Player rating for tournaments across all installments of Heroes.

2AlexeyPank
As I mentioned before, your bonus is too small to differentiate tournaments by strength.

2AmberSoler

I think adjustments will be needed here as well. Why is the constant 'a' under the summation sign? The number of players without a rating is not equal to the number of players in the tournament... And in your case, it turns out that this coefficient will be taken into account exactly N times in the final sum... Something is not right... Maybe it was meant to be ∑(Ri)+a*n(a), where n(a) is the number of players without a rating?

No, now everything is written exactly as intended. When I wrote the formula, I meant that the constant 'a' represents not so much some assumed rating for a beginner, but rather a contribution "for participation." And only players with a rating have a contribution "for strength." An alternative to this approach is, of course, to assign a certain rating to a beginner and then sum ONLY the ratings. But I stayed with the first option based on the following reasoning:
Let players A and B have the same skill level in some part of the game, but one of them participated in tournaments, and the other did not. Due to some nuances of the tournament, their results will differ in favor of the experienced player, but this difference will disappear after 1-2 tournaments.
Next, let the average rating reflect the strength of the participant, and we assign a certain rating value to the beginner - X, then the beginner's contribution is
(X-Y) - in the first tournament, he will not realize his full potential!!!! The contribution of an experienced player remains equal to his rating - R. Now, we simply shift the scale to the right by Y, the beginner's contribution is -X, the experienced player's contribution is R+Y. For now, it is assumed that X=Y=a. In this case, we can take a=30. If we write it as you suggest, it will probably be clearer.

∑(Ri)+a*n(a),

THEN the physical meaning will remain the same, but a will be no more than 20.

What does the divisor 1000 represent? Why exactly this value?

1000 is a simple normalization so that the multiplier to the base rating is 1 for an average tournament. 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

And within what limits will this coefficient be, in your opinion?

On our portal, it's somewhere between (0.5;3)

For now, it seems to me that it depends exclusively on the number of participants, and not on their average rating. Why don't you divide the sum by N? If you compare a tournament with 5 players (all of whom are aces) and a tournament with 50 players (all of whom are beginners), the difficulty of the second will be almost an order of magnitude higher! This is not logical...

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

Why don't you divide the sum by N?

It's obvious why, otherwise a tournament with 10 aces will receive a higher category than a tournament with 10 aces and 10 almost aces, but to win, you need to beat both of them. More precisely, to win in the second case, you need to beat all those that you need to beat in the first case, and also 10 almost the same players.