Here is another question:
How much more, if at all, will a series of random moves beat a 1300 player vs beat a 2700 player?
It seems you can't reliably use the frequency of error vs good moves because the winner isn't necessarily the one who made fewer mistakes.
Or another way to ask perhaps is, is the winner more commonly than not, the player who made a fewer number of mistakes?
A computer who does truly random moves would have a bigger chance to win agains a GM, than a 1300 rated player.
However, the 1300 player would be (almost) infinitely stronger than this computer.
For non-infinite very large numbers, we could have:
A always wins against B
B always wins against C
But C sometimes wins against A!
This is a cool observation for the way performance (in terms of win/loss/draw) against one opponent does not intrinsically predict performance against other opponents.
This undermines the whole enterprise which strives for an ideal rating system by using past results to predict future results... at least in the sense that when it interacts with reality that it produces ideal results.