Player rating for tournaments across all installments of Heroes.

If you have any other fundamental and specific requirements regarding the dependence of the rating on the position (i.e., they can be represented as specific properties of the function), please state them. This will narrow down the search.

"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. Then, averaging the linear and non-linear components only smoothed the function, but did not change its essence... And now you are suggesting introducing another differential coefficient. It is much simpler to add a "weight" to the oscillator formula, shifting the arithmetic mean towards the non-linear function, and we will get a greater curvature, which is what you advocate for... We can experiment with balancing endlessly, but there will be no point in it because there is too little material for analysis, and it will not 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 suggest leaving everything as it is. And if we are going to optimize, then let's do it within the framework of the proposed and used calculation methods. As an option, we can put in some effort and choose one single method from all the methods currently in use. But we should not create a new one. Just another one out of many...