How do chess ratings work? Elo, Glicko and your club rating

A chess rating isn’t a measure of talent, and it isn’t a score you add to. It’s a prediction: given two players’ ratings, how is a game between them likely to go? Every rating system in chess does the same three things:

1. 1

   Predict. Before a game, the ratings say how much each player is expected to score.

2. 2

   Compare. After the game, the system compares what happened with what it predicted.

3. 3

   Adjust. Both ratings move by how surprised the system was. No surprise, small change. Big upset, big change.

That’s why the number on its own means less than you’d think. What matters is the difference between two ratings, and it only means something between players in the same pool: people who play each other, or play people who play each other.

The system most of chess grew up with is named after Arpad Elo, a physics professor and chess player whose method was adopted by the US Chess Federation in 1960 and by FIDE, the international chess federation, in 1970. Its central idea is the expected score: what a player should score against an opponent, where a win counts 1, a draw ½ and a loss 0.

The expected score depends only on the rating gap. Equal ratings: 50% each. Rated 200 points higher: about 76%, or roughly three points out of four. Rated 400 higher: about 91%. The curve is steep in the middle and flat at the ends, which is why nobody is ever guaranteed a win, however big the gap.

For the curious, here’s the formula, for a player rated R against an opponent rated R_opp:

E = 1 / (1 + 10^((R_opp − R) / 400))

The 400 sets the scale: it’s why ratings run in the hundreds and thousands rather than single digits.

After a game, Elo moves your rating by the difference between what you scored and what you were expected to score, multiplied by a number called K:

new rating = old rating + K × (score − expected score)

Say you’re rated 1500 and you play someone rated 1700. You’re expected to score about 0.24. With a K of 20:

Beating a stronger player is worth a lot; losing to one costs a little. Losing to a weaker player costs a lot. And whatever one player gains, the other loses, when both use the same K.

K sets how fast ratings move. FIDE uses 40 for newcomers and most juniors, 20 for most players, and 10 for players who have reached 2400. A bigger K reacts faster; a smaller one is steadier.

Elo has a blind spot: it’s equally sure about everyone. A player with three games gets the same treatment as a player with three thousand. In the 1990s, the statistician Mark Glickman fixed that with the Glicko system, and a few years later with Glicko-2.

Glicko gives every player a second number, the rating deviation (RD): how uncertain the system is about your rating. Your real strength is very probably within about two RDs of your rating either way. A brand-new player might be 1500 with an RD of 350, meaning “somewhere between about 800 and 2200. We have no idea yet.”

• RD shrinks as you play. Every game tells the system more, so the range narrows.
• RD grows when you don’t. Take a long break and the system becomes less sure of you again.
• Uncertain ratings move fast; settled ones move slowly. Your first games swing your rating around, and that’s the system learning, not you getting worse.
• Uncertain opponents count for less. Beating someone the system knows little about tells it less than beating someone it knows well.

Glicko-2 adds a third number, volatility: how erratic your results are. A player who is improving fast, or having a very odd month, gets a rating that’s allowed to move more.

Because early ratings are guesses, most systems mark them as provisional until there are enough games behind them. Lichess shows a question mark next to a rating it isn’t sure of yet. US Chess marks ratings based on only a few games as provisional. FIDE doesn’t publish a first rating at all until you’ve played enough rated games against rated opponents.

Castle Gambit’s social rating goes a step further: for your first five games you don’t see a number at all, only tally marks. After the fifth you get a number with a question mark (like “1489?”), and the question mark goes once the system is sure enough.

Notice how much the number jumps early on (1500, then 1302, then 1501) while the range is wide, and how calm it gets by the end. That’s exactly why it’s hidden at first: an early number mostly measures luck.

The big rating pools, and the systems behind them:

The details inside each (starting numbers, floors, K-factors, how they handle new players) differ, and they change from time to time. The idea underneath is always the same: predict, compare, adjust.

It’s the most common question at any club: “I’m 1600 online, what am I over the board?” The honest answer is that there’s no conversion, because a rating only means something inside its own pool, and the pools are different in every way that matters:

• Different people. Who plays online and who plays at a club overlap, but they aren’t the same crowd.
• Different time controls. Most online games are much faster than club games, and blitz skill and slow-chess skill aren’t the same thing.
• Different starting points and rules. Each site and federation starts new players somewhere different and moves ratings at a different speed.
• A different game, a little. A real board, a real clock and a real person across the table change how people play.

So your online rating is useful as a rough starting point and nothing more. That’s how Castle Gambit uses it: link a chess.com or Lichess account and your social rating starts near it, with plenty of uncertainty, so your first real games correct it quickly.

It depends entirely on the pool, which is an unsatisfying answer and the true one. The average rating on any list depends on who’s on it and how that system starts people off, so a number that’s strong in one pool can be ordinary in another.

The top end does have landmarks. FIDE’s titles need a rating to go with them: FIDE Master needs 2300, International Master 2400, and Grandmaster 2500, the last two along with strong results called norms.

For the rest of us, the useful comparison isn’t anybody else’s number. It’s yours, a few months ago. A rating that’s slowly climbing means you’re getting better, which was the point all along.

Castle Gambit keeps its own rating (we call it a social Elo; the app just says “rating”) for the games most club players play most of the time: casual games across a real board. It’s separate from FIDE, US Chess, chess.com and Lichess, and it measures one thing: how you play.

• Glicko-2, one game at a time, applied when a result is confirmed: both players reported the same result, or the organizer settled it.
• Only games played in person at Castles (chess clubs). No online games.
• Hidden for your first five games, which show as tally marks. Then a number with a question mark, until it settles.
• A starting point, if you want one: your chess.com or Lichess rating, or a level you choose, so your first pairings aren’t a shot in the dark.
• Private by default. Only people who share a Castle with you can see it, unless you make it public or keep it to yourself.
• Never on show. No ratings in the lobby, on the club TV, or next to your name when you’re paired. Nobody sizes you up before you sit down.
• Fair to the room. The same two people’s fourth game within twelve hours still gets played, but doesn’t count, so a rating can’t be farmed. And if a result is corrected, every rating it touched is worked out again as if it had been right all along.