Player rating for offline Heroes 3 tournaments!

No, let's better take abstract characters, for example - Johnson and Johnson :)

:D

So, what am I getting at? The fact that dividing into difficulty levels according to a fixed system leads to completely different results depending on the map. On large and complex maps, the advantage of the normal difficulty is minimal. On small maps, it is undeniable. And how to take this into account in the rating?

That is, first you suggest calculating separate ratings for tournaments of different difficulty levels, and now you suggest adding a parameter to the formula that takes into account the size of the map? By the way, on large and complex maps, but poor ones, imagine a desert where there is no easy loot anywhere, and everything is guarded, one starts with 0 coins, and the other with 5000 coins or whatever I don't remember. Therefore, even on some very large maps, the advantage of the normal difficulty may still be noticeable. Say that there are none, but someone will take and draw one. Then you need to add another parameter to the formula, in addition to the size, also a parameter of the map's poverty / richness. What else haven't we taken into account? Cast a resurrection spell on Lobachevsky and let's start composing a formula :)

Isn't it legitimate to apply a coefficient of 1.5 in both cases?

Yes, it is legitimate. This coefficient takes into account everything that we cannot yet take into account in the formula without Lobachevsky. And it is also legitimate because it will make the conclusion you made below, by the way, correct, work automatically, precisely thanks to the assigned coefficients :) Even if they make a tournament with 5 difficulty levels, players will go for the rating on impossible. And if someone settles on easy, then the rating, and even some kind of coefficient, is absolutely irrelevant to him :) He will get his small rating, and he doesn't care about it. And so what? Who will be offended?

Hence the conclusion - one save, equal conditions, and therefore - an objective rating. Otherwise - no way.