Player rating for tournaments across all installments of Heroes.

Yes, a player with a zero rating will receive a bonus. However, as could be seen, this bonus is not very significant and will not be able to substantially change the overall situation. And over time, when the number of regular players noticeably exceeds the number of newcomers, it will be completely unnoticeable.
In general, this bonus can address the following tasks:
1 Account for the number of players.
2 Account for a player's previous results in relation to new ones.
3 Account for the average rating of the tournament (i.e., if there is one strong player and others are much weaker, the average rating will be lower and, consequently, the bonuses will be small).
I am not arguing that the formula I proposed may be incorrect. But has anyone proposed another one that takes into account all the points I listed?
P.S. And still, it is better to calculate the linear component not from zero, otherwise what is the point for a weak player to participate among the strongest?