At least a quarter of NFL players who died between 2016 and 2021 had chronic traumatic encephalopathy, according to a study of 878 players published in the British Medical Journal on Tuesday, ESPN reports.

The researchers worked from brain donations collected between 2008 and 2021, of which 93 percent showed CTE, then narrowed the sample using donation timing along with demographic and death certificate data.

Why the headline number is a floor

The 93 percent figure cannot be read as a prevalence rate, and the study does not treat it as one. Families donate a brain when they suspect something was wrong, so donated brains are not a random sample of players.

The method here is an attempt to correct for that, and the result is a range rather than a point. Daniel Daneshvar, the lead author, called 25 percent the "low end". The study's maximum estimate is about 97 percent, and he said the true figure is "somewhere in the middle".

That is an unusually wide range, and reporting only one end of it in either direction would misrepresent the work. The finding is that at least one in four is defensible as a minimum, and that the real rate is probably considerably higher.

The clinical association

More than 90 percent of Stage IV CTE samples also carried a dementia diagnosis.

CTE can currently be diagnosed with certainty only after death, which is the central difficulty in this field: the disease is studied in people who can no longer be asked anything, and living players cannot be told what they have.

What the parties said

The NFL Players Association said: "This study is a sobering reminder that football carries real risks, and those risks can have lasting consequences for players and their families."

The NFL said it "continuously strives to make the game of football safer, including by implementing strategies to reduce concussions and head impacts."

Azeez Al-Shaair, a Houston Texans linebacker, described the position players are in: "The reality of the game is that it's aggressive. It's violent."

Those three statements are not in conflict, which is what makes this an unusually settled argument. Nobody quoted disputes that the risk is real. The disagreement, where there is one, is about magnitude and about what follows.

The researchers say they will publish an overall prevalence study across all NFL players in the coming months.

What we could not establish

We could not establish how the sample was narrowed in detail, the players' positions or career lengths, how the maximum estimate of 97 percent was derived, or whether the study was peer reviewed in the usual way. We verified this account from a single publication and have not read the paper.