Player rating for tournaments across all installments of Heroes.

I wasn't even trying to do that, although maybe I should have. If you read carefully, I was just suggesting combining the IronAxe and VDV Forever systems. Their linear combination would not contain any obvious contradictions. Moreover, if a system had already been chosen for the tournament, I would not challenge it, considering it part of the rules.

It might not be worth delving deeply into mathematics, although you are absolutely right in your reasoning... I will try to simplify.

1. Any sequence of values "100-95-91-86-83-...-5-1" is abstract and does not contain anything in itself, because it does not explain why exactly these coefficients were introduced. The goal is to find a method that will generate coefficients each time, depending on objective factors that characterize the player's achievement. What are these factors?

1.1. Map difficulty. In my opinion, it doesn't matter. All participants are in equal conditions, and therefore it is not appropriate to divide them according to this criterion, although, at first glance, it seems necessary to take this criterion into account.

1.2. Number of participants. It matters. And directly proportional - the more opponents you manage to beat, the higher the level of the game. A tournament for five players and a tournament for a hundred are significantly different. But: at the moment, it is customary to award 100 points to the tournament winner, and therefore we initially abandoned this parameter. The only way to take this into account is to give a higher delta to players in the upper part of the table compared to the rest when the number of participants increases... And this automatically leads to a compression of the ranking of players in the lower part of the table.

1.3. Average strength of players in the tournament. This is fundamentally important - even more so than the number of players. Beating the top five strongest opponents in a tournament with only ten participants is more significant than beating a hundred conditionally weak players in a tournament where the strong do not participate. But for this, it is necessary to take into account the current rating of the player, as well as assess the strength of all new participants, which is impossible in principle.

Conclusion. The only parameter that we can somehow optimize is indicated above (highlighted in color). But, against the background of the rest of the balance distortions caused by objective factors, it does not seem particularly significant. In other words, increasing the accuracy of measuring one of the parameters of the system in the case when this [accuracy] is lower than the error of the entire system as a whole (which we are observing in our case) does not make practical sense. We have already discussed this, and I believe that a reasonable solution will not be found.

If we do not take into account the strength of opponents, but only the number of participants in the tournament, the rating will not approach its true value, no matter how hard we try to balance this criterion. That's why I say - it's not necessary. Although, for theory, this issue can be tried to be solved purely mathematically, but whether to apply it or not is a matter for the future...