NEW YORK — Like any major American institution dealing with a crisis, or something that has the look of a crisis, the NFL likes to let you know that its best people are working on the problem, and that it has a lot of best people. The NFL has had a problem with concussions and head injuries for a while. So last week, in a conference room at its Park Avenue headquarters, five executives and experts who work either for or with the league sat together on the long side of a long table for its annual health and safety briefing.

There was Dr. Allen Sills, the NFL’s chief medical officer. There was Nyaka NiiLampti, Ph.D., the league’s vice president of wellness and clinical services. There was Jeff Miller, the league’s vice president of health and safety policy, formerly its chief Washington lobbyist, formerly staff director for the Senate Judiciary Committee antitrust subcommittee. Yes, there is the problem of concussions and head injuries, but there is also the problem of perception: whether the NFL has been saying and doing the right things about concussions and head injuries. And fixing that problem requires more than being proactive and sticking to the science. It requires persuasion and a little salesmanship, too.

Fortunately for the NFL, it appears that it has a fairly persuasive case to make of late. Just last week, the league received a public-relations boon when the Washington Post published a scathing profile of Dr. Bennet Omalu, the scientist who has credited himself with the discovery of chronic traumatic encephalopathy, or CTE, and who was portrayed by Will Smith in the 2015 film Concussion as a brave and valiant savior, standing alone against the dark forces of football and corporate America. As it turns out, Omalu might not even be diagnosing CTE correctly, earns a pretty penny from distorting research and findings and peddling specious science, and generally approaches head injuries and brain disease not from the detached view of a doctor but with the religious fervor of an anti-football zealot.

The timing of the Omalu profile — it appeared online the day before the health and safety briefing — couldn’t have been better for the NFL and the story it wants to tell. Since the start of the 2018 season, the league has implemented several rules and equipment changes designed to cut the number of concussions suffered by its players: better helmets, ejections for helmet-on-helmet hits, the elimination of the blindside block, and others.

In 2017, in the preseason and regular season, NFL players suffered 281 concussions, according to the league. In 2018, that number fell to 214, a 24% drop, then went up slightly to 224 this season. Still, that figure was statistically similar enough to 2018, Miller said, that the league regarded it “as a new benchmark. We feel as if we’ve found a new place from where we need to continue to push down concussions.”

In a perfect world, that push would come organically from the players themselves. They would deliver fewer hits and blocks that might result in concussions, and they wouldn’t hesitate to admit when their brainpans had been rattled. Sills said that in recent years, about one-third of all concussion/head injury evaluations — those recorded by the unaffiliated neurotrauma consultants on the sidelines during games — “had some element of self-report.” That is, one way or another, the player is alerting the trainers and doctors that something might not be right.

“Anecdotally, those of us on the sidelines perceive that the culture of self-reporting continues to grow and continues to be a change over where the game was in general maybe a decade ago,” Sills said. “I think players understand the magnitude of the injury and what’s involved with that. Obviously, I was quoted recently about a very high-profile player and that very issue.”

That player, of course, was Carson Wentz. When Wentz removed himself from the Eagles’ Jan. 5 wild-card game against the Seahawks because of a concussion — even though the on-site spotters hadn’t noticed that he’d suffered one — he cast in sharp relief the contradictions and hard choices that the league, its players, and its fans still face on this issue.

The reverberations of Wentz’s decision reached the league office. Here was an emerging star, one of the league’s top young quarterbacks, showing exactly the sort of discretion and prudence that the NFL’s experts want all players to show. It’s no coincidence that, within a week of that game, Sills told the Associated Press that Wentz’s decision was “heroic.” The NFL wants as many heroes in this regard as possible. For the sake of all football players’ health, everyone should.

But the NFL also wants everyone to keep watching football, and the players themselves want to keep playing it, and the sport’s intrinsic violence often sets those aspirations and goals against each other. The league can’t avoid that mixed messaging; it can only hope no one picks up on it. Yes, Wentz should take himself out of a game when Jadeveon Clowney cracks him in the head on a bang-bang play, and we at the NFL applaud Wentz for it. But no, we’re not going to reprimand Clowney and send a clear signal that we don’t tolerate such borderline hits. And we can do our share of shady science-framing, too, even when the news we’re delivering is mostly good.

For instance, one thing the league learned this season, Sills said, is that players who participated in preseason games but did not make the roster “were three times as likely to have a concussion as those who did make the roster.” That’s one way to put it. Another way to put it — as former Eagles quarterback Cody Kessler can tell you — is that a player who participated in preseason games and suffered a concussion was three times more likely to be cut. A concussion during the preseason makes a player, particularly one competing for a roster spot, less reliable, less useful, more dispensable.

Pro football remains that unforgiving. Those who play it know it, and those who watch it should, and even the NFL’s best people can do only so much about it.