Over all, the Jets ranked 20th last year in red-zone offense, but an analysis of their performance inside the 20 by Football Outsiders revealed the extent of Sanchez’s inefficiency. There were 102 passing touchdowns from 15 to 20 yards, but Sanchez threw none of them. In fact, he attempted only four in that range in the red zone, and he failed to complete a pass longer than 13 yards. He gained a paltry 2.4 yards per pass attempt. He also threw eight touchdown passes; the league average was 15.6.

The data suggests a quarterback not yet entrusted with riskier throws or firing the ball into compact spaces — 13 of his red-zone pass attempts were screens or swing passes behind the line of scrimmage — but Schottenheimer disagreed, crediting defenses that were intended to prevent touchdowns and long gains. Still, Schottenheimer said that while analyzing film from last season, he detected deficiencies that were “pretty glaring.”

He said he noticed the Jets’ problems usually began on first down — an unproductive run, an incompletion, a penalty. In turn, that placed more pressure on Sanchez, who is aggressive by nature. It thrust him into second- or third-and-long situations in which he would try to force in a difficult throw instead of exploring other options.

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In response, Schottenheimer said the Jets had emphasized to Sanchez two things: the importance of making better decisions, of not feeling as if he has to push the ball downfield; and completing passes, regardless of length. Gaining even a yard or 2 will help him fall into a rhythm, lifting his confidence and perhaps allowing him to take a deeper shot later.

“Sometimes, we build it up — now it’s like, We haven’t been good in the red zone, we have to do something,” Sanchez said. “That doesn’t mean you have to do something big. It could mean a 4-yard run on first down.” He added, “That’s fine, that’s a victory, just getting something positive on first down and then getting into a third-and-manageable.”

That realization underscores Sanchez’s evolution, especially considering that, according to the quarterbacks coach Matt Cavanaugh, in his rookie season, he was so unsure about some of the defenses he was facing that he would spend too much time on one receiver. And if that receiver failed to get open, Sanchez tended to shift his attention to the next one too late. In his haste to make a perfect throw, he would not set his feet properly.

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Cavanaugh said Sanchez’s footwork had improved, though Cavanaugh often reminded him to listen to his feet: they will tell him whether to throw the ball. By the time Sanchez has finished dropping back, he should know whether his first option is open. If not, he should move on.

“Nobody in this league is going to complete 65 percent of their balls to their wide receivers if that’s all they’re throwing to,” Cavanaugh said. “The league is too good on the other side of the ball to let you do to that. So we tell Mark all the time: ‘When you need to make plays, we’ll let you know, but in the meantime, just take what’s given to you. Big plays will come to you.’ He’s coming to understand that.”

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Dilfer praised Schottenheimer and Cavanaugh, whom he called friends, but he suggested that Sanchez’s red-zone efficiency could improve if more passing plays were called on first down. Because the Jets espouse a bruising running game — especially on first-down plays in the red zone, where Football Outsiders reports they rushed 35 of 50 times, for an average of 2.11 yards — Sanchez does not receive many early opportunities to pass.

“When coaches say that quarterbacks are carrying the team, what they’re really saying is that they trust them more in early downs because the safe, easy thing in this league is to call a run,” Dilfer said. “If you get a big play down to the 12, most coaches probably run it twice and try to get to third-and-2. Great coaches I’ve played for say: ‘Oh man, there’s a lot of room left. There’s a lot of passes we can use to get a first down or score.’ Until the Jets are a little more freewheeling throwing the football and not waiting until third down, I just don’t think Mark will put up big numbers in the red zone.”

The arrivals of Mason and Burress, whose height and hands could help obscure Sanchez’s imprecision, may establish a greater balance. The Jets so far have been encouraged by Sanchez’s preseason showing: 18 for 27 with a gorgeous 26-yard touchdown fade to Burress against Cincinnati last Sunday night. It did not count as a red-zone completion, but the elements of the play — Sanchez’s read of the defense, his accuracy, Burress’s adjustment — signified progress. Dilfer said that he admired Sanchez’s abilities, that he had been impressed with how Sanchez had guided the Jets to two A.F.C. championship games and that Sanchez was more than capable of winning a Super Bowl. Just when might depend on what took Dilfer eight years to figure out.

“Mark has the brass; now he needs to have the discretion,” Dilfer said. “That’s where he is. That’s where his main development needs to be.”