Probably the method as mentioned is very much simplified.
however, one thing makes it a bit trustable - I'm in the Gold II which is at the median position among all leagues.
I gave it another thought as what you mentioned, the distribution. I think the distribution for Bots, rental account and card owner account pretty much different. I would say something in below picture. it could also different from it depends on the profitability. since i did not see the bots/rental account at Gold II compared to Bronze, so i believe below distribution is still valid in a certain way.
