# Is there a metric that combines recall and precision other than the F1 score?

I am looking for a machine learning optimization metric that combines recall and precision.

One such metric is the F1 score, which is the harmonic mean of the precision and the recall of a model. The problem with this metric is that it puts too much emphasis on the recall. For example:

• A model with 5% recall and 90% precision has an F1 score of 9%.
• A model with 90% recall and 50% precision has an F1 score of 64%.

So for the F1 score, a model that makes lots of mediocre predictions is better than a model that makes a few great predictions.

Is there an alternative?

• The Fowlkes–Mallows index will give you the geometric mean of precision and recall, and no doubt if you had good reason you could use the arithmetic mean instead. But if you prefer precision above anything else, then you could just use that - or if that is too extreme then weight the two. Commented Jan 9, 2022 at 10:00

However, you can give more importance to one of the metrics via $$F_\beta$$ score, by setting $$\beta$$: $$F_\beta=(1+\beta^2)\frac{pr}{\beta^2p + r}$$
A high $$\beta$$ would give more importance to recall, a low one gives more importance to precision. This is like a weighted harmonic mean. When $$\beta=1$$, it's the usual $$F_1$$ score.