Player rating for tournaments across all installments of Heroes.

...explain logically why, if players complete the game in the same number of days, have the same resources and oil, but one takes second to last place and the other takes last place...

You are twisting things. In the case you mentioned, two players will take the same place, and their tournament rating for this tournament will be the same.

...It's a different matter when comparing the results of a linear system and an oscillator; I didn't like that balancing.

That's a different matter. It would have been worse if you liked everything. :)

...And admit it, Amber Soler, who found the error in the formula in your documentation for the third game (it's good and helped me in the tournament because I haven't played in a long time)? I remember you sent me to it. You admitted in a private message that the formula wasn't yours. But how did such a nonsensical formula end up in your documentation if you are so good at math? :) And why didn't anyone else notice this except for me?

Yes, that's absolutely correct. The reference book doesn't only contain my calculations. It also contains a lot of information that was taken from other sources - that's why there are links everywhere. It's impossible to keep track of everything and check every number manually. Sometimes inconsistencies pop up. And then I myself, rolling up my sleeves, try to analyze everything in detail. But now, I think, there are practically no such moments left. Why didn't others notice? I suppose they did. They just didn't want to participate in this issue... So they kept silent. And you - well done. By the way, I reworked that formula and made it right.

...And according to AlexPanka's coefficient, there also seems to be an unsolvable situation, when a player with a zero rating receives a bonus after the game, like a starting bonus. I personally don't see the point of any bonuses when calculating the rating.

Not just a starting bonus. Any player whose current rating has dropped due to low activity will receive this bonus regardless of their skill level. But, I agree, the bonus is still not very big. And this is a reasonable price to pay for a more balanced system. You insist on not taking anything into account except the player's result. I believe that it is more reasonable to take into account all factors. And that's enough about that. There is no argument here.