What Is Elo Rating?

Elo is a way of ranking people by who they beat, not by how often they win. Beat someone stronger than you and you gain a lot. Beat someone weaker and you gain very little. Lose to someone weaker and it costs you more than losing to someone stronger.

That one idea is the whole system. Everything below is detail.

Where it came from

The system is named after Arpad Elo, a physics professor and competitive chess player who built it in the 1960s to replace the US Chess Federation's older ranking method. FIDE, the international chess federation, adopted it in 1970.

It spread well past chess because the problem it solves is not specific to chess. Any time people compete head to head and you want to know who is actually best, counting wins gives you the wrong answer — it tells you who plays the most.

How the maths works

Every player starts on the same rating. Here that number is 1200; chess federations often use 1500. The number means nothing on its own. Only the gap between two ratings matters.

Before a match, the two ratings are compared to produce an expected score — the share of the result the stronger player should take on form. A player rated 200 points above their opponent is expected to win roughly three times in four.

Afterwards, each rating moves by the difference between what the player actually scored and what they were expected to score:

• Win when you were expected to win, and you gain very little. You did what the ratings predicted.
• Win when you were expected to lose, and you gain a lot. The ratings were wrong about you, and they correct hard.
• A draw moves both ratings slightly toward each other.

How far any of this moves the numbers is set by the K-factor. A high K makes ratings swing quickly and track recent form. A low K makes them stable and slow to shift. It is the one genuinely subjective dial in the system.

Because every point one player gains is a point the other loses, the total never inflates. Ratings drift toward the truth on their own, with nobody adjusting anything by hand.

Why it suits a casual group

The usual alternative is a win tally on a whiteboard, and a win tally has one specific failure: the person who turns up every week out-scores the person who turns up occasionally, regardless of how well either plays. In a group where attendance is uneven — which is every casual group — that makes the leaderboard a record of availability.

Elo does not care how often you play. It cares who you played. Someone who shows up four times a year and beats the best players will out-rank someone who shows up weekly and beats beginners. That is almost always the answer people actually wanted.

Where raw Elo stops short

Classic Elo assumes two players, one match, one winner. Real groups are messier:

• More than two sides. A six-way board game has one winner and five people who lost by varying amounts, which the original formula has nothing to say about.
• Teams. If four people win together, who gained the rating?
• Ties for a place. Common in trivia and party games, rare in chess.

These are solvable, but they have to be solved deliberately rather than assumed. Custom Elo Games scores a result of up to ten sides by breaking it into every head-to-head pair inside it and running each pair through the standard formula, dividing the K-factor so a six-way exposes you to the same total rating movement as a one-on-one. A side made up of several players competes at the average of their ratings, and every one of them takes the full change — so a rating always reads as strength per person, not per team.

The honest limitations

Elo is not magic, and it is worth knowing what it does not do.

• It needs games to settle. A new player's rating is a guess until they have played a fair few matches, and Elo does not track how confident it is in a number. Systems like Glicko-2 do — see Elo vs Glicko-2.
• It only compares people who play each other. Two separate circles of friends who never meet cannot be ranked against one another, however many matches each of them plays.
• It cannot tell luck from skill. In a game that is mostly chance, Elo will faithfully rank who has been lucky.

For a group of friends who play each other regularly, none of these matter much. For anything competitive and official, they matter a great deal.

See it happen

The quickest way to get a feel for it is to put two ratings in and watch them move. The Elo calculator does exactly that: pick two ratings, pick a winner, and it shows the new numbers, the points exchanged, and the expected score it worked from. It needs no account and nothing is saved.

When you want that done automatically for a whole group instead, that is what the rest of this site is for — see the ways people use it.