Sean Payton has earned his reputation as one of the NFL's most brilliant offensive minds during 10-plus years as head coach of the New Orleans Saints.

But during that same decade, Payton also has burned through four defensive coordinators. He is now on No. 5, Dennis Allen.

Most of them have been fired because the defense just plain stunk -- it set the NFL record for yards allowed in a season under Steve Spagnuolo in 2012 and set NFL records for TD passes allowed and opponents' passer rating last season before Rob Ryan was fired in November.

Other times there have been some personality clashes -- such as with Gregg Williams, who helped lead the Saints to a Super Bowl in 2009. And Ryan burned some bridges on his way out, complaining that Payton and Saints management tried to force a defensive scheme on him that he didn't agree with.

It's hard to pinpoint exactly how much blame falls on the shoulders of Payton himself, how much falls on the front office and how much falls on each individual defensive coordinator.

But if chemistry has anything to do with the equation, then Allen should have the best chance of success yet.

For the first time since Payton hired Gary Gibbs on his original staff in 2006, Payton actually has a relationship and a history with his defensive coordinator.

Payton first hired Allen as a defensive line assistant in 2006. Allen coached defensive backs during the Saints' Super Bowl run before moving on to become the Denver Broncos' defensive coordinator and head coach of the Oakland Raiders.

"I don't know [how much of a difference that makes]," said Payton, who pointed out that a big part of the Saints' success in 2009 came because of the defense -- even though he had never worked with Williams before he hired him that year.

"When you hire a staff, there's probably half of the group that you have experience with and the other half you don't," Payton said. "The key is getting staff guys, team guys, that aren't independent operators, and I think that really goes for any side of the ball or special teams. And Dennis is someone that I know is really well respected in our room. He's worked hard to get to this position. And he's gonna take full advantage of it.

"He's much like I was when I was first coordinating in New York, then having those opportunities in Dallas. You want to improve, and you want to make a difference. And I think he's smart enough where he sees, 'Hey, we can only get better.'"

Allen, who experienced the relationship from the flip side when he hired two offensive coordinators in his three years as the Raiders' head coach, said results matter more than the relationship.

"I think Sean and I have a good relationship. But at the end of the day, I have a job to do," said Allen, who said how much rope a coordinator gets usually depends on how well he's performing.

"As long as you're seeing the execution, and the product that's going on the field is good, you're pretty much gonna let guys do their job. That's what you try to do, you try to hire good people, you try to give 'em the direction and what you want to get accomplished. And then you kind of get out of the way and let 'em go work.

“And look, Sean's been great to me, not only since I've been back but previously."

ESPN analyst Herm Edwards said it's not a requirement for a head coach to have a previous relationship with his coordinators, but it does help.

When the defensive-minded Edwards got his first head coaching job with the New York Jets in 2001, he said his first hire was offensive coordinator Paul Hackett, whom he had known since the early 1970s.

"There was a trust factor there, that, 'Hey, that's a guy that I can go in and sit with and visit with and he wouldn't feel like I was trying to undermine his authority,'" said Edwards, who doesn't believe a head coach should try and dictate the coordinator's scheme too much.

"When you hire a guy, you do your due diligence on the defense he likes to run, you're familiar with it, you like his system. You don't want to have any guy come in there where you want to change what he's doing. Now, you can always have the conversations. And I think for Sean, just like for me, what he brings to the table to a defensive guy, he can say, ‘When we see this coverage or we see this blitz, that gives us problems.' That's the unique relationship."

Allen's approach so far this summer is that simpler is better, because it allows players to play and react faster without thinking so much.

"The belief is that we have to be a fast, aggressive, attacking style of defense. You can't play defense sitting back on your heels," said Allen, whose style is similar to Williams', including a penchant for blitzing.

Players have responded positively so far, both in their words and the speed of their play.

"It's the fastest defense I've ever seen since I've been here," fourth-year guard Tim Lelito said.

"[Allen] just wants to play violent football. If you can play fast, you can play violent, nasty football," said safety Kenny Vaccaro, who was a big supporter of Ryan but pointed out that it was a nice change this summer when the defense arrived to training camp and continued installing the same playbook they had already been practicing during OTAs and minicamp.

Defensive end Cameron Jordan now has played for four coordinators in six years with the Saints, going to the Pro Bowl twice under Ryan, in 2013 and 2015.

Jordan said the relationship between head coach and defensive coordinator doesn't really affect him as long as they figure out how to make it work on the field.

"We've had a great time when the head coach and defensive coordinator have bumped heads. Sometimes it's a good thing," Jordan said. "And then when they're one the same page, I can only hope for the better."