How to use the elo rating calculator
- Optionally list starting ratings as name, rating, one player per line. Anyone you leave out starts at the default rating.
- List the games in order, one per line: "Ana beat Ben" for a win, "Ana drew Ben" for a draw. You can also write ">" for a win and "=" for a draw.
- Set the K factor, which controls how far one game can move a rating. The 32 shown is an example, because organizations choose their own.
- Read the ratings after the last game, with each player's change and games played, and the table of each game with its expected score and rating change.
Formula
expected score of A against B = 1 / (1 + 10^((rating B - rating A) / 400))
new rating = old rating + K x (actual score - expected score)
a win scores 1, a draw 0.5 and a loss 0
the two players' changes are equal and opposite
A player who does better than expected gains points, and one who does worse loses them. Ratings are updated one game at a time in the order written, so the order of games can change the final numbers.
Three players and five games
Ana starts at 1600, Ben at 1500 and Cleo at 1450, with K = 32. Ana beats Ben, and since Ana was expected to score 0.640, Ana gains 32 x (1 - 0.640) = 11.5 points and Ben loses 11.5. Ben and Cleo then draw, Cleo beats Ana, Ana beats Cleo and Ben beats Cleo.
After all five games, Ana is at 1599.6 (down 0.4), Ben at 1501.7 (up 1.7) and Cleo at 1448.8 (down 1.2). The total of the three ratings is still 4,550, the same as at the start, because every point one player gains another loses.
What an Elo rating measures
An Elo rating is a running estimate of skill built from results. A difference of 400 points means the stronger player is expected to score about 91% of the points. The rating is relative, so only differences matter and the starting number is arbitrary. Because it only moves when results differ from expectation, a player who keeps beating weaker opponents gains little.
To turn results into a standings table, use the League Table Generator, and for a knockout draw the Tournament Bracket Generator.
Where real systems differ
Organizations add rules this page does not model: a larger K factor for new players, a lower one at high ratings, rating floors, provisional periods, and ratings updated once after a tournament round instead of game by game. Use those rules when matching a published list.
More tools for scores and odds
For other games, odds and fair splits, try the Balanced Team Generator, Race Pace Chart Generator and Dice Probability Calculator.
Assumptions and limits
- Every game has a single winner or is a draw.
- The same K factor applies to every player and every game, which is what keeps the total of all ratings constant. Both K and the starting rating are conventions, not fixed values.
- Names that differ only by letter case count as the same player.
- Games are applied in the order listed.
Frequently asked questions
How is an Elo rating change calculated?
Find the expected score from the rating difference, subtract it from the actual score (1, 0.5 or 0) and multiply by K. Add the result to the winner or lower the loser by the same amount.
What is the K factor in Elo?
It is the maximum number of points one game can move a rating, reached when a player scores a full point they were not expected to. Higher K reacts faster but is less stable.
What does a 400 point difference mean?
The player with the higher rating is expected to score about 91% of the points. A 200 point gap means roughly 76%, and a gap of 0 means 50%.
Does the order of games matter?
Yes. Each game uses the ratings as they stood at that moment, so the same results in a different order can give slightly different final ratings.