Player rating for tournaments across all installments of Heroes.

I propose two options for calculating the rating, both of which are strict and fair. First, let's look at the general principles of their calculation: R(i) = R(n) + R(l) + R(b), where R(i) is the player's rating, R(n) is the non-linear rating, R(l) is the linear rating, and R(b) is the bonus rating. The non-linear rating is calculated using the formula proposed by IronAxe: R(n) = 100 * n(1) / n(i), where n(1) is the result of the first place, and n(i) is the player's result. The linear rating is calculated using the modified formula proposed by AmberSoler: R(l) = 25 - 25 / (m(l) - 1) * (m(i) - 1), where m(l) is the last place in the tournament, and m(i) is the player's place. The number 25 was chosen after analyzing all the tournaments. In my opinion, the linear component of the rating should not be more than 1/4 of the non-linear component. However, these numbers can be debated. In total, the maximum rating for these two components is 125 points. Now, let's move on to the bonus. For its calculation, I propose two options: 1. R(b) = R(tr) / R(iSr) * R(l) * k, where R(tr) is the actual tournament rating, equal to the average non-linear rating of the tournament, R(iSr) is the average non-linear rating of the player, R(l) is the linear rating, and k = R(tr) / R(tp) is the tournament coefficient, and R(tp) is the expected tournament rating, equal to the average rating of all participants in the tournament. This rating option takes into account the strength of the tournament and the previous results of the players, i.e., a player with a lower average rating receives a higher bonus in the tournament. This allows compensating for the difference between the non-linear rating and the other two. 2. R(b) = k * R(l), where k is the tournament coefficient (see the previous formula), and R(l) is the linear rating. This formula is simpler but does not take into account the player's previous results. In addition, to increase the rating for official tournaments, coefficients for the bonus rating can be introduced, as proposed by VDV_forever for the Grail tournaments: 1.4 for ВК tournaments and 1.6 for ВоВ tournaments. I am attaching tables with calculations for all tournaments for Heroes 1 and 2.