To the family of the former N.H.L. player Jeff Parker, the posthumous diagnosis of C.T.E., or chronic traumatic encephalopathy, was the predictable conclusion. All those hits to the head, including that final one that knocked him out of the game altogether, and all those subsequent years of struggle? In the final, difficult years before Parker’s death last September at age 53, the family figured that it must be C.T.E.

“It just makes me sad,” John Parker, Jeff’s younger brother, said through tears. “It doesn’t bring him back. It just makes you feel sad, that he was living with this, and it’s a thing. It’s a real thing.”

To the N.H.L. and its commissioner, Gary Bettman, the diagnosis is likely to be the latest piece of evidence to dismiss or combat. Even as links build a chain bridging the sport to C.T.E., the degenerative brain disease associated with repetitive head trauma, and some of the game’s most revered names push the league to take a more open-minded approach, the N.H.L. has denied any connection between long-term brain damage and hits to the head.

The N.F.L. did the same, for many years, until the evidence became too overwhelming, the numbers too much to counter with plausible deniability. Facing a huge class-action lawsuit, the N.F.L. eventually admitted to the connection and agreed to a roughly $1 billion settlement with former players. (That has not kept the sides from continuing to fight over the payouts, amid accusations of fraud and intimidation.)