What is precision and recall?

Precision

Precision tells us how many, out of all instances that were predicted to belong to class $X$, actually belonged to class $X$. The precision for class $X$ is calculated as:

$$\frac{TP}{TP+FP}$$

$TP$ = the number of true positives for class $X$.

$FP$ = the number of false positives for class $X$.

Recall

Recall expresses how many instances of class $X$ were predicted correctly. The recall is calculated as:

$$\frac{TP}{TP+FN}$$

$TP$ = the number of true positives for class $X$.

$FN$ = the number of false negatives for class $X$.

Example

Suppose that we have the following confusion matrix:

Binary classification problems often focus on the positive class; therefore, precision and recall are calculated for the positive class.

Precision

The precision is equal to:

$$\frac{13}{13+4} = 0.7647$$

This shows that $76.47\%$ of the records that were classified as positive were actually positive.

Recall

The recall is equal to:

$$\frac{13}{13+3} = 0.8125$$

This shows that $81.25\%$ of the positive instances were classified as positive.