Rating system for online games in Heroes of Might and Magic IV.

Just post the part of the document that directly describes the calculation formulas and discuss it here with the mathematicians. Everything is explained in detail, in my opinion.

Okay, I'll post it. But what about exceeding the player limit? (regarding the calculation system)

The system is like this because there are no tournaments, it just takes into account the number of wins and losses for each participant.
But aging should still be considered and figured out properly, as you rightly pointed out.

I personally don't know how to do this. We can think about it, but it's better to decide as a team so that everyone is satisfied with the organization. Share your ideas, and we'll figure it out!

Added after 20 hours 26 minutes
So, here's the calculation system. I personally didn't understand much of it. """First, the game rating for each player is calculated:
Rgame = 1000 * (X + 2 * X^3)
where X = (N - Place) / (N-1)
(Here, "Place" means the position in the game that the i-th player took and takes values 1, 2...N, N is the number of players who finished the game).
If some players share several (K) places, then their game rating is averaged:
Rgame = 1/K * Σ Rgame[j]
j runs through all such players
The rating of the entire game is calculated as the average of the ratings of all players, which they had at the end of the game:
Rgame = (1/N) Σ Rafter_end_of_game
i=1
And finally, the current rating is recalculated:
Rnew = 2/3 * Rold + Rgame * (1 + Rgame/6000)"""