What I did bring was my math background, which really played a huge role in all of this. These doctors were telling me this condition, CTE, does not happen in regular people—it does not happen unless you bang your head over and over and over and over and over again. So this is a million-to-one shot that’s come in three times in a row on NFL players who have been examined for it—Mike Webster, Terry Long, and now Andre Waters. [Webster, a star offensive lineman during the 1970s and ’80s, suffered from dementia and depression after retiring; he was diagnosed with CTE after his death at age fifty in 2002. Long, a teammate of Webster’s, was found to have CTE after he committed suicide in 2005 at age forty-five.]

If I didn’t know anything about neuroscience, I did know enough about conditional probability to know that something was different about this group of football players. And when the NFL, or the NFL doctors, tried to tell me that those three didn’t mean anything—that their published studies asserting that everything was hunky-dory were the last word on the matter—they were attacking my core belief system. They were telling me that two plus two equaled five, and I knew they were wrong. Because the point is not that there are hundreds of football players out there who are not suffering any of these types of deficits. The point is how many of them are having the deficits, and how that compares to the general population.

In February of 2007, I heard that the league was soliciting applications for a fund to help former players who had been diagnosed with dementia and Alzheimer’s, what was known as the 88 Plan. I knew instantly that that was going to be their downfall. Their strategy had always been to discredit the data or the methods of every study that had linked football with cognitive impairments. And here they were collecting the data—they were blessing the data.

And I knew that once the number of people in the plan reached a certain point, about sixty or eighty, there would be a decent sample to analyze, in terms of at what age these players were starting to show signs of dementia. I needed to wait. But I always had in the back of my mind, “I can’t wait to get my hands on that list.”

In January of 2009 I found out that the number of players in the plan was ninety-five. A little while later I was on the beach in Puerto Rico, with my wife. I should have been more with my wife, but I was thinking about this stuff—I just knew I was on to something. And I started sketching the numbers out on this little Marriott pad, literally while I was on the beach. I was doodling around—if there’s this many people alive, what would the curve look like?

When I got home, I started calling as many people as I could, trying to find out who was in the plan. It wasn’t that I needed the names themselves, but it was important to know the players’ birth years, to get a sense of how old they were when they started to experience dementia. I thought somebody would just leak the list to me, but holy shit was that thing locked down. It was virtually impossible; you always heard the same small group of names. Eventually, I pieced together sixteen, and that was actually enough to have a pretty good idea of what was going on. You could basically know what the age-distribution curve was going to look like.

So the next question was, what’s the denominator? How many retired players are alive? I knew that there were about 13,000 living ex-players, so I sketched out a reasonable estimate of their age groups. I also happen to have a good friend who has the best biographical data on athletes of anybody, so with his help I got those numbers almost exact.

Greg Marx is a CJR staff writer. Follow him on Twitter @gregamarx.