Player rating for tournaments across all installments of Heroes.

We've been waiting for a long time...

Let N be the number of players participating in the tournament. Each i-th player has an average rating Ri in this part of the game. Then, we define the tournament category as:

K = (∑(Ri + a)) / 1000, where a is a constant that determines the contribution to the tournament category of a participant who does not have a rating.

A player's base rating consists of two parts:
1. For days: Rd = 50(M/m), where m is the number of days the participant played, and M is the number of days the winner played.
2. For placement: Rp = 50((N - n + 1 + b) / (N + b))^2, where n is the participant's placement, and b is a regulating constant.
Rb = Rd + Rp - base rating

The final rating is equal to the product of the base rating and the tournament category:
R = K * Rb

Now, about the two constants, it is obvious that they can be discussed. The constant a should not be too large. A new player is a priori not considered strong. My opinion is: a = 20.
The constant b may be necessary to smooth out the rather sharp (but this is a matter of taste) behavior of the dependence when N < 10. For large N, it does not play a role at all. Personally, the behavior of the function seemed most correct to me when b = 3