Elo Expected Score
Calculator
Results
- Expected score
- 0.240253
- Win probability (%)
- 24.025307
- Opponent expected score
- 0.759746
- Rating difference
- -200
Gaming results
| Expected score | 0.240253 |
| Win probability (%) | 24.025307 |
| Opponent expected score | 0.759746 |
| Rating difference | -200 |
formula-map diagram
- Expected score
- 0.240253
- Win probability (%)
- 24.025307
- Opponent expected score
- 0.759746
- Rating difference
- -200
Game math relationship
Formula
E = 1 ÷ (1 + 10^[(Rb − Ra) ÷ 400])= 0.24025307335204
Note
This is a simplified model: it applies the standard probability or game-math formula to the numbers you entered. Real games add pity systems, drop-rate tiers, rounding, server-side variance and balance patches, so treat the result as an estimate rather than a guarantee.
More in Gaming and probability
See all →Frequently asked questions
What does "expected score" mean in the Elo rating system?+
Expected score is the probability-weighted outcome a player is predicted to achieve against an opponent, expressed as a number between 0 and 1 (roughly interpretable as win probability in a two-outcome game), based purely on the rating difference between the two players.
How is expected score calculated from two Elo ratings?+
Expected score for player A is 1 divided by (1 plus 10 raised to the power of ((opponent's rating minus player A's rating) divided by 400)); this logistic-curve formula is the core of the entire Elo system.
Why is a 400-point rating gap associated with roughly a 91% win expectancy?+
The Elo formula's constant of 400 was chosen so that a 400-point difference yields about a 10-to-1 expected outcome ratio, which works out to roughly 90.9% expected score for the higher-rated player against the lower-rated one.
Does expected score account for anything other than the two players' current ratings?+
No — the standard Elo expected score formula uses only the rating difference and nothing else, which is intentional simplicity, though it means it doesn't factor in recent form, specific matchup history, or other context a human predictor might consider.
Why do two players with equal ratings have a 50% expected score against each other?+
When the rating difference is zero, the exponent in the formula becomes zero, which makes 10 raised to that power equal 1, giving an expected score of 1/(1+1) = 0.5 — an equal rating implies an equal predicted outcome by design.