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

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

We'll only find out if our forum mathematicians respond to this topic. Because I can't say anything definitive here either :(

So, this is the rating calculation system. I personally didn't understand much there)
"""First, the player rating is calculated for each player:
Rplayer = 1000 * (X + 2 * X^3)
where X = (N - Place) / (N-1)
(Here, "Place" refers to the position in the match occupied by the i-th player and takes values 1, 2...N, N is the number of players who finished the match).

In my opinion, this part of the system calculates the player rating for a specific, single Tournament. The rating depends on the NUMBER of players and the POSITION occupied in the Tournament. After the online Tournament, all this data is known. But how to distribute places in the Tournament itself is up to the organizers. For example, 2 points for a win, 1 for a draw, and 0 for a loss. After counting the points and distributing the places in the Tournament, you can calculate the rating of each player using this formula.

If some players share several (K) places, then their player rating is averaged:
Rplayer = 1/K * Σ Rplayer[j]
j runs through all such players

This part adjusts the rating of players who occupy the same places in the Tournament.

The rating of the entire match is calculated as the average of the ratings of all players, which they had at the end of the game:
Rmatch = (1/N) Σ Rafter_end_of_match
i=1

This part of the system takes into account the STRENGTH of the Tournament (match rating, which takes into account the existing ratings of the players who participated in the Tournament) when calculating the rating for each player in the Tournament.

And, finally, the current rating is recalculated:
Rnew = 2/3 * Rold + Rplayer * (1 + Rmatch/6000)"""

Here we see that in the final formula for calculating the rating for each player after the Tournament, there is an aging of the rating of their current rating before the Tournament:
2/3 * Rold
And then it is added to the rating earned by the participant in this Tournament. I am confused by the number 6000? Where it came from - who knows. Perhaps this system calculated the rating for Tournaments in which no more than 11 players could participate (this was limited by the rules of the game for which the rating was calculated using this system). Maybe this number is related to this fact??? Who understands formulas? Say something? :)