Is 80 points FIDE equivalent to twice as good a player? I read somewhere that if you're around 80 points better than another player, statistically you should get around twice as many points against the same opposition. This impressed me because it's not how we generally think about ratings. I worked out that Magnus Carlsen is about 64 times the player I am, which sounds about right.

My question is, can anyone verify this using the mathematics of the Elo system?
This can't be true. I (rated ~1900) expect to score 100% against a 1000 player. I don't think a 1980 rated user is able to score 200% against the same opposition.

In table 8.1b in the FIDE rating regulations, you'll find the expected scores corresponding to a rating difference. A rating difference of 80 corresponds to an expected score of 0.61, which is much lower than twice the 0.5 expected score for equally rated players. 

The only point in the table where a rating difference of 80 corresponds to a doubled expected score is at the very end. Against opposition rated 500 points higher than you, your expected score is 0.04; against opposition rated 580 points higher it's only 0.02. The expected score formula is explained on Wikipedia:


  If Player A has a rating of RA and Player B a rating of RB, the exact formula (using the logistic curve) for the expected score of Player A is 
  
  EA = 1 / (1 + 10 (RB - RA) / 400)