“The one thing about the brand of ‘Spider-Man,’ it’s not going to expire,” he continued. “If we show up in London five years from now, no one’s going to say it’s an old property.”

This bullish outlook derives from the show’s robust weekly box office sales since early summer, and what the producers say is $12 million in advance ticket sales driven by tour and school groups, and visitors from outside the New York region. (Those visitors from farther afield account for about half its audience.) Mr. Cohl said the musical has had advance ticket sales of about $1.6 million a week on average this month, a sizable amount. Those advance sales numbers could not be independently confirmed; they would be less than those for hit shows like “Wicked,” “Lion King,” and “The Book of Mormon,” but still enough to demonstrate staying power.

Mr. Cohl said he was also emboldened by surveys of those attending “Spider-Man” that indicate half its audience were people attending their first Broadway show.

“When people get off the plane in New York and think about Broadway show, we’re now one of the shows they talk about,” he said. “One year on things are moving in the right direction.” Last winter audiences were buying tickets at least partly in a ghoulish game of seeing what glitch or disaster would be next; now they know they are coming to see a finished show.

Turning a profit in New York would be all the more surprising given that “Spider-Man” was mercilessly mocked last winter for its high costs and cast injuries, and then opened to dreadful reviews in June. But the show has pulled itself together since its early previews, when performances would halt in mid-action so the backstage crew could fix technical problems with the flying stunts.

That first preview last Nov. 28 had five interruptions — “We’re going to stop,” intoned the voice of a production stage manager, C. Randall White — including a moment at the end of Act I when Spider-Man was left dangling over the audience as crew members struggled to reel him to the stage.