Of course, he didn't miss them. He has been spared. And while he seems like the sort of person with the strength of mind to preserve his sense of self no matter what others think, he nonetheless lives in perpetual danger of having his character reappraised in light of the last big kick. When asked how he imagines his career will end, he couldn't find the answer. "That's a hard thing to think about," he said. My N.F.C. executive, who happens to think the world of Vinatieri, says: "Adam Vinatieri's career isn't going to be over until somebody loses confidence in him. And the only way someone is going to lose confidence in him is if he misses a clutch field goal." The only question is: what happens then? Will his miss be forgotten in time, or will it be the sort of kick — say, a chip shot to lose the Super Bowl — that causes everyone to rethink his miracle kick in the snow? In theory, they can never take away from him those kicks he made. But, in practice, they do.

His game against Denver was accident-free. But the game just two weeks before that, against Tennessee, offered an example of just how effortlessly the perception of Adam Vinatieri might change. His first extra-point attempt was blocked. He made his first three field-goal attempts, but the third came out a bit low and, once again, a Tennessee player got a hand on it. "All of a sudden I'm thinking too much," he said. "I'm thinking, 'You got to go a little faster.' " He went a little faster — and missed an easy 36-yard field-goal attempt that would have put the game pretty well out of reach. "You get a field goal or an extra point and somebody gets a hand on it, it gets in your head," the color commentator Dan Dierdorf told millions of television viewers. "Even if that head is on Adam Vinatieri's shoulders." The camera zoomed in on Vinatieri as he walked off the field, wearing the dazed expression of the loser. "I wish I could have that one back," he says now. "It left my foot and I thought, 'Oh, give it back to me.' "

Meghan Crosby tends bar in a New Orleans restaurant called Zeke's, and on one of its walls there is a shrine to the kick her father made 37 years ago. Between framed football jerseys is a black-and-white photograph of the split second after the ball has left his foot. Apart from Dempsey and his holder, Joe Scarpati, it shows a grimacing member of the Detroit Lions, Alex Karras, stretching and diving to block the kick. He doesn't look like he's not trying.

Her father joined me for lunch at Zeke's recently. His hair has gone grey, but apart from that he didn't look much different from his photo in the old Saints program. As he talked over lunch, he hid his hand in various ways — behind a napkin, under the table. But his foot he talked about easily and without prompting. As he warmed to his subject — the Kick — he recalled that under orders from Pete Rozelle, then the N.F.L. commissioner, Tex Schramm phoned him to apologize for saying he had an unfair advantage. "But he didn't really apologize," Dempsey said. "He still thought I had an unfair advantage. I guess if not having any toes is an unfair advantage, I have an advantage." Then there was the matter of the shoe. "Everyone said I had steel in it," he said. "But they X-rayed it. It was just a thin piece of leather." He thought his shoe — created at the insistence of the former San Diego Chargers coach Sid Gillman, for whom Dempsey tried out — may have helped his accuracy but had no effect on his distance. He knew he had that sort of distance the first time he kicked a football, at Palomar College, in Southern California. His coach decided that his current kicker didn't have enough leg to kick off, so he asked everyone on the team to line up and kick a ball off a tee as far as he could. Dempsey didn't think he'd have sufficient control of his shoe, so he took it off and, with his bare foot, kicked the ball out of the end zone. Thus began his career.

His father had consciously raised him to live a useful lie: that it didn't matter one bit that he lacked a hand and a foot. Dempsey suspects that he was born right-handed, but he's not really sure, because his right hand was never usable. He taught himself how to throw left-handed, and even played baseball. But his body was better suited to football, and much of what he did to play it — lifting weights, for example — built great strength in his legs. That strength paid off the year he became Palomar's field-goal kicker and, in his stocking feet, nailed a 65-yarder against Compton City College. At least he thought he nailed it; the refs called it wide. ("Their excuse was it was too high for them to see," he said.) But the Compton City College coach thought it was good, too, and wrote a letter to Vince Lombardi, the coach of the Green Bay Packers, saying he had seen this kid with no foot make a 65-yard field goal. Sight unseen, Lombardi hired Tom Dempsey and put him on a farm team. After a brief time with the taxi squad in San Diego, Dempsey found himself playing for the Saints. That same year, at the end of a game against the Detroit Lions, and with the ball a long way from the goal posts, he overheard his offensive coordinator say, "Tell Stumpy to get ready." And improbable as it seemed to everyone else, he trotted out onto the field without too much concern about the distance.

Thirty-seven years later, a great deal has obviously changed. It's considered bad form even in the bleachers to jeer at physical deformities. (They now mock what they take to be deformities of spirit or character.) Dave Whitsell is dead, as is my father's friend Charles. Tulane Stadium has been razed, and the spot from which Tom Dempsey launched his field goal is a grassy patch below sea level.

And yet some things haven't changed. Tom Dempsey's record stands, for instance. In 37 years it has been tied — by Jason Elam of the Denver Broncos, who was kicking a mile above sea level — but never broken. Field-goal kickers are still defined by the tiniest sliver of their professional career. "I made a lot of big kicks, but all anyone wants to talk about is that one," Dempsey said. And, finally, there is still some faint resistance to the notion that a kicker could ever really do anything great. Brett Favre can throw 10 more game-ending interceptions and fans will still cherish his moments of glory. Reggie Bush may fumble away a championship and still end up being known for the best things he ever does. Even offensive linemen whose names no one remembers are permitted to end their days basking in the reflected glory of having been on the field. Kickers alone are required to make their own cases.

Every so often someone still comes up to Tom Dempsey to put his achievement into perspective. Not long ago, a total stranger approached him wanting to talk about the Kick. "And he said to me," Dempsey recalled, " 'You're really nothing but a one-kick kicker.' And I thought: 'Yeah, but I kicked it once. What the hell did you do?' "