In a development that will surprise absolutely no one who has ever watched a human head collide with another human head at full speed, a new study estimates that three out of four former N.F.L. players who died between 2008 and 2023 most likely had C.T.E. - chronic traumatic encephalopathy - in their brains at death. That's 75 percent, for those keeping score at home, which is roughly the same percentage of people who will read this and think, "Well, yeah."

The study, published Wednesday by the same research team that sent reverberations through the football world this summer, used statistical techniques to home in on a more precise number. Their earlier study found that at least 25 percent of retired N.F.L. players who died over a recent six-year period had C.T.E. But most of the other 75 percent of deceased players were never tested, leaving the actual prevalence open for analysis. Now, the team has estimated that three out of four deceased ex-N.F.L. players most likely had the neurodegenerative brain disease associated with repeated hits to the head. In contrast, the same researchers studied brain banks reflecting the general population and estimated that only 0.6 percent of people have C.T.E. - a disparity so stark it's almost showing off.

This remarkable gap sharpens the question faced by current players, N.F.L. retirees, football fans and parents: Just how dangerous is football? It's a question that has lingered since the first time someone decided that ramming into another person at full speed was a reasonable way to spend a Sunday afternoon. The new estimate doesn't answer it definitively, but it does make the answer seem increasingly like "very."

The study's findings are likely to deepen concerns among players and families who have long worried about the long-term effects of repeated head trauma. The N.F.L. has yet to comment on the new estimate, though one imagines the league's public relations department is having a very long meeting about it. Meanwhile, the rest of us are left to ponder the eternal mystery of why a sport that involves so much head-banging remains so popular - and whether the occasional concussion is simply the price of admission for a really good touchdown.