Twenty years into its C. T. E. era, the N.

F. L. is more popular and profitable than ever. Revenues rise even as the math becomes clearer for the once immeasurable price paid in brain damage sustained by football players.

Fans know too much to plead ignorance. They now know, thanks to a new study, that at least one in four former N. F.

L. players had C. T. E. among the nearly 900 who died between 2016 and 2021.

We are living in an era of cognitive dissonance, sociologists said. How many C. T.

E. cases, they wondered, are too many for fans’ collective consciousness? What would it take to quit watching, or to quit sending children into the scrum? How many irreversibly damaged brains in the N. F. L. would turn away the masses? "I doubt that any number is going to do it," said Steve Almond, a lifelong football fan and the author of "Against Football: One Man’s Reluctant Manifesto." Mr. Almond is among the millions who cannot turn away from what he has called "our unholy appetites." He’s just more thoughtful about it.

He says football is "morally troubling." "The vast majority of fans aren’t sitting there saying, ‘I want people to get hurt and I have this blood lust,’" he said. "I think, like me, they’re getting off on a beautiful, narratively thrilling sport that has an unfortunate adjunct to it — the fact that it’s absolutely unsafe to play." In the past two decades, hundreds of former N. F. L. players have died with chronic traumatic encephalopathy, or C.

T. E., a brain disease caused by the cumulative effect of repeated hits to the head. Now a new peer-reviewed study reveals that 25 percent of them over a recent six-year period were found to have had C.

T. E. — posthumously, the only way to diagnose the disease with certainty. That one-in-four ratio is certainly low, since it does not account for the nearly 75 percent of deceased players in that period whose brains were not examined because they had not been made available to researchers.

If the one-in-four rate extended to the upcoming season, that would mean, on average, 13 players per team and more than 400 active players in the league would have C. T. E.

They, too, might experience C. T. E.’s dementia-like symptoms, possibly including memory loss, confusion, impulsivity and depression.

They, too, might have shorter life expectancies and far higher rates of addiction and suicide than those lucky enough not to get it. By any standard of workplace safety, C. T.

E. is an epidemic. There may be no industry that does so much damage to its workers. And we know that the damage sometimes also reaches teens who play the game just for fun.

Yet millions of children continue to play tackle football. American universities spend billions of dollars on it — higher education leaders knowingly fostering a sport that leaves some of its students addled with a neurological brain disease. The pipeline of players, an inexhaustible resource, keeps flowing toward the N.

F. L. And fans keep cheering.

Football has a unique hold on American culture. There is a gauzy nostalgia to the game, but it is thriving like never before, too. Roots run deep.

The college game predates the N. F. L. by decades, but the N.

F. L. has been around for more than a century. Today, the league’s game telecasts are most of the most-viewed shows on television.

It’s not just entertainment. Football permeates the American landscape. Entire cities identify with pro teams.

Entire communities thrive on the tradition and pomp of the college game. Small towns and suburbs across the country glow with Friday night lights. Traditions are passed down and communities are uplifted, through tailgates, game-day rituals and a steadfast devotion to team colors.

Millions are bet on the games, even if only through office pools or fantasy football. Children play football in schoolyards and backyards. The Super Bowl is one of the few cultural events that still connects people from all corners.

The latest research paper may not be enough to upset that devotion.