A measure that combines precision and recall is the harmonic mean of precision and recall, the traditional F-measure or balanced F-score:

formula_9

This measure is approximately the average of the two when they are close, and is more generally the harmonic mean, which, for the case of two numbers, coincides with the square of the geometric mean divided by the arithmetic mean. There are several reasons that the F-score can be criticized in particular circumstances due to its bias as an evaluation metric. This is also known as the formula_10 measure, because recall and precision are evenly weighted.

It is a special case of the general formula_11 measure (for non-negative real values of formula_12):

formula_13

Two other commonly used formula_14 measures are the formula_15 measure, which weights recall higher than precision, and the formula_16 measure, which puts more emphasis on precision than recall.

The F-measure was derived by van Rijsbergen (1979) so that formula_11 "measures the effectiveness of retrieval with respect to a user who attaches formula_12 times as much importance to recall as precision". It is based on van Rijsbergen's effectiveness measure formula_19, the second term being the weighted harmonic mean of precision and recall with weights formula_20. Their relationship is formula_21 where formula_22.

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Probabilistic interpretation
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