Player rating for tournaments across all installments of Heroes.

If we are to compare, the following conditions must be met:
1) a constant number of participants, i.e., no one joins or leaves... or if someone joins in the middle, their losses in the Tournaments that have already taken place should be counted... and if they leave, they get zero points for the ones that will take place.

That's right! :) If someone joins in the middle, all the Tournaments that have already taken place are worth zero for them, which means their rating is zero. This is self-explanatory. If they leave, we add zero to their rating for each Tournament, and then we update the rating. And so on - until it is completely reset... You probably haven't fully understood the calculation method, which is why this confuses you so much... Please, take a closer look at the issue...

2) a time limit, i.e., from 01.01.2001 to 03.03.2003.

This is not important at all. If you manage to play the required number of Tournaments during this period, then it is included in the cyclic rating (annual, quarterly, etc.). If you don't manage, then it is not included. It's very simple. And for the current rating, the period is not important at all, because the aging procedure reduces the importance of past Tournaments for all players... And there comes a moment when a Tournament that you played six months ago no longer gives you any advantage over someone who didn't play it... Everything is well thought out! :)

3) equal competition conditions, i.e., one save, one version of the game (The Shadow of Death and TE are different versions), etc.
and maybe something else... that I'm missing right now...

This is a fundamental condition for rated Tournaments... BB is a test, and the "normal" save will not be included in the rating. We only play on SoD. This is self-explanatory... And it is simply necessary to adjust the starting conditions of the Tournaments for this.

Everything else, I'm sorry, is NONSENSE!

There is no "everything else"!!! :smile13: