Player rating for tournaments across all installments of Heroes.

I reviewed your calculation method. It is correct.
However, the conditions for its application cannot be called a "solution to the problem in a general form." And the caveats, "all the same people were invited, but the leaders didn't show up again," suggest that the example is contrived and tailored to a specific effect that you desire.

I wouldn't say I'm tailoring it to a desired effect, but rather trying to test the system specifically in extreme, critical situations. This is what testing anything is all about. Let's say, in the example provided, not all of the players I banned showed up for the tournament :) But only three. What would happen? Do I have to calculate that again? I already have one example where the test parameters were specifically increased.

Now, I'll refer you to my post #193 in this thread, where the situation is broken down, and it has a significantly higher probability of occurring than the one you mentioned.

Why are you so sure that the probability of this situation is higher than the one I presented? In the example I provided, I guarantee that Dmitry will not complete this map in 5 days. And a significant gap between him and the majority of players could only occur if the players I mentioned did not show up. And in the example, we see that a non-linear rating would show a more accurate rating of the participating players. After all, we know the real situation because, thank goodness, we were able to complete the map together with Grandpa Mozai :)

It is very easy to simulate this in the table that you have in front of you. Just take my original calculation and set the leader's map completion speed to, for example, 5 days. And your first coefficient will give all the other players a rating in the range of 1-10. The outsider will be only 5.7 points behind your result... :) This is probably much better in your opinion...

Absolutely correct!!! The rating will be accurate because I won't see many players at this tournament. Aiden, Harvey, and many others. But if no one shows up, and I suddenly become "cool." But at the next tournament, if a cool monster or monsters show up, they will quickly put me and everyone else in their place by completing the map ten times faster than us. And the proposed example for modeling only confirms this.

And one more thing. I believe that while we are delving into the depths of the calculation, ...
Calculate as you see fit. In any case, I will not be in charge of rating calculations. So, the cards are in your hands. However, if you need my help, I will not refuse.

We won't delve into it :) I already have a solution. I will have to keep the rating for VDV tournaments in Heroes using two systems to REALLY assess which one is more suitable for Heroes. I know the main points and formulas of yours.
So, let's do this - with your system, everyone gets a 10% aging penalty - will there be a bonus or not? With my system, there will be a bonus of 1-2 skips. But the aging penalty will be 33%.
And this - since you won't be calculating, but you won't refuse to help, prepare the forms or use the template. I got tired of coloring the example - I don't really know Excel. Therefore, in addition to the forms, I need instructions on how and where to enter the data to calculate the next tournament, because you saw what I'm capable of - no more. Then you wanted to add some more coefficients later, will that be later?

Sage! I'm taking Heroes 3, maybe even the first one. What will you take? I can't take more. I need to keep the rating for two systems in parallel. Will you choose the system you will use? I can't choose yet, so I will find out in practice?

Everything I wanted to say about this, I have said and more than once. It is incorrect to reduce the "significance" of the second component. I have already thought about this. Second place cannot have less significance...

You thought poorly. The place in tournaments in Heroes should not have such a strong influence. And certainly not dominate over the component that is formed by the approximation of the result to the leader in days.
The significance of the SECOND "free" place does not decrease. Let the player be recorded in the Hall of Fame, and let them be showered with full pockets of Grails.

if the leaders did not participate in the game. In this case, the result of any tournament can be questioned and called a fluke...

The main thing is that when they show up - at the next tournament - they will dispel our doubts about the fluke results of the past, when they will outperform everyone by tens of times and immediately get a worthy rating for it, and with your component, how long will they have to prove and catch up with the supposedly cool ones who have accumulated a ton of points over five years? So what if someone worked on their rating for a year, but can't play? A monster comes along who can play and immediately restores the status quo with their super-fast completion times, far ahead of everyone else. Why should he spend a year if he can play? And if he leaves, he will also quickly fall off the rating :) We are talking about the CURRENT rating - have you forgotten?

... if we take into account that there are players somewhere who could beat everyone, but they just didn't show up...

And does this mean that my game rating should become better if I still take a long time to complete maps compared to even the players on this resource? The point is that this system, in the long run, for the GENERAL rating, both between resources and for different versions, but let's not talk about that yet.
They didn't show up, so what about your statement that you need to defeat a bunch of Masters to achieve something? A player who takes a long time to complete maps cannot have a high rating, regardless of what place they took. He will only be lucky if he takes first place :) And the same goes for everyone else :) But at the next tournament, speedsters can throw them so hard that it will be noticeable :)

Each specific tournament is considered separately and regardless of whether someone did not show up. My task is solved in a general form, and for the average tournament, it is more acceptable... IMHO, as always.

Therefore, if someone did not show up, you will get a bag of Grails for second place. So, second place will be rewarded. The monsters who didn't show up missed out on a bag of Grails. But what does this have to do with the game rating? A monster doesn't show up - his rating sharply decreases - he returns - he plays well - he will quickly catch up with the imaginary leaders by making super-fast completions, far ahead of everyone else. Do you get the idea? So, what you want to present as a disadvantage of this system is actually its advantage :)

Added 2 minutes ago

By the way, in many tournaments (not only in Heroes), non-participation is automatically counted as a defeat, so the option proposed by AmberSoler most fully takes into account the interests of both the first and the second...
With respect.

Maybe there are super-cool players who don't even know about this resource! Let's not look ridiculous if they accidentally drop by here :)