In my experience, people generally get a rank within 6-10 games. If they consistently defeat much stronger players, it can be even sooner. I’m not sure your investigation is reliable because it does not consider the effect of alt sandbaggers. Alt sandbagging is a major problem on OGS, as on all servers. If a sandbagger has high SDK or low dan strength, they can rank their account up to their level in 6-10 games (i.e., not merely get a rank), at which point they abandon the account and start all over again. I’m afraid this hugely distorts the statistics you are relying on.