Player rating for tournaments across all installments of Heroes.

First, please give me a clear answer regarding the issue with the oscillator. Otherwise, no one bothers to explain anything, and I'm just rambling here :)

Do you mean this? If so, let me explain:
As far as I understand, you are comparing two Tournaments for the current rating, but these tournaments cannot be compared because they do not meet the conditions that I described here. That is, either combine them into one Tournament (if the initial save is the same for everyone), or don't compare them. This is what I am talking about... it is necessary to abandon the current rating because this comparison is like comparing a 100-meter race and a 400-meter hurdle race!
Therefore, the bug that you showed is not an oscillator bug, but a bug in comparing Tournaments for the current rating.

Further:

The current rating is needed to show the current strength of players who are currently active, whether they have overtaken inactive players in terms of rating, taking into account the aging of the rating.

Hmm, how will you distinguish, by just one number, between an active average player and an inactive strong player?

It is also possible to look at the current strength of each player in connection with this, regardless of whether he played or missed a Tournament.
...
One thing I can say for sure - the numbers in the General current ranking table will be next to each player and next to the leader as well. Accordingly, the table shows the current strength of each of these players in Heroes on THIS RESOURCE! Is that clearer?

And what is this term "current strength"? :eek:

Sincerely.