“Hamilton” is the overwhelming favorite to win the most coveted Tony Award this year, the prize for best new musical. But four other musicals hope to benefit simply from being nominated in that category: “Bright Star,” “Waitress,” “School of Rock — The Musical” and “Shuffle Along, or, The Making of the Musical Sensation of 1921 and All That Followed.” Those shows can now market themselves as best-musical contenders, hoping the nominations will help them at the box office.

“We call it the HamilTonys, and we know this is as far as we can go, but it’s great to have got this far,” said Andrew Lloyd Webber, the composer and lead producer of “School of Rock,” which is an adaptation of the Jack Black film about a failed musician who lies his way into a job as a substitute teacher and then trains his pupils to perform rock music. (Alex Brightman was nominated for his exuberant lead performance.)

That musical is a significant comeback for Mr. Lloyd Webber, best known for his enormous successes in the 1980s, including Tony Awards for “Evita,” “Cats” and “The Phantom of the Opera.”

“I haven’t done a musical on Broadway for quite a while,” he said in a phone interview from London. “It’s fun to be able to do this.”

The race for best new play is likely to be more competitive.

The nominees are “Eclipsed,” by Danai Gurira, about a group of Liberian women kept captive by a warlord; “The Father,” by Florian Zeller, about a man’s struggle with dementia; “The Humans,” by Stephen Karam, about a close-knit family grappling with disappointment; and “King Charles III,” by Mike Bartlett, imagining a crisis that might ensue after Queen Elizabeth II’s death.