Last summer Brodeur told me that it was the team’s success that prompted him to keep playing after what was a rough patch. In 2010, he was benched by the Canadian Olympic team after playing a terrible game against the United States. (I spotted a him a couple of nights afterward on a street in Vancouver, and he seemed lonely and forlorn.) That same year, for the second time in a row, the Devils failed to get through the first round of the playoffs, and the following season they failed to make them altogether. Brodeur, who for the first time ever posted a losing record, thought about quitting. “If I ever had another season like that. . . .” he said, shaking his head. “When you have fun and you win, you don’t realize how hard it is and how old you are,” he added. “You just want to play. I felt really comfortable out there last season. I enjoyed being with everyone.”

Brodeur, the youngest of five children, probably gets his personality from his parents, his father especially. Denis Brodeur is a charmer and a storyteller. Short and roly-poly, he doesn’t look at all like his son, who is 6-foot-2 and has a torso shaped like an upside-down coat hanger. But Denis was a good-enough goalie to play for the 1956 Canadian Olympic team, and knocked around the American Midwest as a minor-league baseball player before concluding that he was unlikely to succeed as a professional athlete. (The oldest Brodeur child, Claude, was a pitcher in the Montreal Expos system before blowing out his shoulder.) Denis then reinvented himself as a photographer, and his athletic history and easygoing manner enabled him to become the official team photographer for both the Expos and the Canadiens. He and his wife, Mireille, still live in the house Marty was born in, a split level with a big bay window, in the St.-Léonard neighborhood of Montreal. (Roberto Luongo, the goalie for the Vancouver Canucks, grew up just a few blocks away.) The place is now a virtual archive, and Marty’s old room is a minishrine to his accomplishments, with lots of Stanley Cup photos and pictures of Marty at the Olympics. But there are fewer trophies from his teenage years than you might find in any suburban hockey player’s bedroom these days. Brodeur was good back then, but not a prodigy. “To tell the truth, I was not sure he would make it,” his father told me.

To a certain extent, Brodeur and all the French Canadian goalies of his generation labored in the shadow of Patrick Roy, the Canadiens’ goalie in the ’80s and ’90s, who was probably the most brilliant practitioner of the goaltending style known as the butterfly, in which the goaltender, often wearing extra-large pads and chest protector, drops to his knees and fans out his legs, blocking the lower part of the net while fending off higher shots with his arms and upper body. When Brodeur was a teenager at goalie camp, Francois Allaire, an influential coach, tried to convert him to this technique, but Brodeur resisted. He found an ally in Vladislav Tretiak, the great Soviet goaltender, who was teaching at another camp, and later in Jacques Caron, then the goalie coach for the Devils, who frowns on the butterfly. “Those guys, they just throw themselves where they think the puck is going to be,” he told me. “Marty knows where it’s going to be.”

Caron is a protégé of Eddie Shore, the fabled Boston Bruins defenseman of the ’30s who went on to become an eccentric and tyrannical owner of the Springfield Indians in the A.H.L. He so hated goalies who dropped to the ice that in practice he made them wear a rope around their necks that would strangle them if they tried to drop; other times he’d tie their legs together. But Shore, a great skater himself, also emphasized mobility in his goalies, and Caron said this was what he tried to teach Brodeur — to keep his balance and skate, not slide, across the crease. “To follow the play, you have to have mobility and get yourself in the right angle and stay square to the puck at all times,” he explained. “This way Marty can be more patient, and he can control the rebounds. He cuts down a lot of extra shots by controlling the puck and not just letting it bounce off him.”

Despite people like Caron, the butterfly is now nearly orthodox among young goalies. Resch compares the old, stand-up style to playing tennis with a wooden racket. Last season Brodeur finally switched to larger leg pads and has adopted some of the newer technique, so he is now a sort of hybrid. He sometimes goes to his knees but more often comes out of the net and challenges the shooter. He makes some of his best saves on his side, diving across the goal mouth and stacking his pads one on top of the other. Shooters say he’s hard to score on because they’re never sure what he’s going to do. There aren’t many such goalies left in the N.H.L. anymore. One is Tim Thomas, the Bruins’ goalie when they won the Stanley Cup in 2011, and another is Brodeur’s backup on the Devils, Johan Hedberg, who the team’s detractors like to point out is only a year younger than Brodeur. “We’re dinosaurs,” he said after practice recently.

Resch and Caron are convinced that Brodeur’s way of playing puts much less wear and tear on a goaltender and is why he has been able to play for so long. “Quick can’t play like that in 20 years,” Caron said, referring to Jonathan Quick, the aptly named Los Angeles Kings goalie, who won the Stanley Cup M.V.P. last year after his team defeated the Devils in six games. “In 20 years their backs will go, their knees will go. I think Marty is smart enough to readjust his play according to what he can’t do. Your reflexes go a little bit, but by being in the right position and in the flow of the game, it compensates for a lot of that.”