Player rating for tournaments across all installments of Heroes.

2 IronAxe
Here's a small comment regarding your "lyrical" approach.
I was considering the situation where out of one hundred players, one player completes the map very quickly (they pulled off a clever trick – the original source is here) – let's say in 10 days, the second takes 1000 days, and all the other 98 are even worse. The example is exaggerated, just to illustrate the point. In this case, all 99 people, compared to the leader (who will have 100 points), will receive a rating from 0 to 1, which is disproportionate to the effort they put into competing for the prize.

And I told you how I would avoid this situation. I will calculate each player's rating up to 7 decimal places, then each tournament rating will be added to each player's old rating, taking aging into account. There should no longer be zero due to the presence of an old rating. However, if this does happen, there will be numbers after the comma. In the final general table, multiply each result by 10 or 100. As a result, proportions will not be violated, and the current strength of each player will be correctly expressed in numbers, without any distortions associated with linearity.

You – I believe – simply didn't grasp the idea behind my example. Naturally, I don't think you intentionally distorted it... In your comments, you omitted the first "fast" player from the analysis and considered all the others, so in that case, the very essence of my example is lost.
Let's read on:
This is incorrect on your part because it is the oscillator that smooths out this imbalance ...

The oscillator actually introduces an imbalance. Regarding the last players, I already talked about it using an example – the last one has their tournament rating halved. You all like to say that we should look at real examples, so go ahead and look – many people have already downloaded your Excel spreadsheet. See how Izualu's rating was reduced by half.
Now let's look at the top places:
-------- Days -- Nonlinear -- Oscillator
Dmitry 36 -- 100 -- 100
Radik 39 -- 92.3-- 93.9
VDV 56 -- 64.3--77.6
..
Axe 71 -- 50.7--64.0

Don't you notice anything? The oscillator straightened out my nonlinear rating for Radik by as much as 1.6 :) But then, for VDV who followed, the oscillator only smoothed out my nonlinear rating by a total of 14.3 :) And what's the logic there? Why is the player who took second place with a small gap from the leader being penalized in this way? And why did player VDV perform better, taking third place with a large gap from the leader in terms of days? Well, and further down, everyone has been nicely "smoothed" out; it even almost corrected mine by about 14. I have already shown two specific flaws using a real example. Show me a flaw in my nonlinear column on this same example ???

Regarding the second component, it's good to calculate. Without considering the nonlinear component. There, yes, it doesn't matter how many days I completed the map – but if I happened to take second place after 1000 days, give me a bag of grails, but what does the tournament rating having half the value of the leader have to do with it if the result in terms of days is far below average?!

Added after 13 minutes

Well, that oscillator corrects this flaw... :) What else should we develop? In the oscillator, there is no such flaw - I showed this flaw in IronAxe's methodology solely as an example of inefficiency...
So, if you are adopting the oscillator, then you shouldn't think about random discrepancies. This sometimes happens, but it will not affect the final calculation...
Take the calculator that I suggested and conduct an experiment. Second place, regardless of the gap from the leader, will be rewarded with at least 50 points, the rest – evenly from 0 to 50.

The oscillator doesn't correct the flaw; it pulls up a mediocre player by the ears based on their rating to someone who is actually good, if it turns out that second place was taken by a player with 1000 days.
But in a single tournament, this is still somewhat acceptable, but what does it have to do with people who didn't play in the tournament and suddenly become neighbors in the ranking? Even aging by 33% won't create such a mess if calculated purely based on the nonlinear component :)