Player rating for tournaments across all installments of Heroes.

But, still, it's more rational to justify the coefficient... than to use a linear function.

Ah, if only I had your confidence... :) There's nothing more rational here. These are absolutely equal options... The question is, a geometric progression (or some other non-linear function) is a more flexible tool for calibration... But, on the other hand, it will also have a much larger error in case of a mistake in balancing the formula. The problem we are trying to solve here on the fly is much more complex than it seems.

That's why I suggest not overcomplicating things. There's no need for it. We're wasting a lot of time, when we could already be creating tournament brackets, attracting players, and creating motivation for clan battles based on the rating calculation methods that already exist. In my opinion, they are quite acceptable... And mathematics is just a pastime for a few players, while the rest don't really need it...

Maybe we should leave these developments aside? :)
Take the simplest calculation scheme from the ones already proposed and forget about the rest?

And I think I know how to take into account the strength and number of opponents. And the difference between a warm-up match and a main battle will be quite noticeable. And, if necessary, I can present my system to the public for review.

Well, we've been waiting for a long time...