Player rating for tournaments across all installments of Heroes.

You mean this one? If so, here's the explanation:
As I understand it, you are comparing two Tournaments for the current ranking, but these tournaments cannot be compared to each other.

But they can be compared – we were talking about VDV Heroes III Tournaments.
He held one tournament, then another. Since I maintain the Current Ranking for all players, I need to combine all six participants into a single general Rankings table. Take another look at what happens there, but pay attention this time, or you won't understand anything again. This topic discussed not only the ranking system for Kanighem's Tournament, but also the General Current Ranking for players in version three of this resource. The system I proposed can be applied to other versions of the game as well.

because the conditions I described here are not met. That is, either combine them into one tournament (if the initial save is the same for everyone), or don't compare them to each other. Which is what I'm saying... you need to abandon the current ranking because it's like comparing: a 100-meter race and a 400-meter hurdle race!

And AmberSoler told you in that very post that you gave an incorrect example, that it was irrelevant, but you somehow shouted "Hooray" and plunged into further details :)

Therefore, the bug you showed is not a bug with the oscillator, but a bug with comparing tournaments for the current ranking.

This is actually a bug with the oscillator – if you understand the given example correctly. What does bug with comparing tournaments for the current ranking mean? In other words, you suggest maintaining a Current Ranking for each Tournament, so express yourself clearly about what you mean by Tournaments of different game versions. But there can also be Tournaments of the same game version. I am not against having separate Current Rankings calculated for different versions of Heroes. But in the example with the bug that I provided, I repeat once again, we are talking about Tournaments of the same version, for example, version three. It just happened that two Tournaments were held for version three, and we tried to combine all players from version three into one general table. This creates inconsistencies, which are caused precisely by the places occupied by the players. Take another look at the results of the Best tournament. You have already been assigned a rating based on the experimental system. We are waiting for another tournament from VDV for version three; hopefully, you will participate in it; otherwise, your rating there will simply decrease by 10%. By participating and showing a good result, you will compensate for the decline, and your current rating will improve :)

hmm, how do you distinguish, by a single number, an active but average player from an inactive but strong player?

I personally won't distinguish anything there. I will look at my ranking and compare it with the results of others. I think other players who play for the ranking will do the same. Accordingly, whoever is higher in the General Current Ranking table – they get the bragging rights. Whether they played or not is not a problem for the ranking, but for the players.