What is the Elo rating system and why does it work?

Elo in one sentence

Every candidate has a rating. When it wins a duel it takes points from the loser, and how many depends on how surprising the result is: beating a favourite earns a lot, beating a much weaker rival earns very little.

Nobody has to sort a whole list at once. Plenty of one-on-one duels are enough, and the ratings fall into place on their own.

Where it comes from

Arpad Elo was a physics professor and a chess player. He proposed his system to rank the players of the United States Chess Federation, which adopted it in 1960; FIDE, the international federation, has used it since 1970.

Since then it has spread far beyond the board, in many variants: competitive video games use it to match players of similar skill, national football teams and other sports are ranked with it, and so is anything that needs to be ordered from head-to-head results.

How it works: the formula

1. Expected score. Before each duel, the chance that A beats B is computed from the rating gap:

E_A = 1 / (1 + 10^{(R_B − R_A) / 400})

2. Update. After the duel, each side gains or loses points based on the gap between what happened and what was expected:

R′_A = R_A + K × (S_A − E_A)

S_A is 1 if A wins and 0 if it loses. K sets how much a rating moves per duel: a high K lets newcomers find their place quickly, and a low one keeps established candidates stable.

A worked example

A is rated 1600 and B 1500, with K = 32. By the formula, A wins 64% of the time (E_A = 0.64).

• If A wins, as expected: A gains 32 × (1 − 0.64) = +11.5 and B loses the same.
• If B wins, the upset: B gains 32 × (1 − 0.36) = +20.5 and A loses the same.

That's the key: predictable wins barely move the ranking, and upsets correct it fast.

Elo calculator

Change the ratings and see how many points are at stake in a duel.

Why it works

• Choosing between two is easy and reliable. Hardly anyone struggles to pick between two options, but sorting thirty at once is tiring and inconsistent. Psychologist Louis Leon Thurstone formalised pairwise comparison as a way to measure preferences back in 1927.
• It accounts for who you beat. Beating the best is worth more than beating the worst, something a plain win count can't tell apart.
• It self-corrects. A candidate rated above what it deserves loses duels it was expected to win and drops quickly. Errors don't pile up.
• Nobody has to vote on everything. With N candidates there are a huge number of possible pairs, but each person only needs to vote on a few: the ratings link every duel together.
• It's transparent. It's a simple formula anyone can check, with no black boxes.

How DuElo uses it

• Every candidate starts at 1500 points.
• K adapts: 48 for a candidate's first 10 duels, 32 up to 30, and 20 after that.
• Smart matchmaking: the server picks duels between candidates with few votes and similar ratings, which carry the most information. The ranking settles with fewer votes.
• Every position shows a margin (±) that narrows with each duel, and is marked provisional until 8 duels.
• Each person votes on each pair only once, so nobody can boost a favourite by repeating the same duel.
• Your votes build your own ranking and show how much you agree with the crowd, and the Ranking tab charts how it has changed over time.

Its limits

• With few votes it's only a guide. That's why we show the margin and the provisional label.
• Vote order matters a little, because each vote is computed with the ratings of the moment. With many votes the effect fades.
• It measures what voters think. If a poll is mostly voted on by one group, the ranking reflects their taste.