Player rating for tournaments across all installments of Heroes.

I disagree with some of the statements.

In other words, increasing the accuracy of measuring one of the system's parameters when this accuracy is lower than the error of the entire system as a whole (which we observe in our case) does not make practical sense.

This statement is true for errors that are statistical in nature (having a variable sign, lucky or unlucky, it was there - it wasn't, etc.). Factors that shift the measured value in a specific, defined direction should be eliminated, because such errors add up with statistical errors according to a linear law, not a quadratic one. Of course, it may turn out that even in this case they can be neglected, but I am not sure that this is our case. However, it is not yet possible to prove or disprove this.

However, we need to talk about the strength of the participants separately. After a certain number of tournaments have been played in a given version, this strength can be reasonably estimated. Each participant will contribute a certain number of points through their participation. This number will be determined by their average rating in this part of the game + some constant addition for everyone, so that even beginners are taken into account. Based on the total points, the tournament will be assigned a category (as in chess), which will then turn into an ordinary multiplier for the overall rating, as once planned, but the category will not be arbitrary, but strictly defined.
A high category can be obtained by both a large-scale tournament and a cool head-to-head competition.

However, all of this is not applicable to determining the winners in the Van Caneghem tournament, in which, by its idea and spirit, all stages should be equivalent.

My bonus depends on the average strength of the tournament. It was also not taken out of thin air, but from tennis, where for a strong player winning against a weak player, the winner receives a lower rating than for a weak player winning against a strong player.

That's why I noticed a familiar expression. Alan already mentioned motorcycle racing, and now tennis has surfaced. The idea of borrowing an already proven system is indeed tempting, but we need to be careful.