Player rating for tournaments across all installments of Heroes.

1. The difference in linear ratings for 1st and 2nd place is equal to the difference for 11th and 12th. This not only diminishes the importance of the top places but also, with a large number of participants, very quickly reduces the difference between them.

What function do you propose for constructing the curve if you are not satisfied with the linear one? The function, in any case, must take into account the number of players, even if it is non-linear.

2. The bonus, although it depends on the correct parameters, is truly negligible. It does not reflect the difference between a warm-up gathering and a BB, and it is not very clear either.

Then, according to what criteria will you differentiate between a warm-up tournament and a BB? In my opinion, the only criterion is the composition of the opponents. That's it. What difference does it make whether you run 100 meters or 400 meters if Ben Johnson is running next to you? And again, we return to our topic - without knowing the strength of the opponent, it is impossible to calculate the relative significance of your victory, and therefore to correctly take this result into account in your rating.

What can be proposed? By default, provide each player with a conditional strength parameter equal to five on a ten-point scale (or 50 on a hundred-point scale - it doesn't matter). Then, from game to game, this parameter will be adjusted up or down. Any newcomer receives exactly the average parameter, not zero. Because the average value of the strength distribution of any set of players will tend towards the median as the sample size increases. Previously, we started from zero; perhaps this is where the mistake lies... It is impossible to underestimate the true strength of unknown players, thereby unreasonably lowering the rating of the tournament... And in each tournament, there are enough players whose rating has not yet been determined...

Next, we calculate the level of relative strength of the opponents in the tournament and take it into account as a parametric coefficient when calculating the bonus. And no numbers should be taken out of thin air! Someone here said that in mathematics and physics, many coefficients are taken from the air, and that's okay... :)
I am not yet familiar with such mathematics...