Player rating for tournaments across all installments of Heroes.

In other words - the rating for you is like your space races, which you admired somewhere and now wish to see everywhere...

Not exactly. Because in my example on my system, Mozay barely reaches VDV, while according to your system he rapidly overtakes Radik. How do you explain that? So, an average player under your system took a HIGHER place in the rating than under mine after completing only two tournaments, let's say, due to the absence of some players.

So I consider the dispute closed :) We initially set different goals and both achieved them in a sufficiently correct way. Congratulations to us both! :) And five pages of flood are the price of the question...

I thought, and still think, that dependency on party strength and number of players could be added to my system. But in such a way that it doesn't introduce great distortions to the main component - GAME STRENGTH IN DAYS close to the leader's result. Perhaps dependency on the place taken could also be added, but the requirement is the same.

1. (IronAxe) The rating is not elastic and instantly reflects all changes occurring in tournaments, correctly showing the current short-term situation, however it depends significantly more on the results of specifically the last completed tournament than on the results of previous ones...

I can agree, but not with everything. Yes, the rating promptly reflects the situation after each of the tournaments. But it will be inelastic in cases where all players fall behind the leader by dozens of times in days, or conversely, the Leader overtakes everyone by dozens of times—regardless of the reason, whether some players were absent, or everyone played poorly, or the Leader just had a moment of brilliance, take it however you like :)
Moreover, my system is not to blame in this situation. People played; it only reflects what happened. Furthermore, it doesn't grant any additional bonuses to leaders or underdogs—everything depends on the players themselves. Learn to play better - show Walkthrough results closer to the leader and bring your rating closer to the leader's rating - that is its motto.

The victory of an average player in the last tournament will almost always put them in first place, but only until the next tournament, unless they win it again.

The example provided again disagrees with you. Mozay's victory in the second tournament under my system didn't even let him reach second place, only fourth, ALTHOUGH almost all top players were absent from the tournament.
Under your system, however, Mozay reached second place, and along with him a couple other players overtook Radik. So you've mixed something up here :)
But I agree again that this could happen under my system too, if a player won the last tournament by beating all participants dozens of times faster in days, and the rating would reflect their surge because it is the Current Rating. But why did Mozay jump so sharply under your system? Simply because he took second place, even though the result in days was mediocre.

Because even second place does not guarantee him a high result.

It guarantees it! In the case where his result is close to the leader's in days. The place itself has nothing to do with it. Therefore, a high result is guaranteed for almost everyone if all are close in days to the leader's result. In your system, this is possible ONLY with absolute equality of places taken, which practically never happens in Heroes tournaments. So I consider that a plus for me :)

However, it should be noted that rating decay always proceeds at exactly 10% of the nominal value, and therefore such a situation can often be observed where, based on tournament results, a player who achieved a decent result will see a decrease in their absolute rating.

Decay under my system is originally 33%. A grace period for missing 1-2 times.
Speaking of a player with a decent result, AmberSoler means the place they took, not how fast the player completed the map and how far behind the leader they were in completion time. That is, if the leader finished in 50 days, and another player finished in 500 days but still took second place, then in AmberSoler's opinion - that is also considered a decent result. Well, I fundamentally disagree with this, which is why I made a different rating calculation system. We seem to be done with mine.

2. (AmberSoler) The rating is elastic and distributes the result more evenly among players. i.e., it gives a bonus to a player who achieved a high place in the tournament (even with a large gap from the leader -- IN DAYS -- ), ...

AmberSoler's system is not a Current Rating, in the sense that I understand it. A current rating is a rating reflecting the current state of affairs in tournaments, with sufficient consideration of previous tournaments. I would more likely call AmberSoler's system an accumulative rating, which at this current moment might show not exactly the player's current rating, but their Current :) rating, which they now have thanks to the tournaments of the whole year. Even if they performed poorly in the last few tournaments. But there is no escaping past merits :)

but the price for this is the cutting of the tournament rating in case a player took one of the last places. Last place in a tournament brings the player a loss of 50% of their tournament (but not current) rating. However, as a rule, this amounts to no more than 10 nominal points.

The main Price of the cut is paid specifically by the player in LAST place. I didn't quite understand the 10-point nominal value. But if a player somehow got 4 rating points, imagine for them 50% is ONLY two points. And personally, I think that's not a small amount for them. Why take it away from them?
Just to linearly level the rating for others and raise it for the top half of the tournament table, whose players—even with a large gap from the leader—took second places?

A feature of this calculation variant is the fact that to significantly move the position of the current leader, winning one or two tournaments is not enough. This process will be difficult, unlike the previous calculation variant, but on the other hand, it should be noted that the current leader also spent considerable effort in their time to achieve a high result. So, its relative stability can be considered a deserved reward.

Correct, because after each tournament the rating is stretched linearly in different directions - Leaders get a bonus increase in rating, and underdogs get a bonus decrease, depending on places taken and without considering days.

So, we have two balanced systems, but pursuing opposite tactical and strategic goals.

I personally think my system is more balanced :)
Because AmberSolera's tactical and strategic goals are already being shaped into dolls and grails on the resource. The tactical and strategic goals of my system are the prompt reflection of current reality. Without artificial bonuses for anyone. Even if it be a NOVICE.

I am not saying that AmberSoler's system is bad. It is good. Perfectly suited for awarding grails in tournaments. And much from it can be added to my system, but only not by simple addition of two components, and then dividing by 2. But since our tactical goals were initially different, as AmberSoler correctly says, the formula never developed in that direction. Maybe this will be done later.

There is no bad or good rating. There are only different ways of transferring tournament results to the general balance. Both ratings use the results shown by players to calculate coefficients, and there is not a single unjustified number.

AGREED. In principle, in both systems, everything ultimately depends on each player's personal game and luck. Luck is also an important matter, although it's better to rely on one's own strength :)