The short answer is that they have the personnel to do it, and often force situations where it's advantageous to have six defensive backs on the field. The long answer is much more nuanced, and easier to show than to tell.
Two of the Rams' biggest defensive plays against the Saints on Sunday came out of dime personnel.
On a 3rd-and-9 early in the game, the Rams showed blitz with two deep defenders, as safety Jaylen "Tank" McCollough crept up on the center from the linebacker spot. When the ball snapped, he dropped back into coverage, taking away the check down in the middle, and L.A. rushed four. Outside linebacker Jared Verse took on a double-team to give one-on-ones to the rest of the line, resulting in defensive end Braden Fiske's first sack of the season.
McCollough's presence in the middle of the defense caused confusion at the line and gave the Rams single-coverage advantages with defensive backs across the board. Even if Saints quarterback Tyler Shough was given time to throw, there would have been nowhere for him to go with the ball.
"The advantage of doing that from a defensive perspective is now we're on the attack," said safety Quentin Lake. "I think it's really good for us because we have such a good rush and you want to get those guys a lot of the times in one-on-one situations and then bring an extra cover guy in when you know it's passing situations."
The Rams' 34.6% dime personnel rate leads the league by a considerable margin, according to Next Gen Stats. It allows them to generate favorable coverage matchups, with McCollough as the extra defensive back, and defensive coordinator Chris Shula combines that with distinct pre-snap looks to make quarterbacks hesitate in obvious passing situations.
"It's been our calling card," McCollough said. "It's been our advantage, I like to say."
The Rams' 5.5 yards per play allowed with that personnel grouping is the third-fewest among teams with at least 25 snaps – the Rams have 177, according to Next Gen Stats. Meanwhile, three teams haven't rolled out a single dime package this season, and a total of 13 teams run it less than 5% of the time, which shows just how much of an anomaly this Rams defense truly is.
It helps that L.A. has forced the most third-and-longs per game (7.4), according to nflverse data, which has given them ample opportunity to bring an extra defensive back onto the field. They already use nickel personnel (five defensive backs) nearly half the time, so throwing McCollough in adds yet another wrinkle for offenses to deal with.
L.A.'s safety depth and versatility contribute to their success in dime. McCollough, Lake, Kam Kinchens and Kam Curl are all chess pieces that can be moved around to fit each play's purpose, giving Shula the resources to creates a variety of looks within the dime package and stay unpredictable.
"You don't want to be in it so limited that you're playing the same thing every single time with the coverage variation and things like that, so we want to be able to play a lot of stuff out of dime, and Tank allows us to do that," Shula said.
On 4th-and-4 with just over five minutes remaining against New Orleans, the Rams showed a six-man front with six defensive backs on the field and one deep safety in the middle. When the ball was snapped, two rushers on the left side dropped back and L.A. brought four, including Curl, again creating one-on-one matchups with simulated pressure.
This time, McCollough lined up 12 yards deep down the seam and then jumped forward to cover the underneath zone. He took away Shough's first read, Taysom Hill on a short in-cut, as pressure forced the rookie quarterback up in the pocket. His off-platform throw to an improvising receiver was intercepted easily by cornerback Emmanuel Forbes Jr. for his first as a Ram, and Los Angeles iced the game from there.
Those simulated pressures work so well because the Rams often bring extra rushers out of dime looks. But even when they don't, the ones hunting the quarterback are not always the players that offenses would expect, as illustrated by the two plays above.
Getting McCollough on the field is a primary incentive for Shula to use dime packages, as he called the second-year safety one of L.A.'s "top guys" on defense. His strong communication, football IQ and tackling make him valuable as both a blitzer and coverage player in those situations.
"He can do it all," Lake said. "And there's a reason why we want to get into those dime packages, it's because you're bringing another really good player out on the field that, especially as rookie year, made a ton of plays. And any time you can bring a guy that has a knack for the ball, something good is gonna happen."
Last season, McCollough tied for the team lead in interceptions with four while only starting one game. This year, his two sacks lead all Rams defensive backs, and that varied production mirrors his usage. He's taken 99 snaps in the box, 53 in the slot, 40 at free safety and even five on the line of scrimmage through eight games, according to Pro Football Focus. That versatility makes him the perfect dime backer for this Rams defense.
"They do a good job of keeping me close to the ball," McCollough said. "I like being close to the ball."
And the Rams like him there, because it usually leads to an impact play, even if he's not the one making it.
