Player rating for tournaments across all installments of Heroes.

Well, I'll add my two cents.

1. The most important thing is not to go too deep into the details so that we stop understanding each other. Because, as practice shows, even people who think logically and understand numbers can no longer keep track of our conversation... :) Kyle is an example – he understands the essence of all our calculations perfectly, but because he hasn’t been following the topic for some time, he has already lost the thread of our discussion. We three are still managing somehow... :)

2. As always, I strictly adhere to the following principles: solving the problem in a general form and avoiding any arbitrary figures. The first principle helps avoid wasting time analyzing specific and highly unlikely cases, and the second is simply the only correct and reasonable approach to balancing the system. Because even one figure taken out of thin air significantly disrupts the entire balance.

Therefore, I agree that the idea of averaging the top three results – which is itself new and interesting – will reduce the likelihood of a large gap appearing. However, the number "3" itself is taken arbitrarily and undermines the consistency of the system.

Let me explain. Why do we take the top five players or not just two, but specifically three? There is no hidden meaning in this number. And please note that this point clearly gives an advantage to the leader, and with some probability – to the player who came in second. If we take the top five results, the leader's advantage will be even greater, and there will also be chances for bonus points for players who finish from 2nd to 4th place. And so on – endlessly. That is, taking N top places already implies an unfair attitude towards the other players. Moreover, they have less influence on it :) Of course, you can say “nothing prevents them from taking the top places,” but that would be stretching things...

Also, there is quite likely to be a persistent gap between the top three players, which makes it impossible to solve the problem in a general form. The probability is lower, but consider the recent BB tournament. Two players significantly outpaced the rest. It could have been three...

2 IronAxe

A small comment about your "lyrical digression."

I was considering a situation where, out of one hundred people, one player completed the map very quickly (pulled off a trick - the original source is here) – let’s say, in 10 days, the second took 1000 days, and all the remaining 98 people did even worse. This example is exaggerated just to illustrate the point. In this case, all 99 people, compared to the leader (who will have 100 points), will receive a rating from 0 to 1, which is incommensurate with the amount of effort they put into competing for the prize. Moreover, the map was indeed difficult – it's just that the first player turned out to be an “overwhelmingly” strong competitor compared to the others.

With you:

The situation is that suppose the player who finished in 1000 days turns out to be the leader. The rest are even worse. And in this case, nothing prevents them from getting a full rating. The leader will get 100 ranking points, everyone else will get the corresponding rating, depending on how close their result is to the leader's result.

You probably just didn't grasp the idea of my example. I certainly don’t think you intentionally distorted it... In your comments, you left out the first "fast" player from the analysis and considered all the others; accordingly, in this case, the essence of my example is lost.

Let's read further:

However, such a situation cannot be resolved by AmberSolera's formula either, so he did not actively promote this argument against my formula during the discussion.

This is incorrect on your part because the oscillator smooths out this imbalance by distributing additional points for the places taken. In the case of the oscillator, the leader will receive 100 points, the player in second place will receive 50 points, and the rest will evenly receive from 0 to 50 depending on the position they took. You shouldn't distort reality after all... :) And if my lack of activity tells you that your statements are correct, then you can demonstrate the opposite... :) But do we need to? Let's remain reasonable and, above all, listen to each other, rather than pay attention to emotions. For now, it seems to me that you simply don’t hear what exactly I am saying and have distorted my thoughts more than once.