Questions, answers, and resolution of disputes regarding the online rating in HoMM5.

The only remaining question is whether the rating is calculated for each duel or for a series of duels, and if for a series, then why?

For each duel, the win/loss ratio is calculated.
The rating is awarded for winning/losing in a series.
That's how I understand it.

System 2.
Everything is very simple - we discard the old formula, and calculate the rating based on the position occupied by the duelists.

The calculation is as follows: the number of wins is divided by the number of losses, based on a ratio of 5-10 (your number?) games. Let's say, 6 wins, 4 losses. With 1.5 points, you enter the main table. Then, a sequential number is assigned to the player, depending on the points initially scored (win/loss ratio).

Then, we proceed based on the sequential number, which directly depends on the rating.

A win is calculated as follows: we divide our sequential number by the number of the losing player. The lower the player is in the table, the more points he will receive for winning against the leaders of the table. And vice versa - the lower the player is with whom the leader plays (in this context, the player who is higher in the list), the fewer points he will receive. We add the points.

A loss is the same, only the points are subtracted.

Example:

Player 1 (1st place) won (meaning in matches, for example, with a score of 3-2) against Player 2 (5th place). Then 1/5 = -0.2 is subtracted from the rating of Player 2, who is in 5th place. The same amount (0.2) is added to Player 1.

A bias occurs when Player 2 wins. Then 5/1 = +5 points for Player 2 and -5 for Player 1. We need to think about introducing a coefficient, for example.

For adequate calculation, we can introduce increasing/decreasing coefficients (for example, 0.8 or 0.6 or 0.4 - decreasing, 1.4 or 1.6 or 1.8 - increasing), then:

Player 1 (1st place) won (meaning in matches, for example, with a score of 3-2) against Player 2 (5th place). Then 1/5 * 1.6 = +0.32, and for Player 2, 1/5 * 0.6 = -0.12

Player 1 (1st place) lost to Player 2 (5th place). Then 5/1 * 0.6 = +3, and for Player 1, 5/1 * 0.6 = -3.

All this is quite raw (the coefficient system needs to be refined). All this is as an alternative suggestion.

I'm listening...

Added 7 minutes later

You have an error in your calculations here; in case of a loss, if the difference in rating between the players is 500 or more, the number we multiply by 0.04 is positive, that is, we add twenty to minus fifteen and, accordingly, we get +5;)
Therefore, my suggestion is to consider the maximum difference to be 375 points (when multiplied by 0.04 = 15)

Okay, what if it's like this:

650-(15+0.04*500) = 615 ;)