"We're all good," he said. "We all bring something to the table."
York, a transfer from Fullerton College, is the most experienced back among the group but has been slowed by injuries.
He missed three games due to an ankle injury in 2012, and turf toe sidelined him for most of spring.
Interestingly, he is trying to replace John White, a guy whose own durability was questioned by the coaches. But the little 5-foot-8 back proved to be one of the toughest backs the Utes have ever had.
White became the only rusher in Utah history to gain 1,000 yards in back-to-back seasons, finishing with 2,560 yards and ranking fourth all-time in career rushes (534).
Utah coach Kyle Whittingham believes York can have a 1,000-yard season too as long as he stays healthy.
"That has always been his issue," Whittingham said.
York just smiles in response. He learned more from White than just how to run against Pac-12 defenses, he said.
"He had a lot of determination and a big heart," York said. "I remember the Colorado game he broke his arm on one play and still scored a touchdown. He had a lot of heart and determination, and I want to be like that. I looked up to John a lot, and I want to be tougher."
If he isn't, York knows the other guys are right on his heels.
Poole, a redshirt freshman, has good hands and fits well into co-offensive coordinator Dennis Erickson's plans, while Williams is a converted fullback who has slimmed down more than 20 pounds to be in the 230s, while the 5-8 Radley is a tenacious back.
Williams had one of the better efforts in the spring and is determined to keep the pressure on York, he said.
"Losing weight has helped my speed," he said. "I feel good about what I'm doing, but I know we have a lot of practices to go."
Also emerging as someone who could get snaps is freshman Troy McCormick, whose catching abilities might earn him some time as a slot guy, Whittingham said.
"We've got a lot of depth there, and that is a plus for us," Whittingham said. "But they all need to work on their pass protection, too. Running back isn't about just what you do with the ball in your hands, but you have to do other things well, too."