that’s fine. New Orleans is willing to pick teams apart however it can. But, like those dreaming of previous days when the ball was flying freely down the field, this team is also itching to let the ball fly again.

“I think, for one reason or another, we’ve dialed them up, (and) we just had to go elsewhere,” Brees said. “There’s a couple more that we could start making. Obviously, those are difference makers in the game, especially when you talk about the first two weeks of the season the way we lost those games. We’re one play away here and there. Maybe that one play is the one that makes the difference.”

The Saints offense hasn’t been completely bereft of the “big play,” which is internally defined as a run of 10 or more yards or a pass of 15 or more yards. They’re just occurring in different ways than pervious seasons.

New Orleans has had 29 so-called “big plays” this season. Of those, 12 have been rushing plays (four per contest) and 17 have come through the air (5.6 per game). In 2012, the Saints averaged 2.5 big running plays per game and seven through the air.

Brees said the ideal number of big passing plays per game is around eight and believes the team can get to that figure with a few tweaks and more opportunities. He’s also aware that nothing less will accepted.

The standard he has set in this offense demands more. The Saints are expected to pass for close to 5,000 yards every season, win double-digit games, and serve as the modern version of “The Greatest Show on Turf.” Feasting on short and intermediate routes is not going to satisfy the masses.

It also may not satisfy those out on the field.

“In a way we’re kind of competing with the offenses that came before us on this team, within the Saints organization. There’s a level of pride that goes into that,” Brees said. “Not only are you going out and competing with the defense that you’re playing that week and you’re trying to score as many points as you can and play as complementary a game as you can with your defense. But at the end of the day you’re kind of asking yourself how you stack up against the teams that came before us.

“We want to be considered one of the best, and I feel like we have the capability to do that.”

Connecting on a few more shots down the field would go a long way toward helping these Saints beat those Saints.