What is the Elo rating system?
Elo is a way to rate players from their results against each other. Each player has one number. The gap between two numbers predicts how a game between them should go, and after each game the numbers move toward what actually happened.
Where it came from
Arpad Elo was a physics professor at Marquette University and a master-level chess player. In the 1950s US chess used the Harkness system, which Elo found arbitrary, so he designed a more statistical one. The US Chess Federation adopted it in 1960, and FIDE, the world chess federation, followed in 1970.[1] In the preface to his 1978 book, Elo wrote that the system was "applicable to any type of competitive activity in which individuals or teams engage in pairwise competition".[2] FIDE notes that it has since been used in football, baseball, basketball and other sports.[3]
How Elo works in three steps
- Predict. Turn the rating gap into an expected score: E = 1 / (1 + 10^(−gap / 400)). This is the curve US Chess publishes as its "standard winning expectancy".[4]
- Compare. Score the game as 1 for a win, 0.5 for a draw and 0 for a loss, then take actual − expected.
- Adjust. Multiply that difference by K, the "development coefficient" in FIDE's rules, and add it to the rating.[5] A bigger K means faster changes.
Try it in the Elo calculator.
What a rating gap means
| Gap | Favourite's expected score |
|---|---|
| 0 | 50.0% |
| 100 | 64.0% |
| 200 | 76.0% |
| 300 | 84.9% |
| 400 | 90.9% |
These numbers come straight from the formula. FIDE describes a 200-point edge as "about 75% of the points".[3] Expected score counts draws as half points, so it isn't the same as a chance of winning outright. The full table goes up to 800.
Why a draw can cost the favourite points
If an 1800 player draws with a 1600 player (K = 20), the 1800 player was expected to score 0.76 but scored 0.50. They lose 5.2 points and the 1600 player gains the same amount. A draw is only "neutral" between equally rated players.
Things Elo does and doesn't do
- Ratings are relative. A number only means something compared with other players in the same pool. Lichess's FAQ warns that ratings from different organisations can't be compared.[7] See Chess.com vs Lichess vs FIDE.
- It's zero-sum when K is equal. Points move from one player to the other. Different K values, like FIDE's 40/20/10, break this on purpose.
- It has no measure of certainty. A player with 5 games and one with 5,000 games are treated the same unless K is changed by hand. Glicko and TrueSkill add an uncertainty term to fix this.[6] See Elo vs Glicko-2 vs TrueSkill.
- It's one-on-one. Elo was built for two sides. Teams can be rated as single units, but splitting credit between individual teammates needs a model like TrueSkill.[6]
- It ignores margin. A narrow win and a blowout count the same unless you add a margin-of-victory multiplier, as some sports models do. See Elo in sports.
Sources
- Arpad Elo (inductee biography) — World Chess Hall of Fame
- Elo, A. E. (1978). The Rating of Chessplayers, Past and Present (2nd ed.), Preface to the First Edition. New York: Arco. — Book
- Anniversary of Arpad Elo – rating system that changed chess world — FIDE
- Glickman, M. E. & Doan, T. The US Chess Rating System (specification dated 2026-04-06), sections 3 and 4.2 — US Chess Federation
- FIDE Rating Regulations, effective 1 March 2024 (with the 400-point rule as amended from 1 October 2025), sections 7–8 — FIDE Handbook
- Herbrich, R., Minka, T. & Graepel, T. (2006). TrueSkill™: A Bayesian Skill Rating System. Advances in Neural Information Processing Systems 19 — Microsoft Research
- Frequently Asked Questions: Lichess ratings — Lichess