Balanced accuracy is a metric we can use to assess the performance of a .

It is calculated as:

Balanced accuracy = (Sensitivity + Specificity) / 2

where:

• Sensitivity: The “true positive rate” – the percentage of positive cases the model is able to detect.
• Specificity: The “true negative rate” – the percentage of negative cases the model is able to detect.

This metric is particularly useful when the two classes are imbalanced – that is, one class appears much more than the other.

For example, suppose a sports analyst uses a to predict whether or not 400 different college basketball players get drafted into the NBA.

The following confusion matrix summarizes the predictions made by the model:

To calculate the balanced accuracy of the model, we’ll first calculate the sensitivity and specificity:

• Sensitivity: The “true positive rate” = 15 / (15 + 5) = 0.75
• Specificity: The “true negative rate” = 375 / (375 + 5) = 0.9868

We can then calculate the balanced accuracy as:

• Balanced accuracy = (Sensitivity + Specificity) / 2
• Balanced accuracy = (0.75 + 9868) / 2
• Balanced accuracy = 0.8684

The balanced accuracy for the model turns out to be 0.8684.

The following example shows how to calculate the balanced accuracy for this exact scenario using the balanced_accuracy_score() function from the sklearn library in Python.

Example: Calculating Balanced Accuracy in Python

The following code shows how to define an array of predicted classes and an array of actual classes, then calculate the balanced accuracy of a model in Python:

import numpy as np
from sklearn.metricsimport balanced_accuracy_score

#define array of actual classes
actual = np.repeat([1, 0], repeats=[20, 380])

#define array of predicted classes
pred = np.repeat([1, 0, 1, 0], repeats=[15, 5, 5, 375])

#calculate balanced accuracy score
balanced_accuracy_score(actual, pred)

0.868421052631579

The balanced accuracy is 0.8684. This matches the value that we calculated earlier by hand.

Note: You can find the complete documentation for the balanced_accuracy_score() function .