But even as he detailed the list of what he'd like those two to do, Groce had bad news.
Sophomore Leron Black, the 6-7, 220-pound forward Illinois needs to be a rebounding force this season, will have surgery Friday to repair a torn meniscus in his right knee, Groce said. He expects Black to be back in four to six weeks.
Black joins freshman guard Jalen Coleman-Lands and senior point guard Tracy Abrams on the injured list. Abrams will miss a second straight season after tearing an anterior cruciate ligament. Coleman-Lands is out with a stress fracture in his left leg, but should be back for the Nov. 13 opener against North Florida.
Hill and Nunn have been starters for close to two full seasons, Groce said, and he needs them to lead a team heavy on freshmen, sophomores and transfers.
"I'm holding them to a very high standard right now," he said. "I certainly will tolerate more from a freshman, and they know it."
Hill is the leading scorer among the returning players. He averaged 14.4 points for last season's 19-14 team. Nunn struggled to be consistent last season after some summer injuries, but he still averaged 11.1 points.
Scoring is one thing, leading is another, Nunn said.
"It hasn't come natural, but I worked on it all summer," he said.
Groce said the new role for Hill and Nunn is something they'll have to grow into since they haven't been asked to lead the team in previous seasons.
Injury troubles aren't new for Illinois, and that may actually help experienced players like Nunn and Hill understand how to keep playing, and even winning. Rayvonte Rice was the team's leading scorer last season. But the senior missed nine straight games due to injury and suspension, and Illinois went 6-3 in his absence.
"I think all they hear from us is next man up, let's go," Groce said. "I'm not canceling practice because someone's hurt."