The controversy has also cast a pall over the Patriots, the Super Bowl champions, who will be without their starting quarterback until Oct. 18, and will raise fresh questions about Brady and his legacy on a team with a history of controversies. The accusation that he impeded the league’s efforts may prompt some fans to abandon their sympathy for him, while undercutting some analysts who argued that the game balls did not have to be manipulated to lose air pressure.

A deflated football is said to be easier to grip, especially in the cold and wet conditions that the Patriots faced at home in Foxborough, Mass., in the A.F.C. championship game against the Indianapolis Colts on Jan. 18. The Patriots won by 45-7, scoring most of their points in the second half, when the game balls were properly inflated after the Colts had alerted officials to their suspicions.

The Patriots, in a statement, said it was “incomprehensible why the league is attempting to destroy the reputation of one of its greatest players.”

Brady did not comment, but his agent, Don Yee, called the decision “deeply disappointing” and denounced the appeals process as “a sham, resulting in the commissioner rubber-stamping his own decision.” He added that “neither Tom nor the Patriots did anything wrong” and said that the science used to show that the footballs were deflated was “junk.”

The players’ union said it would appeal “this outrageous decision” on Brady’s behalf. It has contested Goodell’s impartiality and standing to rule in the case all along.

A showdown in court carries risks for the league and Brady, who could win a stay of his suspension but later have it upheld and be forced to miss games later in the season instead of at the beginning. And while Goodell has shown every intention of standing firm, fighting such a high-profile player before a judge could weigh down the league and distract fans from focusing on games.