Player rating for tournaments across all installments of Heroes.

We're just reinventing the wheel here... I deliberately introduced a non-linear component into the oscillator so that it would take into account not only the result but also the player's position – the more players you outperform, the greater the bonus you receive.

For a more productive discussion, let's define the terminology. The non-linear component in the oscillator is the one that depends on the number of days, because it is INVERSELY PROPORTIONAL to this number. The part that depends on the position is LINEAR with respect to this position (and non-linear only with respect to the number of participants). Please don't confuse them. And most importantly, don't forget that the number of participants does not reflect the significance of the positions, especially the top ones.

It's much easier to add "weight" to the oscillator formula, shifting the arithmetic mean towards the non-linear function, and we'll get a greater curvature, which is what you're advocating for.

Curvature is determined by the second derivative of the function. Introducing a weight (read: multiplier) doesn't change anything. A straight line remains a straight line, and the second derivative of kx+b is equal to zero.

You can experiment with balancing endlessly, but there's no point in it because there's too little material for analysis, and it won't be possible to see the effectiveness of the formulas for reflecting the real strength of the players. There are no objective criteria that we can use as a benchmark...

I disagree. A rating is needed for a specific tournament on a specific portal. We look at the average number of participants in the Van Caneghem stages and check how the oscillator behaves. The difference between adjacent positions with the same number of days is ALWAYS the same and is approximately 3 points. We think about whether this is good or bad.

I suggest leaving everything as it is.

Not yet. There are several author's, NON-official systems.

And if we're going to optimize, then we should do it within the framework of the proposed and used calculation methods. As an option, make a certain effort and choose one single method from all the ones currently in use.

No offense to the authors of these systems, but none of them can withstand the simplest criticism when applied to a multi-stage tournament.

But we shouldn't create a new one. Just another one of many...

So far, I haven't tried to do that, although maybe I should have. If you read carefully, I just suggested combining the IronAxe and VDV Forever systems. Their linear combination would not contain at least obvious contradictions. Moreover, if a certain system had already been chosen for the tournament, I would not challenge it, considering it part of the rules.