Fireball
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I have some questions.
1. Regarding the first player — not me — who did you copy them from? Are these real tournament results?
Fireball, now can you find something else to nitpick in this system??? The calculation is shown for five tournaments across different versions of Heroes 1, 2, 3, 4, 5. But the same could be done if all five tournaments were, for example, only for one version, say Heroes 1.
You are proposing to calculate the rating using the formula
R=10000(∑(1/Ni))/(∑Ni)
Welcome to our friendly company of "9th-floorers"
This formula distorts the rating in favor of fast maps less than your previous creation, but it still does so very significantly.
Let's look at the same imaginary player who won 4 stages, but got 4th place in the fourth (13 days); he will lose to you, even though you didn't even make it into the prizes anywhere except the fourth, and the 5th is almost a complete... well, you get me. It's just that in 5, there are no "drops," no "graveyards," and a bunch of other legalized bugs/features specifically for the official version. And creating such gaps while playing not against absolute noobs is simply impossible. In general, a person who won 4 out of 5 tournaments, and took 3rd place in one, should never lose on the sum, especially to someone who made it into the prizes only once.
Another example. Let's say there is a person who, like you, plays 4 and 5. And let's say he didn't have time for timeKilling in 4, playing through a bunch of battles (since you wrote that you played everything "cleanly," didn't use Ares anywhere — I'm almost afraid to imagine how many hours you spent on that) and polishing unit movement paths. In most versions, this would likely lead to a loss of parameters, but in this case, with a high degree of probability, it led to +1 day.
That is, let's say the player's result in 4 is 4 days (2nd place), and in 5 it's your same 17 (but with higher parameters). For the first stages: 12 (1st place), 12, 7 (1st place)
Total: the player plays better than you in 3 versions (and equally in two), beat you in 4 out of 5 tournaments, has two 1st places and one 2nd place, but loses to you in the rating.
If you wish, you can check both examples and see the failure of your latest idea.
Fireball, will you say it's demagoguery again? Regarding your claim that all VK stages should be equal — you're out of luck — that's NOT going to happen. Example: Player A is strong in 4, Player B in 3. In the 4 stage, there were very few people. Strong Player A took 1st place, and Player B took 2nd place even though they play 4 very poorly, simply because there were very few people there. But as we see from Punk's and Amber's systems, PLACE gives a decent bonus (28 points). What chance does Player A have of taking SECOND place in 3 (if they play 3 as crookedly as Player B plays 4) given that there are cockroaches' worth of people in 3 and plenty of pros. Player A will clearly be pushed way past 2nd place there. And where is the equality of stages for 3 and 4 for players A and B? Mathematicians, hello?
Absolute equivalence of stages will never happen in practice, but the distortion with the virtual is many times greater.
Now about creating clones in tournaments.
If you had bothered to look at the dependencies more closely, you would have noticed that such actions, even with 12-15 participants, would only slightly push back those behind the cheater and have almost no effect on those ahead. And it takes quite a bit of time to create a clone that doesn't get caught. Who needs that? So far, there have been no such cases. As for several people discussing tactics among themselves, that distorts any system, as they can together achieve a better result, even in terms of days.
4. Conclusion: The more parameters the rating calculation system for Heroes takes into account, the more glitches there will be, related both to the formula itself, as well as protection and many other things. Learn the fundamentals, mathematicians.