Chess Rating Change Formula

Every rating update starts with three values. Actual Score is your game result expressed as a number: 1.0 for a win, 0.5 for a draw, 0.0 for a loss. Expected Score is the probability-based prediction calculated from the rating difference between you and your opponent. K-Factor is the sensitivity multiplier assigned to your player profile (typically 40, 20, or 10).

The formula subtracts expected score from actual score to measure surprise, then multiplies by K to scale the reaction. If you score higher than expected, the result is positive and your rating rises. If you score lower than expected, the result is negative and your rating drops. The greater the surprise, the larger the swing. For a fuller explanation of the rule behind it, read Review edge cases and rounding.

Suppose you are rated 1600 and draw against a 1900-rated opponent. Your expected score is approximately 0.15, meaning the system barely expected you to score at all. Your actual score of 0.50 exceeds expectation by 0.35. With K=20, your rating change is 20 × 0.35 = +7 points. The draw gained you rating because the system considered it an overperformance.

Now reverse the scenario: you are rated 1900 and draw against a 1600-rated opponent. Your expected score is approximately 0.85. Your actual 0.50 falls short by 0.35, producing a change of 20 × (−0.35) = −7 points. Same draw, same rating gap, but you lose 7 points because the system expected you to win.

A win against a much weaker opponent where your expected score was 0.95 produces a tiny surplus of only 0.05. With K=20, that is just +1 point. A win against a much stronger opponent where your expected score was 0.10 produces a surplus of 0.90, yielding +18 points from the same K-factor.

This is the core insight of Elo: the formula rewards the information content of the result, not the result label. Beating someone you were supposed to beat teaches the system almost nothing. Beating someone you were supposed to lose to is dramatically informative.