Tom Brady shouts instructions during the AFC championship game in January. (John Cetrino/EPA)

Isn’t it fun, this game of hide-and-seek that NFL quarterbacks are playing with concussions. Maybe Tom Brady had one, or maybe he didn’t — find his symptoms, win a free prize. Drew Brees says he would conceal one from his own wife, which conjures an image of him popping in and out of the linen closet, while she looks for him behind the kitchen door.

Excuse the sarcasm; it’s a result of exasperation. If Brady and Brees want to calculate the exchange rate between winning a game and how many neurons must be sacrificed to stay on the field, that’s their personal choice. The problem is that they have signaled to four million high school and college football players that hiding symptoms is what the great ones do, and that it’s okay not to tell the woman in your life, or to tell her to keep quiet about it, even though she may have to wipe the food from your chin one day.

NFL players have a difficult calculus to make in weighing the cost vs. benefit of reporting a concussion. Some of the factors that affect their willingness to be honest range from letting down teammates, to fear of stigma, to how receptive their coach is to injury reports, to their own flawed perception of how serious their symptoms are. And then there are the contractual issues. Have a few too many “dings” noted on your chart, and pretty soon you could be feeling the headache in your next salary negotiation, or on your way out of the league like Wes Welker.

“The unfortunate part of concussion awareness is that the financial consequences at the NFL level for reporting them have gone through the roof,” says Chris Nowinski, co-founder and CEO of the Concussion Legacy Foundation.

But if anyone has leverage in this situation, Brady and Brees do. This is the perfect moment for a new tone and message, a more honest if complicated answer from players who are influencers. Honest is what Gisele Bündchen tried to be during her appearance on “CBS This Morning,” when she let it drop that her husband has played with head injuries and had one just last season.

“I mean, we don’t talk about — he does have concussions,” she said.

The responses she prompted have not been especially informative, or clarifying. The NFL issued a statement that no “records” indicate Brady had any kind of head injury, while his agent, Don Yee, said that Brady had not been formally “diagnosed” with one. The Patriots quarterback himself has been utterly silent.

If only someone, a Brady or a Brees, would say the following: “Yeah, I played through a concussion. It was a poor decision I made because I felt responsible to so many other people whose livelihoods depend on the game’s outcome. I won’t know for years whether it was the wrong decision for my long-term health, but what I do know is that no one at the high school or college level should ever make the decision I made, because protecting against neurological diseases is not about eliminating one big hit, but reducing the number of smaller blows you take over a career. That’s why I’ll pull my kids from a game the minute they see stars, and why they won’t be allowed to play tackle football before the age of 14. I advise you to do the same with yours.”

But that’s not what anyone said. Instead, what you heard was a lot of guy-frequency dog-whistling and tacit approval about what’s tough. Brees, now with the New Orleans Saints, acknowledged that he played with a concussion in 2004 with the San Diego Chargers even though, “I knew something was not right,” as he told ESPN. Former Detroit Lions wide receiver Calvin Johnson said he had multiple concussions over his nine-year career even though he never submitted himself to treatment. “I know I got a job to do,” he said. “The team needs me out there on the field.”

Pittsburgh Steelers quarterback Ben Roethlisberger is the rare exception who has pulled himself from a game, but even he admitted to Sports Illustrated, “I haven’t reported things before either.” The subtext to these statements is, “I’m too important to come off the field.”

All of this is a tremendous missed opportunity. A 2014 study published in the Journal of Neurotrauma showed that only one in every six football concussions is actually diagnosed, and now we know why. The study surveyed 730 college football players and found that for every concussion they reported to their team, they experienced 21 so-called “dings” or symptoms they failed to report. What was so discouraging about the study was that it showed the NFL ethos leaching downward to players who aren’t being paid, for whom football is a game and not a job. Denial is simply considered the thing to do.

This is a failure on the part of NFL players. It is not a form of strength; it’s weakness — and dumbness, and egotism. And it’s based in a deep-seated fear of someday being replaced on the field.

“We’re seeing an incredible lack of leadership among NFL players,” Nowinski says.

The NFL as an organization has tried to change the paleo culture of “playing through” concussions. It has hired certified independent neurologists. It has stationed spotters in press boxes. It has increased penalties for vicious headhunting, and put limits on practice time and contact drills. But what is any of that going to matter if a player won’t meet the eye of his own wife?

Here is the truth that no one wants to speak aloud: The NFL concussion crisis is all but unsolvable. The game is violent, and competing pressures on players from financial to peer influence compel them to hide injuries of all sorts. We simply can’t expect all of them to self-report, and the league is never going to be able to devise rules or protocols that make their concussions diagnosable from the sideline. The problem is here to stay, and all the league can do is to provide them with the best medical care and brain health information available.

But there is a lot more that can be done at other levels. NFL players have a responsibility not just to themselves, but to the younger versions of themselves, their mini-me emulators. And they are not living up to it. If they decide to take risks with their health, that’s fine; they are adult professionals. But when they, by word or act or complicit silence, encourage thin-chested, bobble-headed boys to take risks with their brains, that is not fine, not at all, not one bit.