@Riot, Statistical Distribution of Rankings

So, I remember seeing a link/website earlier that showed the distribution of players in ranked, with obvious spikes in the 5th division of each tier, however, the total% of players in each tier seemed to follow a fairly stable statistical curve. I was wondering, what statistical distribution you use to measure player rank distribution since I remember during a balance discussion saying that only around 20% of players are in plat or higher.

I'm asking because I'm curious since I'm taking a Bayesian statistics class, and we've learned about gamma distributions, Normal distributions, beta distributions and will be learning about a few others. From what I saw, it seemed to me that the distribution of players in ranked followed a gamma distribution because it seemed that comparatively few players were in bronze or silver than in gold compared to plat upwards.

another reason I ask this is because I'm interested if the statistical distribution of rankings affect your MMR calculations to affect how many players you want in each tier. Theoretically, there can be an infinite number of players in each tier up to master where it has a hard limit, but my guess is that the MMR calculations automatically adjust the MMR for each division to pseudo limit the number of players in each division which is a necessity in order to clamp the theoretically infinite number of diamond players to just the top X00 players in each region for master and challenger tier