Okay, parsing over the study itself, it looks like the study was completed in essentially 2 stages.
1. A blind clinical survey (i.e. the survey takers don't know the pathological state of the donor) to the families of the deceased, where they essentially assemble the progression of the participant's symptoms, such as changes in mood or cognitive function.
2. A blind pathological evaluation (i.e. the pathologists don't know the symptomatic state of the participants). Basically they look at brain tissue samples and determine whether it has CTE by discrete physiological changes.
Among 202 samples, they diagnosed CTE in 87%. Of those 202, 111 were NFL players, and 110 had CTE.
What was most interesting to me was this:
"There were no asymptomatic (ie, no mood/behavior or cognitive symptoms) CTE cases."
I mean, on one hand, no shit, but on the other, it's makes a compelling case that the physiological state is likely never asymptomatic.
Finally, the authors do lay out the limitations of their study, namely that they only have samples from people who donated, and of course that would bias for people who already have CTE, and this overall doesn't allow us to draw conclusions about the participants of the sport at large.
My question, though, is how much would the public consider acceptable risk? 1 out of 10 players? 1 out of 20 players? 1 out of 100?