I ran with 80/16.5/3.5 as a size estimate because I couldn’t find a statistical structure that better explained what was going on. Turns out I was a bit blind.
My new theory is that the skill brackets are determined using the standard deviation of the rating distribution. The slice between the mean and one standard deviation above the mean is 34.1% of the distribution. The slice below the mean is 50%. 34.1+50 is 84.1, and the difference between 84 and my estimate of 80.5 can be explained by the High and Very High brackets having players that are, on average, more active than the Normal bracket.
This theory puts the High bracket cutoff at 2 standard deviations above the mean, or 13.6% of the population. The remaining 2.3% is the Very High bracket.