Preliminary clan ranking on HW.

For example: General = (AllRating_new1 + AllRating_new2) / 2
Would this be significantly flawed? I'd like to hear AmberSolera's opinion on this.

If we substitute the original formulas into your version and expand the brackets, we get the following:

AllRating_new = AllRating_old + (P1 + P2 +...Pn)*(N+1)/2N

As can be seen from the formula, the last multiplier (N+1)/2N very quickly approaches 1/2.
In other words, we essentially have the following formula:

AllRating_new = AllRating_old + (P1 + P2 +...Pn)/2

That is, the same "Chinese" sum, which depends only on the number of participants.
This is not an oscillator because it only takes into account one parameter - the sum of the ratings of all players.
An oscillator should have at least two independent parameters. :)

I wouldn't rush into delving into the mathematical intricacies of these calculations just yet. There have been enough battles in calculating the individual rating. We don't need to create another mess here. I've expressed my opinion:

AllRating_new = AllRating_old + (P1 + P2 + P3)/3,
where P1-P3 is the tournament rating of the three best players in the Clans in this tournament (not to be confused with the current rating).

Of course, we can discuss the question - why three, and not two or five? I'll say this: given the average number of players in Clans, in my opinion, this is the optimal number of results to be taken into account. If there are ten players in Clans, then it can be increased to 5-7. But for now, more than three is pointless, because not all Clans will be able to field three players in a game...

An oscillator can be tied in. But why? Balancing the Clans rating is more complex than the individual rating - due to the larger number of significant factors... And if the oscillator caused "complaints" in the relatively simple individual rating, then here we will simply get bogged down.
I don't need that.