How ratings work
Petteia uses the Elo system — the same one chess uses — with one change of our own.
Where everyone starts
Every new account begins on 1200. From there your rating moves after each rated game you play, and only after a rated game. There is nothing to opt into and nothing to claim.
The idea behind it
Before a game begins, the system works out how likely each player was to win, from the gap between the two ratings. Afterwards it compares what actually happened with what it expected.
Do better than expected and you gain points. Do worse and you lose them. How much you gain or lose depends entirely on how surprising the result was.
Beating someone rated far above you is a real surprise, so it pays a great deal. Beating someone far below you was expected all along, so it pays almost nothing.
Written out in full, where gap is the distance between the two ratings and score is what you actually got:
gap = their rating − your rating
expected = 1 / (1 + 10 ^ (gap / 400))
change = K × (score − expected)You score 1 for a win, 0.5 for a draw and 0 for a loss. Changes are rounded to whole points.
How quickly your rating moves
K is the multiplier in that second line. The larger it is, the harder your rating swings on a single result.
| Your situation | K |
|---|---|
| Your first fifteen rated games | 40 |
| Established, rated below 2000 | 20 |
| Established, rated 2000 or above | 10 |
New players move fast, so a rating finds its real level in an evening or two rather than grinding up from 1200 over months. Strong players move slowly, so one bad night cannot undo a number that took a long time to earn.
The one change we made
In pure Elo a strong player gains almost nothing for beating a weaker one. That quietly punishes them for accepting the game at all — and a game where nobody wants to play the newcomers is not much of a game.
So Petteia adds a small bonus. If the gap between the two ratings is more than 50 points and the higher-rated player wins or draws, they receive an extra gap ÷ 100 points, to a maximum of 4.
The bonus goes to the favourite only. The underdog's loss is never made worse by it.
What that looks like in practice
These are the numbers the game itself produces.
| The game | White | Black |
|---|---|---|
| Two newcomers, both on 1200 — White wins | +20 | −20 |
| Two newcomers, both on 1200 — a draw | 0 | 0 |
| 1500 beats 1300 | +7 | −5 |
| 1500 loses to 1300 | −15 | +15 |
| 1500 draws with 1300 | −3 | +5 |
| 1800 beats 1200 | +5 | −1 |
| 2100 beats 1900 | +4 | −5 |
| A newcomer on 1200, three games played, beats a veteran on 1600 | +36 | −18 |
Why a loss can cost more than a win pays
Look at the third and fourth rows. A 1500 who beats a 1300 gains seven points. The same 1500 losing to the same 1300 drops fifteen — more than twice as much for the result going the other way.
That lopsidedness is the engine of the whole system. It is what stops a strong player quietly farming weaker opponents: the reward is small and the risk is not.
The two numbers rarely match
You may notice that what the winner gains and what the loser drops are usually different amounts.
Each player's change is worked out using their own K, and two players often have different ones. In the 2100-against-1900 game the loser drops five while the winner gains only four, because the winner is above 2000 and therefore moves at half speed. In the last row a newcomer gains thirty-six while the veteran loses eighteen.
This is normal in Elo systems, and it is what allows a new player's rating to settle quickly. It does mean that the sum of every rating on the leaderboard drifts slowly upward over the years rather than staying fixed — a well-known property of the method, and one we have chosen to accept in exchange for new players finding their level fast.
Fast and slow are rated separately
Every account carries two ratings: one for fast games and one for slow ones. Which of them moves is decided by the game you played, not by anything you select.
Each keeps its own count of games, so you can still be finding your level at one time control while you are long settled at the other.
What does not affect your rating
- Casual games. The result is recorded and the game is kept in your history, but your rating is untouched and the game is left out of your statistics.
- Aborted games — those ended inside the first six half-moves, which is three moves each.
- Abandoned games — where the server restarted mid-game and neither player came back. Taking rating away from somebody for that would be worse than losing the game.
- Games against the computer, and anything played offline.
Resigning and losing on time are both rated in full. They are losses like any other.
Two people sharing one device
Pass-and-play uses exactly the same arithmetic, but those ratings live only in that device's memory. Both players start on 1200 and both reset when the app is reloaded. There is no account behind them.
That is the number you see on the player cards in an offline game, and it has nothing to do with your online rating.