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

It seems you didn't understand me. I was asking about Ppartii because it's Ppartii that calculates the rating for a match, which is one in VGAplanet, but many in Heroes. Should I calculate all matches for each player? I'll go crazy :)

:) Don't go crazy, but approach this creatively. For them, this Ppartii is considered one match that can last from 3 to 6 months. Just call this match a "tournament," and everything will fall into place. In reality, it's an accounting of the "strength of the match (tournament)." It takes the ratings of all players participating in the tournament, adds them up, and divides by the number of participants in the tournament. But why does the formula say that the ratings of players are taken AFTER the tournament ends? It means that a person playing one match in VGAPlanets may be playing a dozen more on other hosts at the same time. And those matches may end earlier than this one for which the rating is currently being calculated. So, this player has already been given a rating for those completed matches. Therefore, when calculating the rating for this match, his new rating will be used to calculate the strength of THIS match.
In other words, you will have this: Ppartii will be called Pturnira and will be calculated as the sum of the ratings of all players in the tournament, which they HAD at its end, and then this number is divided by the number of participants. This is if you want to have a single rating for all online players. Let's say you and Adelaide agree to calculate the players' ratings according to this common system, and you will have two tournaments running in parallel, but her tournament will end earlier. So, when calculating your Pturnira, you will take the ratings that the players have at the moment after Adelaide's tournament.

And in the final formula, it is Ppartii that is divided by 6000.
Therefore, it is Ppartii that needs to be replaced/changed with something.

Optimal, don't complicate things :) Instead, try to simplify and focus for now on Ppartii in VGAPlanets and Pturnira in Heroes. THESE ARE THE SAME THING !!