“Thus, our assumptions result in prevalence rates by age group that are materially higher than those expected in the general population,” said the report, prepared by the Segal Group for the N.F.L. “Furthermore, the model forecasts that players will develop these diagnoses at notably younger ages than the generation population.”

The statements are the league’s most unvarnished admission yet that the sport’s professional participants sustain severe brain injuries at far higher rates than the general population. They also appear to confirm what scientists have said for years: that playing football increases the risk of developing neurological conditions like chronic traumatic encephalopathy, a degenerative brain disease that can be identified only in an autopsy.

“This statement clears up all the confusion and doubt manufactured over the years questioning the link between brain trauma and long-term neurological impairment,” said Chris Nowinski, the executive director of the Sports Legacy Institute, who has for many years pressured the league to acknowledge the connection between football and brain diseases. “We have come a long way since the days of outright denial. The number of former players predicted to develop dementia is staggering, and that total does not even include former players who develop mood and behavior disorders and die prior to developing the cognitive symptoms associated with C.T.E.”