Player rating for tournaments across all installments of Heroes.

No, now everything is written exactly as intended. When I wrote the formula, I meant that 'a' should represent not so much some hypothetical beginner rating, but rather the contribution for "participation."

You consider a beginner to be a player without tournament experience. I consider a beginner to be a new player who doesn't have a tournament rating. However, they may have extensive experience gained on another platform... It's necessary to average this out, which is what was initially proposed. I believe the formula ∑(Ri)+30*n(a) is quite optimal, as already mentioned.

1000 is a simple normalization, so that for an average tournament, the multiplier for the base rating is 1. For example, in a tournament with 5 beginners and 10 participants with an average rating of 60, the multiplier will be (a=20) K=0.9.

The calculation mechanism is unclear. From the formulas, it seems like (10*60+5*20)/1000=700/1000=0.7, or something else? At least provide an explanation of your calculations...

But there's also a nuance here. According to your proposal, the difficulty coefficient for playing against 10 aces (rating 100), for playing against 20 average players (rating 50), and for playing against 50 beginners (R=20) would be the same: k=1. Intuitively, this seems contradictory... This isn't a situation where quantity turns into quality... Because if you combine all the opponents, in your case, the coefficient would be k=3, i.e., we see a linear dependence on the number of players. But it seems to me that by solving the problem of how to beat the top ten strongest opponents, we automatically solve the other two... That is, the coefficient shouldn't increase significantly when these groups are combined, but it also shouldn't decrease. It's necessary to take into account the difficulty due to the increasing number of participants and, consequently, the increasing probability that someone from the relatively weak players will make a leap forward – this is quite acceptable. But this doesn't depend linearly on the number of players...

You are wrong. A tournament with 5 aces (R around 100), coefficient K=0.6, a tournament with 50 beginners will have K=1. It's not that bad, even in this completely unrealistic (extreme) example.

Beating 50 or 100 beginners (if they are truly beginners in the sense you mean) won't be difficult... Beating 5 aces is much harder. I say this from experience in tournament battles, not from pure theory. Therefore, your coefficient isn't tied to reality, which speaks against it.

Obviously, why, otherwise a tournament with 10 aces would receive a higher category than a tournament with 10 aces and 10 almost aces, but to win, you need to beat both. More precisely, to win in the second case, you need to beat all those that you would beat in the first case, and also 10 almost equally strong players.

The number of opponents should increase the coefficient, but not in a linear way...

This is all theory. It's useful for a warm-up.

But in practice, it's not very applicable due to the lack of an intuitively understandable explanation. It doesn't have a physical model as an example. It can't be explained "on the fingers." And that's a minus in our case. I still believe that complicating things is not rational.