Bynum averaged just 1.6 points per game as a rookie in 2005-06. This season, however, he's one of the premier centers in the NBA (18.7 ppg, 12.1 rpg).
Williams would like to emulate Bynum's improvement next season.
"His skill set skyrocketed the last few seasons," Williams told ESPN.com. "[There's] an opportunity for me to take on a larger role next year, and it's something I'm looking forward to."
As a freshman, Williams accounted for just 1.7 points and 2.1 rebounds in 6.6 minutes per game.
Those numbers reflected his on-court learning curve and limited playing time behind All-America big man Jared Sullinger.
But Williams is a former McDonald's All-American who will fill the lane for the Buckeyes next season. Grand expectations will come with that new role in his second season.
"It's just all about preparation, how I prepare myself in the offseason," he said. "I feel like if I prepare myself good this spring going into next fall, I think I'll live up to everything I'm supposed to live up to."
Williams arrived last season with a slate of prep accolades. The 6-foot-11 center led Detroit Country Day High School to a Michigan state title in 2010 and a championship game appearance the following season.
Ohio State coach Thad Matta recruits and develops talented big men. And when he signed Williams -- No. 43 in the 2011 ESPNU100 -- he added another potentially potent post player to his rotation.
But Sullinger's decision to return for his sophomore season meant that Williams played sparingly as a freshman.
With Sullinger recently announcing his decision to go pro, however, Williams will step in as the Buckeyes' go-to big man.
Williams said he recognizes the expectations and intends to put in the work necessary to get ready for a larger role during the 2012-13 campaign.
But he's already had some high level on-the-job training.
Working with Sullinger helped him prepare for future battles with big men in the Big Ten and around the country, he said.
"It helped me improve going against him every day in practice. It helped me offensively and defensively, checking guys his size and learning how to score over guys his size and taller," Williams said.
Youngsters no longer get a grace period at the collegiate level, especially those who compete for some of the top programs in the country. Premier centers sprout like perennial flowers in Columbus.
I feel like if I prepare myself good this spring going into next fall, I think I'll live up to everything I'm supposed to live up to.
”-- Amir Williams
Greg Oden led the Buckeyes to the national title game in 2007, and the Portland Trail Blazers picked him first in that summer's draft.
Two previous Ohio State centers -- Kosta Koufos and B.J. Mullens -- were selected in the first rounds of the 2008 and 2009 NBA drafts after one season with Ohio State.
Sullinger, who's expected to crack the lottery in this summer's draft, earned All-America honors in his two seasons with the program. His career concluded with a trip to the Final Four earlier this month.
Assistant Jeff Boals said it's unfair to compare Williams to other Ohio State centers, specifically Sullinger.
"There's going to be some growing pains," Boals said.
But Williams will give the Buckeyes a tough defensive threat, according to Boals. The post player averaged 0.8 blocks per game even though he didn't average double-digit minutes this past season.
"I think the one thing he'll be different at is he'll be able to affect shots around the rim defensively, where we didn't have that this year," Boals said. "We had it a couple years ago with Dallas Lauderdale. That'll be a big difference defensively. Even offensively, he'll be back to the basket and he'll be able to catch the ball, make a couple dribble moves, right-hand hook, left-hand hook."
Williams said he won't put too much pressure on himself this offseason. He's already working on his conditioning and strength and plans to put in significant time to boost his offensive game, too.
He said he's not worried about the expectations, but he doesn't deny that they exist.
"I'm just trying to prepare myself so I know I'll be able to put myself in a great position for next year," he said. "It's just all about working hard and just trying to live up to all expectations. Keeping a cool head, just work as hard as I possibly can for next season, just have a positive mindset about everything."