I know this thread is old, but it's an interesting one. I'm not a software guy, but I wonder if a chess.com API exists, and whether it can be used to do this kind of statistical analysis. Or perhaps an API isn't needed, just someone that knows how to create a bot that scrubs the site for the needed data.
In any case, I think chess.com should definitely start a stats blog. It would be very interesting.
I think it's an interesting question. Haven't seen any study ... an idea for chess.com. Would be a useful guide to planning, if a gen. trend appeared.