Elo Rating
A rating is not a score and not a reward. It is a prediction: the number says how often you should beat somebody with a different number, and every game you play is a test of that prediction.
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A rating is not a score you accumulate. It is a prediction, and the prediction is about you against somebody else.
Two players, two numbers, and the gap between them says how often the higher one should win. Play the game, compare the result with the prediction, and adjust both numbers by the difference. That is the whole system.
What the gap predicts
The formula is one line. Your expected score against an opponent whose rating
differs from yours by d points is
E = 1 / (1 + 10^(d / 400))
where d is their rating minus yours. Nothing about it is arbitrary: every 400
points is defined to be a factor of ten in the odds.
| you are behind by | your expected score |
|---|---|
| 0 | 50% |
| 50 | 43% |
| 100 | 36% |
| 200 | 24% |
| 400 | 9% |
| 800 | 1% |
Say you are 1500 and you play someone rated 1700. The gap is 200, so you are expected to score 0.24 - which counts a draw as a half. Beat them and you scored 1 where 0.24 was expected, so with a K-factor of 20 your rating moves by 20 × (1 − 0.24) ≈ +15. Draw and you scored 0.5 against an expected 0.24, so you still gain 20 × (0.5 − 0.24) ≈ +5.
That is the part people find strange and it is the point of the system: a draw against a stronger player is a good result, and the number says so.
What the number is measuring
Not memory, and not calculation depth. At every level below master, the thing that moves a rating is whether you see what is on the board right now.
White to move. Tap the black piece you can simply take.
Now the same skill with two of them at once, which is the version that actually comes up. A piece that is attacked and undefended is called en prise, and counting them is the single most rating-correlated habit there is.
Two black pieces are attacked and defended by nothing. Tap both.
The ladder
Ratings from different places are on different scales, so these bands are a rough map rather than a conversion table.
| rating | what it usually means |
|---|---|
| under 800 | knows the moves; hangs pieces most games |
| 800-1200 | sees one-move threats; loses to forks and back-rank mates |
| 1200-1600 | counts material reliably, has an opening, misses two-move tactics |
| 1600-2000 | strong club player; plans, and punishes a hanging piece every time |
| 2000-2200 | expert / candidate master |
| 2200-2400 | national master, then FIDE master |
| 2400-2500 | international master, with norms |
| 2500+ | grandmaster territory, again only with norms |
The titles need more than the number: three norms - performances at title level in tournaments with foreign opposition - as well as the rating. That is what makes a title permanent while a rating goes up and down.
Things worth knowing about the number
- Only the gap is meaningful. 1200 on one website and 1200 on another are two different measurements of two different populations.
- Rating floors and inflation are real. Comparing today's 2700 with a 2700 from 1985 compares two different scales, not two players.
- The K-factor is a dial, not a rule. Bigger K means your rating chases your results; smaller K means it trusts its own history.
- Provisional ratings move wildly, and that is intentional: the system is finding your level, not judging you yet.
- Rapid, blitz and bullet are separate ratings for the same reason a sprinter and a marathon runner are timed separately.
Try it
White to move. Take the free queen.
Common questions
- What is Elo in chess?
- A rating system, named after the physicist Arpad Elo, in which your number predicts your results against other numbers. If you score better than the prediction your rating goes up, and if you score worse it goes down - by an amount that depends on how surprising the result was, not on how many games you played.
- What does an Elo rating actually mean?
- Only the difference between two ratings means anything. A 200-point gap predicts about 76 per cent for the higher-rated player; 400 points predicts about 91 per cent. The absolute number is just a position on that scale, which is why ratings from two different sites are not directly comparable.
- What is a good chess rating?
- The FIDE list starts at 1400 and the median rated tournament player is somewhere around 1600-1700. Online ratings sit on different scales entirely, and a club player with a 1500 FIDE rating is a considerably stronger player than the average person who has ever moved a piece.
- What is the K-factor?
- How much a single game can move your rating. A high K (say 40, used for new and junior players) lets the number find its level quickly; a low K (10, for established masters) keeps it stable. It is the dial between reacting fast and being noisy.
- What ratings do the chess titles need?
- Grandmaster requires a FIDE rating of 2500 at some point plus three norms - tournament performances at that level; International Master needs 2400 and three IM norms. On the standard route the rating alone is not enough - the norms are what make a title an achievement rather than a number - though FIDE also awards some titles directly for results such as winning qualifying championships.
- Is Elo still used?
- FIDE still uses Elo. Most online sites use Glicko or a variant of it, which adds a confidence figure alongside the rating - so a player who has not played for a year is treated as less certain and moves faster when they come back. The idea underneath is Elo's.
