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Player rating for tournaments across all installments of Heroes.

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What function do you suggest for constructing the curve if a linear one doesn't suit you? The function should, in any case, take into account the number of players, even if it is non-linear.

It will depend on the number of participants.
Then, according to what criteria will you differentiate between a warm-up tournament and a BB (Best of Best)? In my opinion, the only criterion is the composition of the opponents. That's it. What difference does it make to 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.
And I think I know how to take into account the strength and number of opponents. And the difference between a warm-up and a BB will be quite noticeable. And, if necessary, I can present my system for public review.