When are we going to start the Tournaments?:p
(I haven't read the whole thread, it's hard to understand the notations)

N - number of players in the Tournament
i - place in the Tournament
^- exponentiation.
Rold - old rating
Gw - won games
Gl - losses:)

What is the purpose of the gradation and the dependence of the coefficients K and K1?
Does it turn out that we derive it empirically?

The gradation is used so that a leader with a decent rating doesn't increase it even further, that is, to give a newcomer a chance to somehow climb up. For example, the rating of Player 1 will be 1700, and Player 2 = 0
Then, for Player 2, the coefficient k (which stands before Gw) will be 3, and k1 (which stands before Gl) will be 1 - this will give the newcomer extra points and a "boost", and for Player 1, the coefficient k will be 0.75 and k1 = 3, to slow it down. If you want to be a leader, you need to try to win. Therefore, having a high rating, you need to keep working hard, otherwise you can go down.