 If Player A has a rating of formula_15 and Player B a rating of formula_16, the exact formula (using the logistic curve) for the expected score of Player A is

Similarly the expected score for Player B is

This could also be expressed by

and

where formula_21 and formula_22.Note that in the latter case, the same denominator applies to both expressions, and it is plain that formula_23.This means that by studying only the numerators, we find out that the expected score for player A is formula_24 times greater than the expected score for player B.