Thanks to the ham-handedness of the National Football League’s Hall of Fame, the inane “deflategate” scandal, which has been the dominant N.F.L. headline this off-season, was pushed to the sidelines this weekend and replaced by a genuinely important issue facing the country’s dominant sports league and its players. That issue is the serious cognitive impairment that appears to affect so many former professional football players.

The embodiment of that impairment was Junior Seau, the perennial All-Pro linebacker who was inducted, posthumously, into the Hall of Fame on Saturday. Three years ago, Seau committed suicide by shooting himself in the chest. He was 43 years old and had been retired from pro football for only three years.

His brain became part of a study conducted by the National Institutes of Health, which concluded that he had a condition called chronic traumatic encephalopathy, or C.T.E. This neurodegenerative disease, which scientists believe can cause depression, anger, loss of impulse control and poor decision-making, among other things, has been found in the brains of many deceased N.F.L. players. Scientists like those at Boston University’s CTE Center, who are studying the condition, believe that repeated hits to the head can cause C.T.E.

Because the Hall of Fame passed a rule in 2010 that forbids relatives of deceased inductees to speak at the annual induction ceremony — gee, I wonder why? — Seau’s daughter, Sydney, was barred from making an eloquent speech she had prepared about her father. (In a compromise, she was “interviewed” on stage during the ceremony, where she was ultimately able to to give a short version of it.)

Although Sydney Seau didn’t mention her father’s C.T.E. in her remarks, she didn’t have to; reporters covering the controversy did it for her. C.T.E. was also at the heart of a legal battle between the N.F.L. and former players, who claimed in a class-action lawsuit that “the N.F.L. held itself out as the guardian and authority on the issue of player safety,” yet failed to properly investigate, warn of and revise league rules to minimize the risk of concussions.

In April, Judge Anita Brody of Federal District Court approved a settlement of the lawsuit. Although the settlement could put an estimated $1 billion or so in the hands of former players who are suffering from dementia and other brain diseases — money that many of them desperately need — the deal has been controversial. Some 200 players have opted out and hope to bring their own lawsuits against the N.F.L. Lawyers for other former players are appealing the settlement, arguing that it doesn’t do nearly enough for players with damaged brains.

And you know what? They’re right. The Junior Seau-Hall of Fame imbroglio prompted me to take a closer look at the settlement. One of the things I learned was that if Junior Seau were alive today, he would more than likely not be eligible for compensation: Although he obviously had C.T.E., his symptoms of erratic behavior and depression aren’t covered by the settlement.

The settlement will help former players who have dementia and Alzheimer’s get compensation, though the older they are, and the fewer years they played in the league, the less money they will get. But those with C.T.E., which seems to be the primary way playing football damages the brain? Not so much. The settlement, to be blunt, is a travesty.

In her lengthy decision approving the settlement, Judge Brody defended this aspect of the deal by saying that retired players “cannot be compensated for C.T.E. in life because no diagnostic or clinical profile of C.T.E. exists, and the symptoms of the disease, if any, are unknown.”

But Robert Stern, one of the scientists at the Boston University center, told me that he expected a test to be developed within a decade that will be able to diagnose C.T.E. in living people. As for symptoms, the real problem is that plenty of people suffer from lost impulse control and depression without having C.T.E. Even so, the primary symptoms the settlement will reward financially are those that suggest cognitive impairment, rather than the behavioral and mood symptoms of C.T.E.

“At a minimum,” said Stern, “former players whose behavior changes in ways that suggest C.T.E. should have full evaluations paid for by the settlement. And treatment would be nice, too.”

It’s hard not to view the settlement as the cynical effort by the N.F.L. to contain its potential C.T.E. liability; indeed, once the settlement is final, it will be nearly impossible for players — past, present and future — to be compensated if they are found to have the disease. Even the plaintiffs’ expert has said that only 17 percent of the roughly 21,000 former players who have become part of the class will ever see any money.

Oh, and did I mention that the N.F.L. has agreed to pay the plaintiffs’ lawyers over $112 million? It’s not the nation’s dominant sports league for nothing.