How a chess rating works, and what actually moves it
Why one win is worth 175 points and another is worth 7, what rating deviation is, and how many games it really takes before a number means anything.
A rating is a prediction, not a score
The one thing to get straight before anything else: a rating is not points you accumulate for playing. It is a single number chosen so that the gap between two of them predicts the result. That is the whole idea, and everything else is arithmetic in service of it.
| Opponent is | You score |
|---|---|
| 400 below | 90.6% |
| 200 below | 75.6% |
| 100 below | 63.8% |
| 50 below | 57.0% |
| level | 50.0% |
| 50 above | 43.0% |
| 100 above | 36.2% |
| 200 above | 24.4% |
| 400 above | 9.4% |
| 600 above | 3.3% |
Read the middle row and the rest follows. Two equal players score 50%. Somebody 200 points above you is expected to take about 76% of the points off you, which is why beating them is worth more than beating an equal, and why losing to them costs almost nothing.
What Elo cannot do, and why this uses Glicko-2
Elo has one dial, K, which decides how far a result moves you. The problem is that K does not know anything about you. A player who signed up an hour ago and a player with four hundred games move by the same amount from the same result, even though one of those two numbers is a guess and the other is not. The consequence is familiar to anybody who has started an account: dozens of games before the number means anything at all.
Glicko-2, which is what runs here, carries three numbers instead of one:
- The rating. The number you see.
- Rating deviation, or RD. How unsure the system is about that number, in the same units. Roughly: your real strength is probably within two RDs of your rating. It starts at 350 and can fall as low as 30.
- Volatility. How erratic your results have been. A player whose results are all over the place gets a rating that is allowed to move faster, because the swings are evidence that something really is changing.
RD is the one that changes how the site feels. It is why a new account converges in a handful of games, and it is why beating somebody whose own rating is a guess is worth less than beating somebody whose rating is established.
The same result, worth eight different amounts
| The game | Your RD before | Result | Change | New RD |
|---|---|---|---|---|
| New account beats an equal, settled opponent | 350 | win | +175 | 248.83 |
| New account loses to an equal, settled opponent | 350 | loss | -175 | 248.83 |
| Settled player beats an equal | 60 | win | +10 | 60.02 |
| Settled player loses to an equal | 60 | loss | -10 | 60.02 |
| Settled player draws an equal | 60 | draw | 0 | 60.02 |
| Settled player beats one 200 above | 60 | win | +16 | 60.24 |
| Settled player loses to one 200 below | 60 | loss | -16 | 60.24 |
| Settled player beats an unproven opponent | 60 | win | +7 | 60.48 |
Four things worth reading off that table. A brand new account moves +175 points on its first game and a settled one moves +10, from the identical result — that is RD doing its job, not a bonus. A draw between equals is worth nothing to either side, which is correct: it is exactly what was predicted. Beating somebody 200 above you is worth +16 against +10 for beating an equal. And beating an opponent whose rating is itself unproven is worth +7, less than beating a settled equal, because you have learned less by doing it.
How many games until your rating means anything
| Games | RD | Still provisional |
|---|---|---|
| 1 | 248.8 | yes |
| 2 | 211.1 | yes |
| 3 | 181.5 | yes |
| 5 | 148 | yes |
| 8 | 120.9 | yes |
| 12 | 101.3 | no |
| 20 | 82 | no |
| 30 | 71.3 | no |
The shape is the answer. Most of the uncertainty is gone after five games, the rating stops being provisional at about 12 games, and everything after that is slow polishing. This is the practical difference between Glicko-2 and Elo, and it is the reason you are not asked to grind thirty games before the site is willing to tell you a number.
Why your rating drifts while you are not playing
It does not, quite. The rating stays where it is; the certainty rots. Somebody who last played nine months ago might have got much better or given up entirely, and treating their old number as reliable would mean everyone who beats them is under-rewarded.
| Away for | RD from 60 | RD from 110 |
|---|---|---|
| 1 day | 60.9 | 110.5 |
| 7 days | 66 | 113.4 |
| 30 days | 82.8 | 123.9 |
| 90 days | 115.7 | 147.9 |
| a year | 208 | 227.5 |
So the first game back moves you further than usual, in either direction. That is not a penalty for being away. It is the system admitting it no longer knows, and asking.
Two ratings, and why they are separate
Reflex Chess carries two ratings and not one, because a fast pattern-recogniser and a good blitz player are not the same person and one number would make each ladder noisy with the other's results. Both use everything above; they simply never see each other's results.
- Puzzle rating vs game ratingThe full argument, and why yours are probably far apart
- Estimate your rating in twelve puzzlesAdaptive, free, no account, gives you a range not a number
- The leaderboardTop 100 on each of the two boards
What is the difference between Glicko and Elo?
Elo moves every player by the same amount for the same result. Glicko carries a second number, the rating deviation, which says how sure it is about you, and moves an unproven player much further than a settled one. Glicko-2 adds a third, volatility, which lets a player whose results have been erratic move faster still.
What does RD mean in a chess rating?
Rating deviation: how uncertain the rating is, in rating points. It starts at 350 for a new account and falls as you play. Your true strength is probably within about two RDs of your displayed rating, so a rating of 1500 with an RD of 50 says a good deal more than the same 1500 with an RD of 300.
Why did I gain fewer points than I lost?
Because the two results were not equally surprising. Beating somebody level with you is worth +10; losing to somebody 200 points below you costs -16, because that result was much less likely and therefore says more.
Why is my rating provisional?
Because its deviation is still above 110. That is the system saying it does not yet trust its own estimate. Playing is what fixes it: the deviation is down to about 148 after five games.
Does everyone start at 1500?
Here, yes, with the widest possible deviation. The starting number matters much less than it looks, because the first few results move it in large steps rather than small ones.