Player rating for tournaments across all installments of Heroes.

1. As I understand it, this coefficient depends on the ratings of the tournament participants. Moreover, its value depends not only on the rating of the leading players, but also on the players whose ratings are not included in the numerator of the coefficient.

But look at the situation from the perspective of the average player – in which tournament will it be easier for him to take a certain place? In a tournament with more strong players or one with fewer? And so on – for each player. It is more difficult to take ANY place by competing with strong players than to take the same place by competing with weak players... therefore, the tournament rank should be taken into account...

...in the end, we will get a coefficient that is smaller in the first case than in the second, even though there were more strong participants in the first tournament...

The absolute strength of the players is not important, but the relative strength is! Let's say that if only mega-dinosaurs, the strongest players, participate in one tournament, then the tournament coefficient is equal to 1. In the second tournament, only beginners participate. The coefficient will also be close to 1. Because everyone is equal, and no one is competing with a stronger player, and in both cases, everyone has equal chances of winning.

Now let's combine the two groups. Beginners have much less chance, and the higher they get in this situation, the more significant their result will be. Do you understand? So, in reality, we always have a combined scenario – there is always a difference in strength, and it is rare when there are several equal players... Moreover, almost every player has opponents who are much stronger than him... The higher the average strength of the opponents, the more difficult it is to succeed in the tournament... This is what the coefficient reflects – the reward for achieving it :)

This is just an idea. It can and should be adjusted as we go. I'm all for it! The main thing is that the balance is as realistically as possible, close to the golden mean, taking into account all interests. As an option, instead of adding a multiplier, we can add a summand. That is, add a single bonus to the rating that is the same for everyone (and not multiply), but the bonus will depend on the tournament rank. And for the winner, the significance of the bonus in the total of his points will be significantly less than for the underdog – which is also correct. The winner had almost no competition compared to the others... Or make the multiplier non-linear... :) In essence, if you don't go into the details, it seems like it's a lot of complications on top of complications... But in reality, the machine will calculate everything. Our job is to develop a methodology... And I think this will be the right approach, so let's keep it in mind...

2. A player who has "fallen short" may have just joined HeroesWorld and have a rating of 0. Then this coefficient will not take such a player into account as you would like.

At the start of the rating, there will be discrepancies. Over time, when there are enough players with a formed rating, such a player will not have a significant impact on the coefficient in total...

Then this coefficient will not take such a player into account as you would like.

The coefficient will never take all factors into account. Our goal is to reduce the unaccounted moments as much as possible.