How does lichess update rating and RD after each game

[LukoTab]

Hi,
I am working on a rating system for my own game and I found out that Lichess uses a modification of Glicko 2, which is weird, because Glicko is supposed to be evaluated only after a given rating period, not after each game, like Lichess does. I would like to understand, how does Lichess achieve this, so I can then implement something similar to my game.

I am not familiar with scala, but from from browsing through this repository, I found the directory lila/modules/rating and I just don't see, how does it update stats after each game. There still seems to be some sort of rating period (there is a variable for it) and the function calculateNewRating takes as an input an array of results, not only one result.

Would someone please explain to me, how does Lichess achieve a new rating and RD after each game with glicko-2?

[niklasf]

Lichess assumes that a rating period is a fixed time interval. For integer rating periods we want to exactly match the Glicko-2 paper. In particular, from step 6 we get:

phi(n+1) = sqrt(phi(n)^2 + sigma^2)

Now Lichess just smoothly extends this to fractional rating periods by solving that recurrence relation, resulting in:

phi(elapsedRatingPeriods) = sqrt(phi(0)^2 + elapsedRatingPeriods * sigma^2)

This is implemented here:

lila/modules/rating/src/main/glicko2/RatingCalculator.scala

Lines 205 to 206 in 7e7d7cc

	private def calculateNewRD(phi: Double, sigma: Double, elapsedRatingPeriods: Double) =
	Math.sqrt(Math.pow(phi, 2) + elapsedRatingPeriods * Math.pow(sigma, 2))