This calculator works out the expected score between two players from their Elo ratings, as used in chess and many games. Enter both ratings; you get player A’s expected score in percent (wins plus half the draws) and player B’s.
Formula
E_A = 1 ÷ (1 + 10^((R_B − R_A) ÷ 400)) and E_B = 1 − E_A.
- R_A, R_B: the two ratings; the 400 is the standard Elo scale
Worked Example
A player rated 1600 against one rated 1500.
- (1500 − 1600) ÷ 400 = −0.25
- 10^−0.25 = 0.5623
- E_A = 1 ÷ 1.5623 = 0.6401, or 64.01%
- E_B = 100 − 64.01 = 35.99%
How to read the result
The expected score counts a draw as half a win, so 64% means A scores about 64 points in 100 games. After a game, the rating changes by K × (actual − expected), where K is set by the rating system (often 10-40).
Limits and common mistakes
- Different games and sites use different K factors and some use other scales; the 400-point formula is the classic one.
- It is an expectation over many games, not a prediction of one game.
Frequently Asked Questions
What is the expected score with a 200 point gap?
About 76% for the higher-rated player.
What if ratings are equal?
50% each.
Does it include draws?
Yes; a draw counts as half.
How much do ratings change after a game?
K × (result − expected); with K = 20 and a win at 64% expected, about +7.
Formula used
in ra | Player A rating | - | 1600 | 0 | 4000 in rb | Player B rating | - | 1500 | 0 | 4000 out ea | Player A expected score | % | 1 / (1 + 10^((rb - ra) / 400)) * 100 | 2 out eb | Player B expected score | % | 100 - ea | 2
Each line is one input (in, sel, list) or one result (out: label, unit, formula, decimals). How the calculators work
Method: the standard formula for this calculation, rounded as each result states. See how the calculators work or report an error.