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Chess guide

How chess ratings work: the Elo system explained

A chess rating is a single number that estimates how strong a player is. Almost every chess organization and website uses a version of the Elo system, invented by the Hungarian-American physics professor Arpad Elo and adopted by the World Chess Federation (FIDE) in 1970. Here is how it works, in plain words and with real numbers.

The idea: expected score

The Elo system does not reward wins as such. It compares what happened with what was expected to happen. Before each game, the difference between the two ratings gives each player an expected score between 0 and 1:

Expected score = 1 / (1 + 10(opponent − you) / 400)

Two players with the same rating each expect 0.5, half a point. A player rated 400 points higher is expected to score about 0.91, so they should win roughly nine games out of ten. After the game, your actual score (1 for a win, 0.5 for a draw, 0 for a loss) is compared with your expected score.

The update: K-factor

New rating = old rating + K × (actual score − expected score)

The K-factor decides how fast ratings move. New players get a large K, so their rating finds its true level quickly; established players get a smaller K, so one bad day doesn't change much. Pawnly uses the FIDE values: K = 40 for your first 30 rated games, 20 after that, and 10 once you reach 2400. To keep things fair, a single game can never move a Pawnly rating by more than 40 points.

Worked examples

These are exactly the changes Pawnly applies after an online game:

Notice that beating a stronger player earns more than beating an equal one, and losing to a stronger player costs less. Draws against stronger players gain points too. Over many games, the system pulls every rating toward the level where you win as often as you lose.

What do the numbers mean?

Ratings are only comparable inside the same pool of players: a 1500 on one website is not the same as a 1500 on another, or a 1500 in official FIDE tournaments. As a rough guide for over-the-board chess:

Ratings on Pawnly

Every player starts at 1200. Online games against a friend or a random opponent are rated with the formula above. If you sign in with Google, your rating is saved and you can appear in the Top players table, which shows only the first four letters of each name. Guests get a rating for their visit only; nothing about them is stored. To keep the table honest, only one rated game per minute counts.

Games against the computer are not rated, but each level is tuned to play at about a given strength, so you can measure yourself against it:

The named computer players in the rankings (tagged "Computer") use the level closest to their rating.

How to raise your rating

  1. Stop losing pieces. Below 1400, most games are decided by hanging pieces. Before every move, check your opponent's checks, captures and threats.
  2. Learn the basic tactics and mates. Read our tactics and checkmate patterns guides and look for them in every game.
  3. Play slower games. Longer time controls give you time to think and to learn from your mistakes.
  4. Review your losses. Find the move where the game turned. It is usually one tactic you missed, not a deep strategic error.
  5. Climb the levels. When you beat a computer level more often than you lose, move up one level.
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