Player rating for tournaments across all installments of Heroes.

I don't object to this coefficient (or bonus increase) as such; I just didn't like the proposed way of calculating it.

I agree; not everything has been polished yet – there's still room for improvement... But this is a solvable problem; just don't rush... If you have any more ideas, let me know.

because in a tournament with less competition for places, as in the second tournament from the example I provided (in which it is easier for any player to take a higher place + a higher coefficient), more points will be earned than in a more intense competition in the first tournament (where it is more difficult for any player to take a high place, and the coefficient is also lower).

It's not clear why it's easier to take a higher place in the second example. From the perspective of a strong player? I suggest looking at it from the perspective of the average player... And therefore, the second example actually requires a higher coefficient – because the range is wider... and the average (weaker in the second tournament compared to the first) player has fewer chances to break through to the top...

Please understand the idea: the weaker the average player in a tournament is compared to the top players, the fewer chances they have on average, and the more a non-linear coefficient for calculating the rating pushes them into a corner (the effect of lowering the bar) – which means that, for balance, the tournament rank should be taken into account... It can be taken into account in such a way that the coefficient provides more support to the weak than to the strong... we just need to think about it...

And in general, there is, of course, no goal to shower the weak with bonuses and make life difficult for the strong, as it may seem... The goal is to prevent a large gap, which will only worsen, and to create a balance of power that will reflect all the key aspects of the game (number of players, their strength ratios, places taken, etc.)… This is a normal approach, and I think it should be understood.