Tournament performance rating calculator
Performance rating asks what rating would, on average, have produced this score against this opposition.
Performance rating
1970
- Rating change
- 47.89
- New rating
- 1827.9
- Expected score
- 3.605
- Points above expectation
- 2.395
- Score percentage
- 0.6667
- Rating difference implied by the score
- 120.4
Show the working
- Games played = 9
- Points scored = 6
- Average opponent rating = 1850
- Your rating = 1780
- K-factor = 20
- Score percentage = 9 > 0 ? 6 / 9 : 0 = 0.666 667
- clamped = clamp(0.666 667, 0.01, 0.99) = 0.666 667
- Rating difference implied by the score = -400 * log10(1/0.666 667 - 1) = 120.412
- Performance rating = 1850 + 120.412 = 1970.41
- Expected score = 9 / (1 + 10^((1850 - 1780)/400)) = 3.605 43
- Rating change = 20 * (6 - 3.605 43) = 47.8914
- New rating = 1780 + 47.8914 = 1827.89
- Points above expectation = 6 - 3.605 43 = 2.394 57
Values are shown to six significant figures here; the arithmetic itself runs on exact fractions and is only rounded where a number is printed.
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The formula
- performance = average opponent rating + dp, where dp = -400 log10(1/score fraction - 1)
- expected score = games / (1 + 10^((opponent - you)/400))
A perfect or zero score gives an undefined performance rating, which is why the score is clamped just short of the extremes.