Pierce was the number two running back for the Super Bowl champions in 2012 during his first season in the NFL, with Rice leading the running game for the Ravens.
Running backs coach Wilbert Montgomery told reporters: "It's going to be hard next year with how you play those guys. We are building a bully and [Pierce] exemplifies that with his play and his attitude.
"He's a quiet guy, but he's still a fun guy, and I think his teammates really love him. They know when he's on the field that he's going to make something happen."
Pierce added: "Nobody is perfect and there's always room for improvement, and that's really how I've always based my game. No matter how much we get praised, or how much somebody thinks you're this great player, there is always room to make yourself better. That's what's going to keep me motivated."
Rice rushed for 1,143 yards in the regular season, while Pierce finished with 532.