You lost me when you introduced a geometric mean in there. There are many ways of dealing with draws in rating systems, but this one seems completely unrealistic. Can you elaborate on the reasons behind this?
Just intuition here. I wasn't able to find anything else for modeling expected ratio of draws to decisive games given a rating gap (and ratings, since for a given rating gap, higher ratings implies more draws)
GM seemed a reasonable approximation but I can't justify it anymore than saying it was an intuitive guess.