New Orleans Saints tight end Josh Hill (89) is tackled by Chicago Bears free safety Eddie Jackson (39) just short of the endzone on a 19-yard pass during the first half Sunday, Oct. 29, 2017, at the Mercedes-Benz Superdome.

Advocate staff photo by SCOTT THRELKELD

The Saints have a diagram in their playbook they dust off every three or four years and present to the public.

It’s a play that’s difficult to defend and so deceptive that without evidence of its previous existence, you might think it was inadvertent and successful only because of a happy accident. But it showed up again Sunday and worked as planned.

“We’ve run that (four) times in 12 years,” New Orleans quarterback Drew Brees said.

The fact that something rare was happening with 4:18 remaining in the second quarter of Sunday’s 20-12 win over the Chicago Bears wasn’t obvious. Those in attendance couldn’t have known how sparsely Sean Payton has called the play since becoming the Saints coach in 2006.

Everything about it looked normal. Brees lined up under center with Alvin Kamara and Michael Hoomanawanui behind him in a split backfield. He faked to Hoomanawanui, turned and looks Kamara's direction.

The line and tight ends blocked as if the pass was going to the running back, and the Chicago defense acted accordingly. Brees pumped and tucked the ball. It looked like the play broke down.

Tight end Josh Hill then peeled off a block and slipped up the seam on a delayed route for a gain of 19 yards with no one around him. The tight end sold the play so well that, for at least a moment, it almost appeared he recognized things broke down and made an adjustment to save it.

But it was all by design, a result of the coaching staff spending late nights scheming for the upcoming opponent. Someone recalled a play on which Brees connected with Mark Campbell for 14 yards against the Dallas Cowboys in 2006, or when Dave Thomas gained 25 yards on it against the New England Patriots in 2009.

The one time the play didn’t work over the years, also against the Cowboys, wasn’t enough to deter New Orleans from bringing it back for a surprise appearance against the Bears.

“It’s been a while, but we have it on cut-up, so of course we’ll pull it up and look at it,” Payton said. “We’ll look at every one, because they run together and kind of give it a formation and bring it up for a game.”

One of the reasons the play worked so well is New Orleans has put together a consistent and effective screen game, somewhat of a change this year. Through seven games, Brees has already connected on 38 of 43 screen attempts for 291 yards, according to Sports Info Solutions. Last year, he hit on 40 of 49 attempts for 302 yards for the whole season.

Mark Ingram (13 receptions for 109 yards on screens) and Kamara (13 for 81) have played a big role in the resurgent screen game, but the addition of Ted Ginn Jr. (five for 57) has been equally important. Having the screen going has been key to the offensive approach this season, and it opens things up when the defense must respect it.

“It’s a complement to the run game,” Brees said. “It’s a complement to the play action. A complement to the drop-back game. When all those things are clicking, they each set one another up.”

The play to Hill encapsulates the dilemma teams face when playing the Saints. Pay too much attention to the passing game, and New Orleans will use its backs, either through screens or runs, to chip away and gain yards. If a defense pays too much attention to Kamara (42 carries for 243 yards) or Ingram (107 carries for 464 yards), Brees can easily find a target down the field.

That’s why the Tampa Bay Buccaneers were singing a different tune about New Orleans this week as they prepare to play the Saints on Sunday.

“Drew Brees is obviously one of the best to ever play the position, but New Orleans is definitely running the ball more,” Bucs coach Dirk Koetter told reporters. “If you don’t go in there to stop the run, they’re going to keep running it at you.”

And if you pay too much attention to the running backs, the New Orleans coaching staff might reach four years back into the playbook and make you pay for it.

Follow Nick Underhill on Twitter, @nick_underhill.​