Brady is always telling his teammates to see Guerrero. Many do, with varying levels of commitment. The former Patriots receiver Wes Welker, Brady’s close friend, was a disciple, as is the current receiver Julian Edelman. The linebacker Junior Seau finished his career in New England, where he worked with Guerrero; Brady says Seau nicknamed Guerrero “Mr. Miyagi.”

“Willie used to be the big Alex evangelist,” Brady says, referring to McGinest. “Now I’m the evangelist.” It can be a tricky part to play with teammates. The Patriots have their own training, conditioning and medical program. When I asked Guerrero if the conventional philosophies that govern training and treatment in the N.F.L. ever clash with what he is doing, he said, “Most of the time.” I put the same question to the Patriots’ owner, Robert Kraft. “It doesn’t come without its challenges,” Kraft replied. “But we have a coach that’s accepting, and we have the leader of the franchise who’s driving it.”

Brady and Guerrero emphasize that the player has the final say over his own training and treatment decisions. Of course, it’s easier to defy the wishes of your team when you’re Tom Brady and not a rookie. Brady gets this. But he feels responsibility now, as a veteran, and speaks of spreading the Tao of Alex in terms of helping people. He shares with me a word he learned in Sanskrit, “mudita.” “It’s like, fulfillment in seeing other people fulfilled,” Brady says.

Brady played the entire opener, a 33-20 loss to Miami. His calf gave him little trouble, but his play was listless; he wilted in the South Florida humidity, like the rest of his team. After leading 20-10 at halftime, the Patriots were outscored in the second half, 23-0, and outgained in yards, 222-67. A few days before the loss, the team’s best offensive lineman, Logan Mankins, was traded to Tampa Bay. The move was widely questioned inside and outside the locker room, in part because protecting the relatively-­immobile-­to-­begin-­with franchise quarterback was presumably one of the team’s highest priorities. Brady was sacked four times in the opener, lost two fumbles and lumbered off the field after each, looking dispirited and every bit his age. “I don’t think we were really jelling anywhere,” Brady said after the game.

I first saw Brady play live this season in its fifth week, when I flew up to Boston and drove south to the shopping mall known as Gillette Stadium, the Patriots’ home since 2002. Patriot Place, as the larger complex is called, emerges along a could-be-anywhere blotch of car dealerships, billboards and fast-food restaurants on Route 1 between Boston and Providence, R.I. Fans from outside New England might envision Foxborough as a quaint village of greens, flinty shop owners and assorted Ye Olde tropes. Returning from commercial breaks, television networks reinforce this Disneyfied version of “New England,” with stock shots of a steeple, a cider mill, maybe a landmark in Boston, which is a 40-minute drive away. (A huge replica of a lighthouse looms over the north end zone, though you’re as likely to see a real lighthouse in inland Foxborough as you are an actual minuteman strolling through Harvard Square.) In real life, Gillette Stadium is a kind of efficient football Oz that reeks of merchandise, corporate sponsorships and winning.

Brady’s calf injury was healed and forgotten, but he was playing abysmally. The team had relied heavily on its running game to win its second matchup, against Minnesota, and it barely defeated Oakland at home the next week. The Patriots then went to Kansas City for a Monday-night game against the Chiefs and were destroyed, 41-14. Brady, who threw two interceptions (with one returned for a touchdown), was pulled in the fourth quarter and replaced by Garoppolo, who threw his first touchdown pass in what was his N.F.L. debut. On the sidelines, Brady appeared not to congratulate the rookie for his milestone, which was noted in the New England news media as evidence of an emerging generational clash. A reporter asked Belichick after the game “if the quarterback position would be evaluated.” The coach chuckled, shook his head and said nothing.

Fans and the press love a deathwatch, especially when it involves a team that always wins. But the Patriots of this century have been widely resented for reasons that go well beyond any jealousy. Fort Belichick is known as a paranoid and joyless place whose inhabitants are not above pushing the rules in the name of achieving a competitive edge — though Patriots haters prefer the far less euphemistic term “cheating.” It’s a charge that has stemmed from the so-called Spygate incident of 2007, in which a Patriots employee was caught illicitly videotaping the hand signals of opposing coaches. For critics, that episode is emblematic of a team willing to do “whatever it takes” to win.