New Official Rating System on the Heroes World portal.

posted by loi
Is there a reason why this particular non-linearity is used, and also a reason for the formula used to calculate the coefficient K?

In principle, it's all the same. The justification is very simple: if you make the curve slightly steeper or more gradual, you won't notice much difference... The coefficient was chosen to be as flexible as possible. And to prevent too many players with very weak results from being excluded, and to avoid ruining the performance of strong average players.