Math of Elo points

Smarmellatore

Hi everyone! after a lot of games i really don't understand the elo count. The only thing i've found is the thing about the "k" factor and number of games played, but isn't a real calculation... someone can explain me how this numbers are made or where i can find the exact formula construction? Can someone explain me also what exactly happend when a player drop (point for the dropper and point for the rest of the players)?
TnX :D

zuli

You can find more info here.
If you need more help let us know

Smarmellatore

oh tnx! :)

ok i've read that page and the elo wiki page, sorry but i've got others questions... :D

in more than 2 players game, the system make every combination of comparison by every couple of players? and then how this comparisons are aggregated? Can you write me down the complete formula that occurs when the game end? or there's a way to find it in the data files?
If someone else dropped during the game, you will win against the dropped player, but the matches against the other opponents are not considered for the elo.

So if you are the only dropper you lost more elo, but if another player drop after you, you can be able to cushion the negative score for that game? i've seen top players (more than 400 elo, and more than 40 games) drop voluntarily a game against low elo players with only the pass move remaining, like some sort of strategy. It is possible?

Talking with some friends we have the impression that for a new player that can't reach over 200-250 elo before his 40th game is impossibile to reach 200 after also playing and winning against players with more elo than him, theoretical the best thing he can do is to open a new account and try to clambing again, but its very sad, it's the opposite of the porpuse that the K factor want to be. GP is a game where 40 games isn't a real big number to learn every possible interaction and variability, and when you are "on the road" a 3rd place can burst 2 or 3 better games that you have hardly play.

Sorry for my english, i hope to have explained that text wall well :D

Smarmellatore

Ps: its not better a k factor based on the actual elo points of the player?
Ex. :
If you are between 100 and 200 elo you have a k of 60
If you are between 200 and 300 elo you have a k of 40
If you are between 300 and 400 elo you have a k of 20

zuli

The formulas are:

prob = 1.0 / (1.0 + Math.pow(10, ((opponent.elo - player.elo) / 400)))
deltaElo =  k * 3 / (numPlayers + 1) * (wlt - prob)

The player's winning probability against the opponent is prob.
wlt states for win - lose- tie. Can be 1 - 0 - 0.5

For each player we calculate the deltaElo against each opponent.
If the player and the opponent both dropped, the deltaElo is 0.
If the player dropped, his wlt is 0, regardless of the score. Therefore the player loses k * 3 / (numPlayers + 1) * ( - prob) Elo points.
If the opponent dropped, the wlt is 1, regardless of the score. Therefore the player gets k * 3 / (numPlayers + 1) * ( 1 - prob) Elo points.
If the game is a dropped game (i.e. someone else dropped), the deltaElo is 0.
In the other cases we calculate the wlt base on the scores, and the we get the deltaElo.

Back to your questions.

You are right. If you are not the only one that dropped, you save some Elo. That's why we introduced the ability to cancel a game. If someone dropped and the other players don't want to finish the game, they can cancel that game. In this situation only the dropped player will lose the Elo.
Anyways, dropping is not an option to save your Elo.
Let's say you have Elo 200, and your opponent has Elo 400. In a 1vs1, after your 20th match, you are getting 15 Elo points if you win. So, it's difficult to go up, but in the long term you will reach your Elo.

I hope this helps!