Player rating for tournaments across all installments of Heroes.

IronAxe: Maybe age the rating by 10% only for those players who missed the tournament? That way, one-day players will drop down the tournament table very quickly!

We have already lowered the aging to 10%. What is it for? A player who has played a tournament should achieve a result that can cover the aging with their tournament rating, and thereby strive to increase their current rating to prove they are not losing their skill, as they are climbing the ratings. If they receive a tournament rating smaller than the value of the rating aging, then the rating may decrease. This danger especially awaits strong players. But that is exactly what they need—to constantly demonstrate their status quo. For weaker players, the amount of rating aging is so small that it is easier for them to cover it with a new tournament rating. As for those who missed the tournament—obviously age them; they will have a clear decrease.

Regarding the Grail award system:
AmberSoler, I would be grateful if you could specify the clear advantages of your system in the GRAILS section! It is possible that your system will become the primary one for calculating the GRAIL RATING!

To be honest, I'm tired of discussing this—everything has already been written and rewritten here. I believe that my specific system should not be used for awarding grails. No aging is needed for grails. An oscillator, as proposed by AmberSoler, would work there. That is, the non-linear part is calculated as I suggested, and the linear part is calculated according to AmberSoler's formula, taking into account the significance of the place taken. Then we take the arithmetic mean and award the player grails. You probably couldn't come up with a better way to award grails.

AlexeyPank, IronAxe, Kyle, Sage and all other interested forum members, I strongly ask you to look at the Grails topic most scrupulously! And express your opinion on it. I wouldn't refuse your participation in developing this matter!

Well, what I said here—I will say there as well.

Added after 20 minutes

Judging by your post: it is exactly you who doesn't understand what I'm trying to tell you... :D

I will answer you in your own style. Judging by your post, it is exactly you who doesn't understand what I'm trying to tell you, so does it make sense for me to keep talking?

And judging by this:
You clearly haven't read our correspondence... So read it, and especially this, and you will see that AmberSoler agreed with me that the "current rating" in its present form is not correct.

And judging by this, you clearly haven't read the whole topic. What you personally said is only one page long. And in what form would it be considered correct? AmberSoler actually said that there is no absolutely right and correct rating at all. Even in your cumulative system, some will play less often, some more often. Whoever played more gets the prize, especially if you consider the place and ignore the days taken to complete, and even without aging :) Your table would only show activity.

Consequently, you admit that the "current rating" does not show the real strength of players... Consequently, why did you claim:

Have I eaten too many belins or something—of course I don't admit it. My current rating is exactly what shows the real skill of play. And if you claim that cumulative is forever, then I told you—some play more often, some less often, and besides, you don't consider results in days or they are eaten up by the second component due to place. A cumulative system especially hits forum newcomers. Someone just arrived, while everyone else has already played 6 tournaments in half a year. Everyone has accumulated everything and nothing decreases without aging. Yeah, right, is he going to wait half a year until you all reset the accumulations—that's a madhouse :)

P.S. as for my question: "What is this term 'current strength'?"

Decided to nitpick words? A player's current strength is the result of their activity in tournaments (played or missed), and the results obtained in completion days relative to the leader, expressed in the current rating. More details in the next post, and maybe it will be the last one in this topic—I'm tired already. I will calculate my rating regardless, even if VDV gives up on it. No one can forbid me from opening a topic and publishing my table there. It doesn't bother anyone. Whoever needs it will look.
And your claims about played/not played—nothing is clear; it will be the same with any rating, especially cumulative :)

Added after 1 hour 25 minutes

The idea was a bit simpler—but in the same vein: compare the player's rating with the average rating of other players in the tournament and add a bonus depending on the place. i.e., if a player takes place N in a tournament among relatively weak players (average rating is low), they receive some small bonus. But for the same place among strong ones (average rating is higher), they receive a larger bonus. The calculation principle is the same—coefficient of proportionality. I think this option is more appropriate because it reflects the strength of opponents, and not the player's own rating...
There is nothing delusional here. Although one person will definitely see delusion here and say "why give bonuses to turtles! give grails by the bagful but I won't give rating for free!" :D

I don't think I was against this coefficient of yours, nor did I say it was delusional. And regarding AlexeyPank's formulas—I'll say the same thing—you are correct. A player is in tenth place in the Rating table. Suddenly they take first place in a tournament because those 9 above them somehow didn't show up and they get a bonus of 100. For those nine, aging will be enough. Ratings must be aged at least out of respect for forum newcomers who also want to play here.
In any rating system, there will be those who miss. And in reality, it's unlikely you can tell what a player represents at the moment by looking at any of them. But it is more realistic to rely on results in completion days than on the place taken, and even more so to give bonuses to turtles. You'd better just not halve their rating for the last place using the oscillator :)

Added after 5 minutes

It's better not with the average rating among players, but with specific results. This is simply more transparent so that problems don't arise with those whose rating before this tournament was 0. And turtles won't get a large bonus unless they have a sharp breakthrough.

If a sharp breakthrough meant a reasonable number of completion days for the map, then YES. But if it only means first place due to the absence of leaders, while the days show a turtle, then what happens here?

Added after 13 minutes

In this case, it's possible to do without aging (by any of these formulas).
Someone please weigh in.

Aging reduces the old rating by 10% for all players. And it doesn't assume any bonuses because they aren't needed. A player receives their bonus in the form of a tournament rating from the current tournament, which is added to their reduced rating. A leader with 100 rating points will have to earn at least 10 points (this is thanks to the insistent requests of the workers to reduce aging from 33% to 10%, otherwise the leader would have had to earn at least 33 points) in order to stay where they are. Want to increase your rating—play according to your previously shown results. For an outsider, it's easier. 10% of 10 points of their old rating is one point. Imagine they play for 10 points again. 10+9=19. They almost double their rating through effort. In this case, you can do without any bonus formulas. Why account for something a second time when everything is already accounted for?