You are rated 1500 and in round three you beat a 1700. Fifteen points. Draw with him instead and you still gain five, because nobody expected you to hold him; lose and you drop five, because losing to a 1700 is what a 1500 is supposed to do. Those three numbers come out of one small piece of arithmetic that Arpad Elo, a physics professor at Marquette University, worked out for the American federation in 1960. FIDE adopted it in 1970 and has used it ever since.
The expected score is the whole system
The only input is the difference between two ratings. Feed it in and you get the score the stronger player is expected to make:
- Level ratings: 50 per cent, half a point per game.
- 100 points apart: about 64 per cent.
- 200 apart: about 76 per cent.
- 400 apart: about 91 per cent.
Then one line of arithmetic. Your new rating is your old rating plus K times the difference between what you scored and what was expected. As a 1500 against a 1700 you were expected to score 0.24. You scored 1. The gap is 0.76, times a K of 20, which is 15 points.
It adds up across an event too. Enter a nine-round Swiss as a 1500 in a field averaging 1650 and the system expects you to score about three and a half. Score five and you gain roughly thirty points, whether that came from five wins or from nine draws.
K decides how fast the number moves
K is the speed limit. FIDE sets it at 40 for a player new to the list until they have played thirty rated games, and for anyone under 18 who is rated below 2300. It is 20 for most adults, and 10 once a player has been over 2400.
So a twelve-year-old improving fast has a rating that sprints after her, while a 2500 moves ten points a tournament and complains about it.
Four ratings that do not talk to each other
You probably have several. FIDE gives you a standard rating, and separate rapid and blitz ones. The big online platforms each run their own system on top of that, usually a Glicko variant that adds a confidence range around the number, with a separate rating for bullet, blitz, rapid and everything else.
None of these pools are calibrated against each other. A blitz 1800 on one site, a blitz 1800 on another and a FIDE 1800 are three different players. Only games inside a pool move that pool’s number, which is why your first FIDE rated event so often produces a number lower than the one you have been staring at online.
Puzzle ratings work the same way, except the puzzle has a rating too and wins points off you when you fail it. There is a longer piece on what a puzzle rating actually measures.
What the number will not tell you
It measures results, not talent, and it measures them slowly. Ten games is noise. It is also a closed system: points come from other players, so for every rating that goes up in a hall on Saturday, one goes down.
The habit I would build instead is to stop watching it between rounds and look at it twice a year. Play the games, fix the thing that keeps losing them, and the number follows. If you want a target instead of a hobby, the thresholds that mean something are the title ratings: 2200, 2300, 2400, 2500.