Editors and publishers have since been betting huge sums on comedians who have the potential to become breakout literary stars, including Amy Poehler, B. J. Novak and Mindy Kaling, whose book “Is Everyone Hanging Out Without Me?” has sold nearly 1.3 million copies. Random House paid more than $3 million to the “Girls” actress and writer Lena Dunham for “Not That Kind of Girl,” a book of essays that has sold 525,000 hardcover copies and e-books since it was published in 2014. Penguin is reported to have paid around $3.5 million for the comedian Aziz Ansari’s recently published book about dating in the Internet era, which has sold some 282,000 copies in all formats, including audio.

Even with such dizzying advances, publishers can still make a profit through foreign rights deals that can add up to millions of dollars, as well as paperback and audiobook sales. Books by celebrities also get a lift whenever the author-star has a new TV show or film. And even when celebrity authors don’t earn out their advances, publishers still have a lot to gain from the burst of exposure and perceived clout.

Image Ms. Schumer Credit... Emily Shur for The New York Times

“Even if you lose money in the short run, it helps your prestige,” the literary agent Russell Galen said. “If you are a big publisher, you need to show the flag, you need to make news, because it helps your entire list.”

Ms. Schumer’s advance could set a new threshold that publishers will feel pressured to match.

“For years now, every agent in town would use the Tina Fey advance as the benchmark for what their celebrity client was worth,” Mr. Morrison said in an email. “Now the bar is sitting atop Amy’s head. I can’t tell you how frustrating those conversations will be for us all.”

Ms. Schumer’s agreement with HarperCollins was shaky from the start, according to several people familiar with the deal and the way it unraveled.

The courtship began in 2012 when Mr. Hirshey, who had seen Ms. Schumer’s standup act and was impressed, offered her about $500,000 for a book. She accepted and said she wanted to write personal essays. But as months went by and Ms. Schumer still hadn’t signed the contract, people at HarperCollins started to worry. Then her raunchy and irreverent Comedy Central show, “Inside Amy Schumer,” debuted, and she was crowned as a fresh and sharp new voice in comedy.