The Elo rating: how it actually works

Take two players with known ratings. The system does not ask who is better - it produces a number: the share of points the higher-rated player is expected to score in a long match.

A game is then compared with that prediction. If the result matches it, ratings barely move. If it contradicts it, the ratings move sharply. That is the whole mechanism, and everything else is detail.

The expectation depends only on the rating difference, not on the absolute numbers: 1200 against 1000 and 2400 against 2200 give the same prediction.

Two hundred points is the interval worth remembering: it means roughly three points out of four for the stronger player - noticeable but far from certain. Which is why upsets at that gap are routine rather than remarkable.

One formula, and it is simpler than its reputation:

The actual score is 1 for a win, 0.5 for a draw and 0 for a loss. The expected score comes from the table above. K is a coefficient described in the next section.

An example: you are rated 1600 and beat somebody rated 1800. The expectation for you was about 0.24, you scored 1, and the difference is 0.76. With K = 20 that is roughly +15 points - and the same 15 come off your opponent, because the system is zero-sum.

Which leads to a useful conclusion: a draw with a much stronger player gains you rating. The expectation was a loss, and half a point beats it.

K decides how strongly one game moves the number. It is not the same for everyone, and deliberately so: a new player's rating is a guess that needs correcting quickly, while an established player's is based on hundreds of games and should be stable.

• New players get a high K. The rating settles towards reality within a few events instead of crawling there over years.
• Established players get a lower one. A single bad tournament should not undo a decade.
• Top players get the lowest. At that level the numbers are already precise and heavily sampled.
• Younger players are often given a higher K, because their real strength genuinely changes faster than the rating can follow.

So a beginner swinging fifty points in one event and a master moving three are not inconsistencies - they are the same formula with different K.

You cannot compute a rating from nothing: the formula needs both players to have one. So the first is obtained differently.

• Play rated players. A first rating is earned in events counted by the rating body, against opponents who already have one.
• A minimum number of games is required. A handful of results is not enough to place somebody on a scale; the exact threshold depends on the rating body.
• There is usually a floor. Ratings are not published below a certain level, so an absolute beginner starts at the floor rather than at zero.
• The first number is unstable by design. With a high K it will move a lot before it means anything - that is the system working, not failing.

Practically: to get onto a national or international list you need events that report to it. A club evening does not produce an official rating, however well it is run - what club events do produce.

Classical, rapid and blitz are rated separately, and the numbers routinely differ by a couple of hundred points for the same person.

• They measure different skills. Calculation over half an hour and pattern recognition in three seconds are not the same ability.
• They do not convert. There is no formula translating a blitz rating into a classical one, and anyone offering you one is guessing.
• Titles are based on classical. Which is why blitz ratings, however high, do not earn norms - about titles.
• Online platforms add more scales. A platform rating is a fourth kind of number and is not comparable with any of these - why online ratings differ.

Three things get confused constantly, and separating them clears up most questions.

For an amateur club the practical answer is usually an internal rating: it gives players visible progress without anybody having to register events with a federation - and visible progress is what keeps people coming back - about retention.