http://www.glicko.net/glicko/glicko2.pdfEvery player in the Glicko-2 system has a rating, r, a rating deviation, RD, and a rating volatility σ. The volatility measure indicates the degree of expected fluctuation in a player’s rating. The volatility measure is high when a player has erratic performances (e.g., when the player has had exceptionally strong results after a period of stability), and the volatility measure is low when the player performs at a consistent level. As with the original Glicko system, it is usually informative to summarize a player’s strength in the form of an interval (rather than merely report a rating). One way to do this is to report a 95% confidence interval. The lowest value in the interval is the player’s rating minus twice the RD, and the highest value is the player’s rating plus twice the RD. So, for example, if a player’s rating is 1850 and the RD is 50, the interval would go from 1750 to 1950. We would then say that we’re 95% confident that the player’s actual strength is between 1750 and 1950. When a player has a low RD, the interval would be narrow, so that we would be 95% confident about a player’s strength being in a small interval of values. The volatility measure does not appear in the calculation of this interval.
Formulas:
To apply the rating algorithm, we treat a collection of games within a “rating period” to have occurred simultaneously. Players would have ratings, RD’s, and volatilities at the beginning of the rating period, game outcomes would be observed, and then updated ratings, RD’s and volatilities would be computed at the end of the rating period (which would then be used as the pre-period information for the subsequent rating period). The Glicko-2 system works best when the number of games in a rating period is moderate to large, say an average of at least 10-15 games per player in a rating period. The length of time for a rating period is at the discretion of the administrator.
Steps (numbering based upon Glickman's PDF):
1. Determine a rating µ and RD φ for each player at the onset of the rating period.
3. Compute the quantity v. This is the estimated variance of the team’s/player’s rating based only on game outcomes.
4. Compute the quantity ∆, the estimated improvement in rating by comparing the pre-period rating to the performance rating based only on game outcomes.
5. Determine the new value, σ', of the volatility. See Glickman's PDF for details.
6. Update the rating deviation to the new pre-rating period value, φ* = sqrt(square(φ) + square(σ')).
7. Update the rating and RD to the new values, µ' and φ':
φ' = 1 / sqrt(1 / square(φ*) + 1 / v)
µ' = µ + square(φ') + sum(result - expected)
What that means in terms of RD/volatility:
* RD decrease (7) is based upon estimated variance (3) based upon opponent rating and RD. See Glickman's PDF for details. Playing against top-10 players produces a low variance (you're expected to lose every game); playing against newbies produces a high variance (no expectation).
* Volatility (5) determines at the end of a rating period (6) how much your RD increases. Volatility is exactly what it sounds like (a player whose results are essentially random as compared to expected variance is volatile; a player whose results are predictable as compared to expected variance is not volatile). Lichess doesn't have rating periods but does gradually increase RD values over time (as for volatility, we'd have to look closely at source code... but even supposing volatility is held constant, then you get Glicko-1 which gradually increases RD values over time).
In simplest terms:
* Getting a low RD is easy if you are human (your results aren't random) and you don't win (or lose) almost all your games, and you aren't trying to game the rating system.
