“Lord,” Wright thought. “I’m in this by myself.”

For the longest time, he was sure that was true. It took Wright nearly 40 years to recognize that he probably sustained a concussion in his first N.F.L. start, one of many head injuries he says he had in 13 seasons with the Cowboys.

Only recently — albeit through the fog of his worsening dementia, which he acknowledged publicly for the first time last week in an interview at his Texas home — has he realized that he is not in this by himself after all.

Wright, 68, is among more than 4,500 players who have sued the N.F.L., contending that the league concealed for years what it knew about the dangers of repeated hits to the head. This month, a federal judge rejected a proposed $765 million settlement that would compensate players young and old for those injuries.

The judge, Anita B. Brody, was exactly right to express concern that the settlement was too small to pay for medical tests and treatment for the thousands of players who face — or could face — health problems related to their N.F.L. careers. She wants assurance that the current proposed payout will be enough, and she has asked the league’s lawyers to justify their math.

Image Wright’s trophy as the 1972 N.F.C. offensive lineman of the year. Credit... Brandon Thibodeaux for The New York Times

The N.F.L. has argued that its offer was “fair and adequate,” but it should be ashamed to even suggest such a figure. The league generates revenue of about $10 billion a year, and the $765 million was earmarked to cover all claims over a 65-year period. It’s no surprise that the N.F.L. is trying to get out of the lawsuit on the cheap after years of denying a link between football and brain injuries. But it could — it must — do better. Much better.