Unanswered questions remain, including why some athletes are prone to develop C.T.E. while others, who played the same position for the same number of years, are not. Also, it’s unclear how prevalent C.T.E. is in people who never played football or other contact sports.

Research by McKee and others, though, has found that the severity of a player’s C.T.E. is related to the number of years that he played football and the number of hits he endured. “Everything is related to the dose,” she said, referring to the number of subconcussive blows to the head that occur in practices and games.

Perfection With a Price

The relationship between the number of head hits and brain damage might help explain why Stanfill, Kuechenberg and Morrall had advanced cases of C.T.E. They played football for decades, starting as youngsters in an era when full-contact practices were the norm, helmets were little more than a hard shell and the fields in many stadiums were synthetic grass on top of concrete.

An offensive lineman like Kuechenberg, who played nearly 200 N.F.L. games over 14 seasons, most likely absorbed thousands of head hits every year during his football life.

Researchers “asked me how many concussions he might have had, and I said, ‘His head was his tool,’” said Alexandra Kuechenberg, his daughter. “Do that math over college and high school.”

Kuechenberg said her father declined rapidly in his final years. He rarely left his home. His memory began to fail. He made poor financial decisions. He drank heavily. He was depressed and contemplated suicide. He kept a journal that she described as maniacal.

After he retired from football, Bill Stanfill became active in business and was the life of every room he entered. Like Kuechenberg, though, he grappled with physical issues, including damaged hips and vertebrae in his neck, which doctors fused to mitigate the pain.