“The set’s a little M.O.R.,” Joel complained, meaning “middle of the road,” the soft-rock category now called Adult Contemporary. He made his way onto the stage and sat down at the piano and knocked out a little Beethoven, before the band members, most of whom have been with him for more than ten years, worked out the backup vocal harmonies to “My Life.” They vamped for a while on “Sledgehammer,” by Peter Gabriel, and ran through the end of “Movin’ Out,” to get the right level for the horns. And then Joel was doing “Just the Way You Are.” He’d written it for his first wife and manager, Elizabeth. When he told her, “This song is for you,” Donna Summer, standing nearby, said, “Does that come with the publishing?”

Before long, at the sound check, he began substituting bawdy lyrics: “I just want someone . . . to have sex with” and “Now you know I’m . . . full of shi-it.” “I couldn’t have loved you any better, unless . . . you grew some bigger tits.” Cohen walked by, shaking his head.

After a while, Joel stopped. “Should we really do that one? Really?”

“There won’t be a dry eye in the house,” the saxophonist Mark Rivera said.

Joel continued to argue against playing it. (He’d wanted to leave it off the album, too, but Linda Ronstadt and Phoebe Snow, dropping by the studio one day, told him he was nuts.) He usually won these arguments. At other sound checks, I’d seen him scrap such mainstays as “Angry Young Man” (the tempo was lagging, and the sentiment felt false) and “Captain Jack.” (“Dreary, dreary, dreary,” he said. “It just goes on and on. I’m sick of the thing. It didn’t age well. It’s been busted down to ‘Private Jack.’ ”) But this time Cohen and Brian Ruggles, Joel’s sound engineer since the early seventies, prevailed.

A few hours later, the arena was full, and he was back onstage with the band, delivering the familiar hits in full voice. He was all in. The cynicism surfaced only between numbers, such as when, after playing “The Entertainer,” he repeated, in a quizzical tone, the line “I won’t be here in another year / If I don’t stay on the charts” and then exclaimed, “Bullshit!” A roar greeted the opening notes of “Just the Way You Are,” and up in Section 106 I could see some women of a certain age singing along and dabbing their eyes. When the song was done, Joel turned to the audience and said, “And then we got divorced.”

Joel’s show hasn’t changed much over the years. Songs cycle in and out, and he and the band play many of them in a different key, to accommodate his aging vocal cords (he says that he prefers his late-career baritone to the tenor of his prime), but for the most part the big hits are always there, presented in the same arrangements and sonic array. The saxophone is the radiocarbon. Close your eyes and it’s 1982, which in many ways is exactly what his fans want. The delivery was tight and strong. Long ago, Joel grew tired of having to look out at the fat cats in the two front rows, the guys who’d bought the best seats and then sat there projecting a look of impatience and boredom that Joel characterizes, using his Vinny voice, as “Entertain me, Piano Man.” So Joel’s people stopped selling the two front rows and instead send the crew into the cheap seats before the show to hand out tickets to people of their choosing. That this usually results in a foreground that is both young and female may or may not be an unintended consequence, but Joel believes that it helps buck up the band.

To close out the set, he sprayed his throat, donned a harmonica rig, and launched into “Piano Man” without betraying any exasperation, only wonder, as thousands of people, many of them about half the song’s age, sang along. You could stand behind the stage and look out at the throngs, lit up by Cohen, and begin to understand why a man might rouse himself from hibernation and go through the motions again. “Gotta feed the elephant,” he likes to say. He means all the stakeholders in Joel, Inc., but the phrase also suggests his own desire for validation or love.

He closed out his customary five-song encore with “Only the Good Die Young.” It’s one of those songs that get the Garden arena, which is built on springs, to start bouncing. The bouncing had hardly ceased by the time Joel’s S.U.V. was gunning down the ramp and west toward the helipad, where the chopper waited. Ruggles and Cohen got aboard with Joel and Roderick. Someone had rescued a gigantic bag of popcorn from the dressing room; Joel liked to have it at home. The helicopter lifted off, tracked north over Central Park, and then out over Queens and LaGuardia. The metropolis alight. Joel leaned over to Cohen and said, “This is a great fucking job.”

Over Long Island Sound, Joel pointed out a mass. “That’s J. P. Morgan’s old island,” he said. “I rented a house there for a while, after I sold the house in East Hampton.” The helicopter cut south along the eastern shore of Centre Island. The helipad’s lights flashed on. As the passengers disembarked, Roderick quietly urged Ruggles, who was going through a divorce and living for the time being in one of Joel’s guesthouses, to take the popcorn.

Joel drove Roderick up the hill in the U.T.V. Soon, the helicopter was gone and all was quiet, except for the whir of katydids and a Beethoven violin concerto on the Sonos. Joel was back out under the trellis with a cigarillo. He’d given up cigarettes—he’d gone to see a hypnotist in Boston. Dock light from across the bay wobbled on the surface of the Sound. Less than a half hour before, he’d stood at the lip of a stage, sweaty and beaming, absorbing an arena’s adulation: Mussolini. Now just a schmuck. The commute had earned him more than a million bucks. He projected contentment and ease, and seemed in control of his appetites, as though he’d learned how to bank the endorphins and draw on the account as needed—rock stardom on time release. Roderick brought out a tray of cheese.

“Did you tell Brian to take my popcorn away?” he asked her. “Did you say, ‘Don’t give him the popcorn?’ ”

“I would never—”

“He’s been with me for fifty years,” Joel said.

“I didn’t tell him to take it away,” she said. “What I said was I didn’t want it to exist in the first place. It was really gross.”

“It’s not really gross,” Joel said. “I like the popcorn.”

They sat outside until almost 2 A.M. and then headed for bed.

People tend to assume, given the recent burst of reputational favor and vigor in performance, that Joel must be sober, that the narrative of redemption must rest on abstinence. But not everyone can be George Jones. Joel steers clear of spirits, he says, and just drinks wine, in moderation. “I think of it as a food group,” he told me. At one lunch, we each had a glass of Chianti. At another, we had a little sake. He ordered sashimi; he was hitting a steak house later with some friends. He likes to eat. “I’m with the Jack Nicholson school, that it’s this flat-belly shit that’s ruining America,” he said. “I don’t think there’s anything more pathetic than a man on a diet.”

“Before we begin, I’d like to thank Ogg for making this wonderful fire, which, up until now, I had not thought him capable of.” Facebook

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He is sensitive about the alcohol thing. He cops to having had lots of problems in the past, drinking to excess, behaving like an ass. He chalks it up to Long Island, the culture of day’s end at the local pub. In the old touring days, the whole band boozed it up, and often they were the last ones standing in the hotel bar, Billy at the piano, crew gathered around with a few stragglers and girls, singing Sinatra and the Beatles: not exactly “Hammer of the Gods.” He claims not to have ever really got into drugs, though they certainly tried things, including heroin, on a 1981 swing through Amsterdam; in videos of concerts from the mid-eighties the clothes and the hair styles alone seem to scream “Cocaine!” You’ll hear Long Islanders tell old stories about the time they saw Joel at this or that Huntington bar, the man not looking his best. There were, in the past decade, a couple of interventions and a couple of stints in rehab, in 2002 and 2005. Still, he rejects the A.A. approach and favors the kind of self-moderation that A.A.’s devotees cluck at.