It's been three weeks since free agency began.

The New Orleans Saints have signed their share of players, retaining some key pieces from last season (Wil Lutz, Teddy Bridgewater, Craig Robertson, Chris Banjo and P.J. Williams) while adding some valuable players who should make an impact.

How well do the Saints think they have done thus far?

"We don't grade how we did in free agency," Sean Payton said last week at the NFL's annual league meeting in Phoenix. "I don't look at free agency as a frenzy like we do in some networks. I think the misnomer is the first day of free agency is a little more of April Fools than it is Christmas. You've just gotta find players that you think fit and avoid all the noise and pay attention. When we've done that with players we have good vision for, we have been more successful. When we've done that for player that the vision has not been as good, we haven't been as successful."

Here's a look, listed chronologically, at the six new players the Saints have signed and what they could bring to the table.

Latavius Murray, RB

The Saints got bigger (Murray is 6-foot-3, 230 pounds, compared to Mark Ingram's 5-10, 215), but did they get better? Probably not. But they may not have needed to. Alvin Kamara, entering his third season, will be featured more in the offense now. Murray will be a serviceable No. 2 guy and should be able to give the team at least close to the same punch that Ingram did. It'll be hard for Murray (or anyone else, for that matter) to bring the energy and leadership Ingram did. But what Murray brings on the field should be serviceable. Payton raved about Murray's speed, acceleration, size, smartness and ability to pick up the blitz and block.

"He'll have a big part of what we do," Payton said.

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Malcom Brown, DT

Most people considered tight end to be the team's biggest need. But Payton said it was defensive tackle. That's because Sheldon Rankins, coming off his best season, will miss the first part of the year recovering from the torn Achilles he suffered in the playoffs against the Philadelphia Eagles. Brown, who just played his fourth season with the Super Bowl champion Patriots, will be called upon to help plug the hole left by Rankins. With the status of David Onyemata also up in the air (he was cited in February for allegedly having marijuana delivered to his home) and Tyeler Davison being a free agent, finding a body or two to help in the middle was imperative.

"He’s strong," Payton said of Brown. "He's a physical player. He’s tough to move out of his gap. He’s been well-coached, obviously, and a guy that we studied closely coming out of Texas and saw a lot of good tape from in New England."

Mario Edwards Jr., DT/DE

The Saints signed Edwards for the same reason they signed Brown: depth up front. Edwards, who played mostly on the inside last season with the Giants, adds some versatility in that he can also play on the outside. That could be big considering former defensive end Alex Okafor has moved on to the Kansas City Chiefs.

Nick Easton, C

When free agency began, no one knew the center position would be a need. But when Max Unger announced his retirement, the Saints decided to go out and get one. Yeah, Cameron Tom and Will Clapp could have played there, but the Saints found a more seasoned player entering his fifth year. Easton can play guard or center but says center is more his natural position. And it's where Payton said he'll line up. Easton missed all of last season after having neck surgery, but he says he's fine now. He'll be counted on to replace a three-time Pro Bowler.

"At the end of the season, we felt like there was a chance we'd lose Max to retirement," Payton said. "Max had a great career. Nick is someone we evaluated as a center. We saw him play guard. We think he'll fill in nicely there."

Marcus Sherels, return specialist/CB

This is one of those signings that fans will likely be appreciate more once the season starts. The Saints offense is typically so good that the team's punt return game usually goes unnoticed. But the Saints' longest punt return last season was one by Tommylee Lewis (who has since signed with the Detroit Lions) that went for 17 yards. Sherels, meanwhile, returned six punts for at least 20 yards last season with the Minnesota Vikings. He averaged 12 yards per punt return, including a season-best one of 70 yards. He averaged 17 yards on kickoff returns, which will help improve field position.

"He’s been pretty dangerous now and a guy that I’m anxious to see in a Saints uniform," Payton said.

Jared Cook, TE

The Saints needed a tight end. Badly. They addressed the need by signing the best one on the market. Cook could be to this season's Saints free agent class what linebacker Demario Davis was to last year's class. Coming off a Pro Bowl season with the Raiders, Cook gives Drew Brees yet another dangerous weapon and should make an explosive offense even more potent.

"I think he can run," Payton said. "I think he's a really good receiver in space. I think he does a good job after the catch, his yards after the catch. He's comfortable playing in a lot of different spots."

Overall, Payton likes what the team has done so far.

"We are pleased we could add some depth at tackle," Payton said. "We've added a tight end we think can help us. We've added a running back, a young player we think can help us. We'll see where we are when we get back."

Follow Rod Walker on Twitter, @rwalkeradvocate.