That evasion may cost the league dearly. Frustration over the league’s stance is one reason nearly 5,000 retired players sued the N.F.L. and Riddell, a helmet manufacturer, for hiding from them the dangers of concussions. A federal judge has preliminarily approved a landmark 65-year settlement that would award millions of dollars to players with severe neurological disorders, and spend tens of millions more to monitor other players.

Unlike concussions, which have an impact on the game and the finances of the N.F.L., the league’s stance on domestic violence is not purely a financial issue. While the league has spent years courting female fans by, among other things, having its players wear pink cleats to raise awareness of breast cancer, Goodell also announced his new policy a week before the start of the regular season and ahead of a three-day weekend, when many people are on vacation.

Goodell initially defended the decision to suspend Rice for two games. He said he spoke directly to Rice and noted that he avoided a trial by entering a counseling program. “He is a young man that really understands the mistake he made and he is out and about and determined to make a positive difference,” Goodell said at the beginning of August.

But as blowback continued, he apparently recognized the issue was larger than just Rice. In his 2,000-word letter and memo, Goodell said that his decision was based as much on the obligation of the league to be held to a higher standard than other sports leagues and institutions.

“Much of the criticism stemmed from a fundamental recognition that the N.F.L. is a leader, that we do stand for important values, and that we can project those values in ways that have a positive impact beyond professional football,” he wrote.

Groups that criticized Goodell for being insensitive to the issue of domestic abuse applauded him for reversing course.

“This decision by N.F.L. Commissioner Roger Goodell to change the league’s policy on how it disciplines players who beat their wives and girlfriends is a big win, not just for women, but for all N.F.L. players, staff and fans,” said Becky Bond, the political director of Credo, a women’s rights group.