Where did you get that formula? It's not a common Elo formulation, nor is it what GR does, but the basic idea is right.

Elo's form is generally:

NewRating = OldRating + k * (actualOutcome - expectedOutcome)

where outcomes range from 0 - 1.

k - the maximum change that a game can give to your rating

actualOutcome - the outcome from a game scored in some way -webdip uses (pointsWon/potSize)

expectedOutcome - some way of predicting your outcome from the scores of the players.

I tried to understand this : http://tournaments.webdiplomacy.net/theghost-ratingslist
Having also in mind k = 34 (in fact it is 32 : http://tournaments.webdiplomacy.net/theghost-ratingslist/ghost-ratings-by-category)

I must not be far away because we can find a lot of players here who have 116 and 84 ELO after playing one game : https://docs.google.com/spreadsheets/d/1JtsweimE2JvRnY0ITgVESVuxQhpA9jcb9rptjX1VEaA/pubhtml

That means they lost or win 16 in one game.

1v1 Elo is not Ghost-Rating based, it's actually just a Chess Elo implementation with the starting value changed to 100 for seemingly no reason.

And do you think the formula is correct ?

Assuming player 1 wins :

New Elo 1 = Former Elo 1 + 32 * ( Former Elo 2 / (Former Elo 1 + Former Elo 2) )

K is not 32 in GhostRating. It's not a constant.

In Elo, there's a logistic curve for the expected outcome. This models the situation where it's much more likely that high rank players will beat low rank players better.

So no, your formula is not correct for Elo or for GhostRating.

For GhostRating, you need to use the variable k factor. I'm on mobile at the moment, but I think it's something like k=(sum of ratings in this game)/17.5.

For Elo (at least in the formulation most people mean when they say Elo- ie the one that chess uses), you need to change the expected outcome to the logistic curve. Details are on Wikipedia.

The changes to GhostRating change the behaviour so much that it's not really useful to think of it as an Elo variant (although that's how it is described on the site).

The most important difference is that players aren't punished more for losing to players ranked lower than them.

The second most important difference is that games with highly ranked players in them are worth more, regardless of your rating.

This makes GR more of a betting system than a rating system. Each time you play, you pony up a percentage of your rating points. If you win, you take points from other players, and if you lose, your percentage is lost.

Elo doesn't behave this way- in Elo the percentage you lose is scaled by your relative placement to your opponentents..

A while ago you mentioned implementing a Truskill-esque rating system. Is that still a thought in the works?

I don't work here any more. But I think it's still a good idea.

CptMike: As above, Elo is written:

NewRating = OldRating + k * (Outcome - ExpectedOutcome)

This is the expected outcome term in Chess Elo:

( 1/(1 + 10^((OldRating1 - OldRating2)/400 )) )

So the whole formula for Chess Elo is:

NewRating1 = OldRating1 + k * (Outcome - ( 1/(1 + 10^((OldRating1 - OldRating2)/400 )) ))

You're correct that the k factor is 32 for 1v1s. I'm not sure why this was chosen.

If we know player 1 wins, we can simplify it to:

NewRating1 = OldRating1 + 32 * (1 - ( 1/(1 + 10^((OldRating1 - OldRating2)/400 )) ))

For players at the same rating (ie, two new players), that's:

1/ (1 + 10^(0/400))

Or:

1/ (1 + 1) = 1/2 = 0.5

An expected outcome of 0.5 is a draw. This is the same result as your guess at the expected outcome term, but via different means.

It will produce different results if the two players don't have the same ratings.

Note that there's also an error in your formula. If you do k*ExpectedOutcome, you're calculating the change for the wrong player (in a two player game). You should instead do k * (Outcome - ExpectedOutcome). Of course, this doesn't make a difference when ExpectedOutcome is 0.5, but it will when you have players with different ratings.

Make sense?

Yes. It makes sense and it is very clear. Thank you for the explanation.