On one of the most troubling issues facing the National Football League, the numbers are running against it. Those numbers don’t involve the PSI of underinflated footballs. They involve the health of your son’s head.

Pro football’s mounting controversy regarding the long-term danger posed by concussions and the game’s apparent direct connection to long-term brain damage made news again yesterday after it became known commissioner Roger Goodell forced out controversial long-time league medical advisor Dr. Elliot Pellman in favor of a full-time chief medical officer. Although no one knows who that will be, you can bet he or she won’t be a rheumatologist, which was Pellman’s specialty.

That fact led to a public relations nightmare for the NFL when it was learned Pellman had little or no expertise in brain trauma even though he’d been an outspoken critic of early studies linking concussions in football to the presence of chronic traumatic encephalopathy.

Pellman was a long-time denier of any connection between football and long-term brain injury, maintaining that position even after private studies showed otherwise. For more than 20 years, he headed the league’s mild traumatic brain injury committee, a group formed in 1994 that routinely produced studies denying any link between football and brain damage and minimizing the effects of concussions.

Those studies have since been repudiated by independent research and the league itself.

The U.S. Department of Veterans Affairs and researchers at Boston University have found evidence of CTE in the brains of 96 percent of deceased NFL players examined and in 79 percent of all football players, regardless of age. Goodell understands this poses a growing threat to the game’s long-term popularity, so he is doing what he can to tamp down the issue at a time when the league can no longer live in denial about the connection between football and degenerative brain injury.

Adding fuel to what seems to be an endless fire, UMass-Lowell yesterday announced 78 percent of the people it recently polled felt tackle football should not be played before the age of 14, and a whopping 84 percent of women opposed it. Even 72 percent of men were against it.

Those kind of numbers are an NFL nightmare. The marketing gurus who run the sport fear that failing to connect children to the game is likely to threaten its long-term popularity. The NFL has grown into a financial behemoth, grossing more than $13 billion in revenues last year, through the almost messianic connection between the sport and American culture.

Once churches owned Sunday. Now the NFL does. But if the mothers of America begin to oppose their sons’ participation in the sport, there is a potential chilling effect on that ever-expanding popularity. Goodell might be a fool at times, but he knows how to count.

In response, Goodell insists the NFL has major concerns about the health of its players and is funding concussion research to improve it. Yet in May, a Congressional report concluded the NFL had pressured the National Institutes of Health to strip a $16 million project from a prominent Boston University researcher and direct it toward members of the league’s own committee on brain injuries, despite the fact the funding was to have come from a $30 million league research grant that was supposed to have no restrictions on its use.

That news hit barely two months after Dallas Cowboys owner Jerry Jones said the following during the annual owners meetings: “There’s no data that in any way creates a knowledge. There’s no way that you could have made a comment that there is an association and some type of assertion. In most things, you have to back it up by studies. And in this particular case, we all know how medicine is. Medicine is evolving. I grew up being told that aspirin was not good. I’m told that one a day it’s good for you . . . I’m saying that changed over the years as we’ve had more research and knowledge.

“We have millions of people that have played this game, have millions of people that are at various ages right now that have no issues at all. None at all. So that’s where we are. That didn’t alter at all what we’re doing about it. We’re going to do everything we can to understand it better and make it safer.”

Comparing the medicinal value of aspirin to brain damage concerns caused by football-induced concussions was not a good take. Neither was Congress’ announcement that the NFL was trying to influence what concussions studies were funded, a charge the league later denied without much success.

Now we have Pellman being given the bum’s rush about 20 years too late and a UMass-Lowell study saying the mothers of America are turning their backs on America’s football obsession. The dangers of the game cannot be swept under the rug nor bought off by “Heads Up Football’’ public service announcements supporting better tackling technique in youth football.

This is an issue that isn’t going away, and if the NFL doesn’t stop treating it like a PR problem, more than its players’ heads will be hurt by it. The owner’s wallets will, too.