Rating system for online games in Heroes of Might and Magic IV.

Actually, the caret symbol (^) is generally used to denote the exponent to which a number is raised, i.e., X^3 = X * X * X.

VBN! Just take a look at the formula; someone should be able to figure it out. You might be right; we should ask a mathematician.

Added 1 minute ago

Yes, I received all the emails, just in several stages... :) I'll start looking into what Iron is proposing on Monday...

I didn't come up with this. I borrowed it from the Planetfall community. It worked for them about 10 years ago, and it probably still works now.

Added 3 minutes ago

Also, the letter N there means the number of players who finished the game. How is that? Or does it mean the number of players who participated in the tournament?

In my opinion, it means the number of players who participated. There can be from 2 to 11 players in a game. A losing player is also considered to have finished the game, even if they quit. The other players continue to play, and sometimes they have to break through his planet's defenses, even though the player has already lost.