The New Orleans Saints defense celebrates an interception by New Orleans Saints safety Marcus Williams (43) during training camp Sunday, Aug. 5, 2018, at Tulane University's Yuleman Stadium.

Three times in the past two days, a New Orleans Saints defender has picked off Drew Brees and taken off for the opposite end zone with the rest of the defense in tow. 

And not just the other 10 men on the field. For the past two days, the entire Saints defense has come off the sideline to escort the interceptor into the end zone, then joined in the team photograph celebrations the Saints made famous after turnovers last season. 

All of this is by design. 

Under Sean Payton, the Saints have always emphasized creating turnovers on defense, and a resurgent New Orleans defense finished tied for ninth in the NFL last season with 25 takeaways — including 20 interceptions, third-best in the league. 

Payton isn't going to be happy with merely taking the ball away this season. He said he wants the Saints defense to convert those turnovers into points.

"Sean kind of challenged the defense the other day in a team meeting," defensive coordinator Dennis Allen said. "Talked about scoring defense, talked about how we used to practice that back in 2009. So we made a pact than when we do that, the whole defense is going to get down there and get the ball in the end zone."

A year ago, New Orleans produced three defensive touchdowns all in the same game, a wild 52-38 win over the Detroit Lions on Oct. 15. 

But Payton and Allen want scoring plays on defense to happen all the time, the way the 2009 team manufactured touchdowns on defense.

The Saints produced seven defensive touchdowns on its way to the Super Bowl in 2009, second-most in franchise history behind the nine they created in 1998.

"I don't know that I've been around a team since that 2009 team that really lived it every day," Allen said. "That's kind of where we're trying to go."

At first glance, defensive touchdowns can seem almost like random bolts of lightning, plays that come when conditions are just right. 

For some teams, defensive touchdowns may come at random. 

Payton and Allen also believe that those types of game-breaking scores can be manufactured, at least to some extent. 

"Well, there's a mindset," Payton said. "You get a little confidence and generally, you don't have to block 10, but you need 10 looking to block two. I saw that first-hand take place, and then once you have one, then you begin to think any type of fumble recovery or interception, there's been a chance."

The Saints enter this season with Super Bowl expectations — the kind of expectations that are met by teams who create edges over the rest of the NFL. 

One of those edges for the 2009 team was a defense that was always looking for the end zone, led by former safety Darren Sharper, who scored three times off of interceptions that year. The most memorable play of the Saints' Super Bowl win over the Indianapolis Colts was a defensive touchdown, when Tracy Porter picked off Peyton Manning and took it back to the house. 

"We kind of talked about, there's been a handful of teams in our league’s history that have had a lot of scoring plays on defense. What the percentages are of winning games when you score," Payton said. "Obviously in 2009, we scored a lot on defense." 

As far as the way the defense has responded in training camp, with every member jumping off the bench to escort the ballcarrier down the field, Payton thinks there might have been a little sarcasm inspiring the defense's enthusiasm in Sunday's practice at Tulane's Yulman Stadium.

Whether it was tongue-in-cheek or not, Payton will take it. 

The more the Saints think about shifting from defender to blocker, the more they will do it in games. 

"For you to be able to do that, score on defense, you've got to practice it every day, just like you do everything else," Allen said. "The first part is you have to be able to take the ball away; that's No. 1. But now, let's get everybody running down the field, getting some blocks, and let's score on defense."

The celebrations will follow. 

Follow Joel A. Erickson on Twitter, @JoelAErickson.