How often would a 1300 beat a 1800?
They have an expected score of 8%.
So 8 wins in 100 games, or 4 wins 8 draws.
However, the rating system doesn't work well with large gaps and above about a 400 gap the higher rated player will score more than they should.
Lower.
Nope http://en.chessbase.com/post/the-elo-rating-system-correcting-the-expectancy-tables
What actual evidence do you have to support this claim? You certainly haven't cited any.
My own experience, and evaluation of players I met here, otb, and in my otb-club.
So in other words anecdoctal evidence. Or to put it more accurately no evidence at all.
The only way to provide actual evidence would be to cite how rating differences predict actual results amongst various rating pools. Not easy to do without the full databases and some actual programming.
But maybe we should avoid making claims for which we don't have and can't provide any actual evidence.
Sorry I have been inaccurate, Fide and chess.com-ratings might be ca. equally presice, the largest downside with fiderating is not presicion, it is the time delay (and usually lower number of games). The Fidenumbers are describing a strenght that was some months ago, and that is the reason the ratings looks very strange, especially when playing talented , hardworking kids who have a strenghtincreasing speed above 200 points a year.
The downside with chess.com rating is that some strong players dont take the game as seriously as they do in fiderated otb-tournaments. Many players use chess.com for joy and testing. Some players drink more alcohol or are more tired or less focused when playing online. And there are timeouters.
I am myself rated maybe 50 points below my strenght on chess.com online, because of playing too much games, and moving to much when tired. In Norwegion otb-elo, I am ca 200-300 points below my strenght because it describes my results from january to june, and I have strenghtened after that.
I will not say that I have a sure truth here, but I am describing how it looks from my point of wiev.