Elo rating calculator
Enter two ratings and a K-factor to see the win probability and exactly how many points a win, draw or loss moves. Then run a whole session of results in order, compare two teams by average rating, or find out how many wins it takes to reach a target.
Result
- Expected score, A
- 64.0%
- Expected score, B
- 36.0%
- Selected result: A change
- +11.5
- Selected result: B change
- −11.5
| Outcome | A change | A new rating | B change | B new rating |
|---|---|---|---|---|
| A wins | +11.52 | 1,611.5 | −11.52 | 1,488.5 |
| Draw | −4.48 | 1,595.5 | +4.48 | 1,504.5 |
| A loses | −20.48 | 1,579.5 | +20.48 | 1,520.5 |
Expected score is the average result you would get from many games (1 for a win, 0.5 for a draw). With draws possible it is not exactly a win probability.
What Elo actually calculates
Elo turns a rating difference into an expected score, the average result you would get if the same two players met many times, counting a win as 1 and a draw as 0.5. After the game, each rating moves by K times the gap between what happened and what was expected. The whole system is two formulas:
- Expected score = 1 ÷ (1 + 10(opponent − you) ÷ 400)
- New rating = old rating + K × (actual score − expected score)
The 400 is a scale choice: a 400-point lead means the stronger side is expected to score about 91%. The table shows how quickly the expectation grows with the gap.
| Rating gap | Expected score | Points for a win at K = 32 |
|---|---|---|
| 0 | 50.0% | +16.0 |
| 100 | 64.0% | +11.5 |
| 200 | 76.0% | +7.7 |
| 400 | 90.9% | +2.9 |
| 800 | 99.0% | +0.3 |
A worked example
Player A is rated 1600 and plays B, rated 1500, with K = 32. The gap is 100, so A’s expected score is 1 ÷ (1 + 10−0.25) = 0.640.
- A wins: 32 × (1 − 0.640) = +11.5, and B loses 11.5.
- A draws: 32 × (0.5 − 0.640) = −4.5.
- A loses: 32 × (0 − 0.640) = −20.5.
The favourite risks twice as much as they can win, which is the point: the system charges you for an upset in proportion to how unlikely it was. Because both players use the same K, whatever A gains B loses, so the total rating in the pool never changes. Try it in the calculator with different K values and gaps. Give the players different K values and you will see the pool stop being zero-sum, which is how ratings inflate or deflate over time.
Choosing K
K is a trade-off between speed and stability. A high K reacts quickly, which suits new players whose rating is still a guess and short seasons, but a few lucky results move it a long way. A low K is stable and hard to distort, which suits established players but takes many games to correct a wrong starting point. Chess federations use small values: FIDE’s rules use 40 for new players, 20 for most and 10 once a player has reached 2400. The presets above (10, 20, 24, 32, 40) are common choices, not a standard for any esports title.
Batches, teams and targets
Batch of results. Paste a session as one line per game. You can apply them after every game, as an online ladder does, or all from your starting rating as a chess rating period does. The table shows expected score and change for each game, and the summary adds your performance rating: the rating at which your expected score over those opponents would equal the score you actually got.
Team versus team. The calculator averages each team and shows two ways to share the result. Use it to see, for example, how much a team of four 1500s and one 1900 (average 1580) is expected to score against a flat 1600 team. Averages hide spread, so a team with one very strong player and four weak ones is not the same as five average players.
Reach a target. If matchmaking gives you opponents near your own level, every win is worth about half of K and every loss costs about half of K, so the climb is a matter of net wins: at K = 32 each net win is 16 points. Enter a win rate to see the expected number of games. At exactly 50% the expected drift is zero; 55% at K = 32 gains 1.6 points a game, so 300 points takes about 190 games. Against a fixed opponent your rating settles where the expected score equals your win rate, so no win rate below the equilibrium ever reaches a higher target.
Elo, Glicko and hidden ratings
Elo has one number per player and one fixed K. Glicko, designed by Mark Glickman, adds a second number, the rating deviation, which is a measure of how uncertain the rating is. A new or long-inactive player has a large deviation, so their rating moves a lot and their opponents’ ratings move less; as they play, the deviation shrinks and the rating settles. You can think of a high K for new players as a crude version of the same idea. This calculator does not compute Glicko.
Most matchmaking systems in modern games build on ideas like these but add their own details, and they rarely publish them. That is why we call this a generic Elo calculator: it is a way to understand the arithmetic behind rating systems, not a window into any particular game’s hidden MMR.
Frequently asked questions
What K-factor should I use?
K is how far one game can move a rating, so it sets how fast the system learns. Use a small K (10 to 20) when ratings are stable and games are few and meaningful, as in chess; use 24 to 40 when players are new, seasons are short or you want a ladder to react quickly. If you are modelling your own league, a common approach is a high K for the first ten or so games of a new player and a lower one afterwards. For predicting how a rating will move in a game you play, use the K of that game’s system if it is published, and treat the answer as an estimate if it is not.
Does a draw always score zero change?
Only between equal ratings. A draw counts as half a win, so the higher-rated player, who was expected to score more than half, loses points, and the lower-rated player gains them. With 1600 against 1500 and K = 32, a draw costs the favourite 4.5 points.
Why do I gain so little for beating a much weaker player?
Because the model already expected you to win. The gain is K × (1 − expected score), and when the expected score is 0.95 that is only 5% of K. The flip side is that one loss to a much weaker player costs almost the full K, which is why long win streaks against weak opponents barely move a rating.
Will this match the rank or MMR my game shows?
Almost certainly not exactly. This is the textbook Elo formula on a 400-point scale. Most game and platform ratings are modified versions (different scale, uncertainty terms, team and performance adjustments) or entirely different systems, and many are not published. Use the calculator to understand the mechanics and to sanity-check the size of the numbers, not to predict a specific game’s rank to the point.
What is the difference between updating after every game and using a rating period?
Online ladders usually update after every game, so game two is calculated from the rating that game one produced. Chess-style rating periods (a tournament, a month) calculate every game from the rating you started the period with and add the changes together. The two agree for a single game and drift apart over many, most noticeably when results are lopsided.
How are teams handled?
The simplest model averages each team’s ratings and treats the match as one game between two averages. Everyone on a team then receives the same change. It is easy to reason about but blind to who actually carried the match. The second option in the calculator compares each player with the opposing average instead, which is fairer to lower-rated players but no longer conserves the total. Real team rating systems usually add more, such as role, performance or weighting, and none of that is modelled here.
How many wins in a row do I need to reach my target?
Use the “Reach a target” mode. Against opponents rated like you, each win is worth about K/2, so at K = 32 a 300-point climb takes 19 straight wins (300 ÷ 16, rounded up). Against a fixed, weaker opponent each win is worth less than the last, so the number grows quickly; the calculator gives up after 200,000 wins.
Is the expected score the same as my win probability?
Only when draws are impossible. Elo works with expected score: 1 for a win, 0.5 for a draw. In a game with no draws the two are the same thing. In a game with draws, a 64% expected score could be, for example, a 55% chance of winning plus an 18% chance of drawing.