If you follow sports in any capacity, it would have been pretty hard to miss a major story this week further strengthening the link between football and chronic traumatic encephalopathy (CTE), the degenerating brain disease.

The brains of 111 deceased former NFL players were studied, and 110 of them — yes, all but one — had evidence of CTE. The study was published in The Journal of the American Medical Association.

Per the New York Times: The brains here are from players who died as young as 23 and as old as 89. And they are from every position on the field — quarterbacks, running backs and linebackers, and even a place-kicker and a punter. They are from players you have never heard of and players, like Ken Stabler, who are enshrined in the Hall of Fame. Some of the brains cannot be publicly identified, per the families’ wishes.

That’s a big deal and some pretty sobering science.

That said, former Vikings center Matt Birk jumped into the dialogue with a tweet late Tuesday linking to the New York Times story but also asking this question: “What about the 15,000 or so deceased former NFL players who lived full lives and didn’t have CTE?”

Birk, 41, is currently a special adviser to the NFL and in 2009 pledged to donate his brain to science when he dies.

The 140 character nature of Twitter doesn’t allow for much nuance, but let’s dissect his words just a little more.

It’s pretty dangerous to say former NFL players who have died but didn’t have their brains studied — therefore showing no direct evidence of CTE — “didn’t have CTE.” It would be more comforting to think CTE only impacts a very small percentage of players — still not good, of course — but the sheer math suggests that a lot of dead former NFL players had it as well. It’s not quite on the level of an argument such as “it’s not hot today so therefore climate change must not be real,” but it doesn’t hold up.

Where there is a discussion to be had, and where it might naturally lead in more than a 140-character space, is here: It stands to reason that a former NFL player who wanted his brain studied had symptoms that made him believe it was possible he was being impacted by CTE.

That said, this argument is addressed by the New York Times:

The set of players posthumously tested by Dr. McKee is far from a random sample of N.F.L. retirees. “There’s a tremendous selection bias,” she has cautioned, noting that many families have donated brains specifically because the former player showed symptoms of C.T.E.

But 110 positives remain significant scientific evidence of an N.F.L. player’s risk of developing C.T.E., which can be diagnosed only after death. About 1,300 former players have died since the B.U. group began examining brains. So even if every one of the other 1,200 players had tested negative — which even the heartiest skeptics would agree could not possibly be the case — the minimum C.T.E. prevalence would be close to 9 percent, vastly higher than in the general population.

 Birk, a St. Paul native who just turned 41, is Harvard-educated and had a tremendous NFL career. He’s taken care of his body, shedding tons of weight from his playing days on the offensive line. We should all hope the Birk and his fellow NFL players, past and present, live long and healthy lives with no impact from CTE.

But the numbers are out there. Out of the 110 players in this study found to have CTE, 44 were linemen. It’s wishful thinking to believe everyone you have watched or will watch on Sundays will be fine. That’s a hard and scary thing to reconcile, but it’s true.

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