Player rating for tournaments across all installments of Heroes.

Suggest a principle based on which this "non-linearity" will be implemented.

For now, there is only one principle: the difference between the places should increase as you get closer to the winners.

The only condition is that each number must be logically justified... We will not take coefficients "out of thin air."

However, this condition is definitely impossible to fulfill. You will inevitably have to resort to making things up, because everything comes down to how quickly the rating curve should decrease with the place. Once this is known, you can simply write some power from 0 to 1 in the formula for the oscillator instead of the expression n-1/N-1 and obtain any curvature of the curve. And this is far from the only way. Therefore, to avoid endless debates that will not have objective arguments, I suggest taking an existing distribution system as an example, using the VDV Forever system as an example.

If you have any other fundamental and specific requirements for the dependence of the rating on the place (i.e., they can be represented as specific properties of a function), please state them. This will narrow the search.