"We're both a little bit nuts when it comes to how we approach the game," said Rivers, smiling.
That passion for the game that both share has led to plenty of success on the field this season.
Rivers had another teammate like that in longtime center Nick Hardwick, but since Hardwick retired in 2014, the Los Angeles Chargers had cycled through six different players before the start of the 2018 season.
The addition of Pouncey, 29, has solved that problem, stabilizing the most important position up front.
Much in the same way that fellow center Alex Mack transformed the Atlanta Falcons' run game upon his arrival in free agency from the Cleveland Browns two years ago, Pouncey has helped morph the Chargers into a physical running team.
Signed by the Chargers in free agency this offseason after the Miami Dolphins released him in a cost-cutting move, Pouncey has been one of the best free-agent additions for general manager Tom Telesco during his six seasons with the team.
Pouncey should be headed to the Pro Bowl for a fourth time in his eight-year career based on his performance this season.
"If I don't get picked for the Pro Bowl, something's wrong," Pouncey said. "But at the end of the day, all I care about is coming here to win the Super Bowl. I feel like with team success comes individual success.
"If you look at all of the guys that have made the Pro Bowl every year, it's the teams that are winning. I feel like if you come in with the mindset that you're here for a team goal, all of the individual accolades will come with it."
One stat specifically points to the affect that Pouncey has had on the Chargers' offensive line.
Gordon's yards before contact during his first season in the league in 2015, per ESPN Stats & information research, was 1.8 yards per carry.
This season, Gordon is averaging 3 yards per carry before contact -- which means the Wisconsin product is regularly getting to the second level of the defense before being touched.
Hardwick has taken notice.
"Pouncey's doing a tremendous job," Hardwick said. "Melvin's got a full head of steam going downhill before he's even being touched.
"The offensive line's athleticism is really showing up this year. They're fast and get to the perimeter. And the fun thing about watching them is the play design has been incredible, not just to use Melvin Gordon or Austin Ekeler's skill set, but they're really finding plays to use Mike Pouncey's skill set and Russell Okung's skill set."
Pouncey was signed to a two-year, $15 million deal, and there were some concerns about his ability to stay healthy after the hip surgery he had two years ago.
However, Pouncey has not missed a single practice or game this season.
"In Miami, the plan was for me to take a day off every other day, and so that's what we rolled with," Pouncey said. "Here, if you can practice, you practice. So that's what we do.
"I was coming off a major surgery, so it was only smart that I eased my way in, and I took days off so I would be game-ready by the time Sunday rolled around. That was the plan, and I rolled with it.
"I hated it because I always had to answer those questions, but it was part of the plan from the second floor of our facility, and that's the way they wanted to go. But I feel awesome. I feel like I'm in the prime of my career. I'm playing awesome football. I'm just thankful I got the opportunity to be here."
Pouncey will get a prime opportunity to strut his stuff with twin brother and Steelers center Maurkice Pouncey watching from the opposite sideline when the Chargers travel to Pittsburgh on Sunday.
"I used to talk about it at the early part of my career that he was just blessed to play with a top-five quarterback," Mike Pouncey said about his brother playing with Ben Roethlisberger. "And that's nothing against all of the quarterbacks I've played with. I've loved all of those quarterbacks. Me and [Ryan] Tannehill still talk all of the time and he's a great quarterback. But when you play with one of the top five quarterbacks in the league, it's a little different."
The Pouncey brothers had been teammates from youth football to college at Florida, where Maurkice played center and Mike played right guard. Mike Pouncey played his last year at Florida at center once his brother left for the NFL draft in 2010, when he was selected No. 18 overall by the Steelers.
Mike said he's 3-1 against his brother, and the only time he lost was in the playoffs while with the Dolphins.
"He said he beat me when it counted most, though," Mike Pouncey said. "So he had a good point."
Pouncey said the entire family will be at his brother's house on Saturday. They'll have a cookout there and hang out before the game.
"I love Pittsburgh," Mike Pouncey said. "I love the people there. Obviously, I'm real close with the organization because my brother has been there for so long. I know all of these guys. I hang out there in the offseason and work out with these guys.
"It's a good group. It's a good defense -- they're top 10 on the run and the pass. They have a good football team. And one of the things you can't look past is a lot of these guys played together for a long time.
"So they're kind of built from within, and these guys have been playing with each other for years. It's going to be a loud stadium and an awesome environment for us to play in, but we've got to play our best football. I know our defense is hyped up to play against my brother. They've been talking trash the entire week."