Player rating for tournaments across all installments of Heroes.

Y(x)=Y(x-1)-Y(x-1)*10%

1. The linear component of the calculation is based on a decreasing arithmetic progression, where Y(x)=Y(x-1)-k. Moreover, k=100/N, where N is the number of participants. That is, everything is strictly interconnected.

2. Your formula Y(x)=Y(x-1)-Y(x-1)*10% is equivalent to this - Y(x)=0.9*Y(x-1), i.e., you proposed a geometric progression (instead of an arithmetic one). This is what we are talking about... The only question is, how is the progression coefficient of 0.9 determined? I suggest k=0.85, and someone might say that this is too much and it is better to take k=0.44... We get an infinite number of absolutely equal calculation options...

The goal is to justify the progression coefficient, to link it to other constants (number of players, tournament level, etc.). If we analyze the behavior of the function (on a graph), we can conclude: the more complex the tournament, the more participants, the higher the average rating of all players in the tournament - the smaller the coefficient should be in order to ultimately increase the bonus for the leaders. The question is - by how much?