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Accuracy is the simplest general-purpose performance measure for a binary classifier: it is the share of predictions that were correct. It is easy to interpret, but it can be misleading when one class is much more common than the other or when false positives and false negatives have different consequences.
What accuracy measures
A binary classifier assigns each case to one of two classes, often called positive and negative. Its predictions fall into four groups:
- True positive (TP): predicted positive and actually positive.
- False positive (FP): predicted positive but actually negative.
- False negative (FN): predicted negative but actually positive.
- True negative (TN): predicted negative and actually negative.
Accuracy counts the true positives and true negatives as correct, then divides by all predictions. Google for Developers gives the formula as (TP + TN) / (TP + TN + FP + FN). For example, if a test set contains 100 cases and the classifier gets 90 right, its accuracy is 90%.
When accuracy is enough—and when it is not
Accuracy is most informative when the classes are reasonably balanced and false positives and false negatives have similar costs. In that situation, its plain-language interpretation—“what share of all predictions were correct?”—matches the question many readers want answered.
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On imbalanced data, accuracy can look strong even when a classifier fails to identify the less common class. If 95 of 100 examples are negative, a model that always predicts negative achieves 95% accuracy while finding none of the positives. Always read accuracy alongside the class distribution and the consequences of each kind of error.
For an important or safety-sensitive application, report the confusion matrix or, at minimum, accuracy together with precision, recall, and balanced accuracy. These measures expose different failure patterns that a single correctness rate can conceal.
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Which metric should you use?
Choose a measure based on the class balance, the relative cost of errors, and whether you are evaluating one decision threshold or comparing scores across thresholds.
| Metric | Plain-language question | Useful when | Main limitation |
|---|---|---|---|
| Accuracy | What share of all predictions were correct? | Classes are balanced and error costs are roughly equal. | Can be inflated by the majority class. |
| Balanced accuracy | How well did the classifier perform on each class on average? | Binary labels are imbalanced. | Hides the separate sensitivity and specificity values. |
| Precision | When the model predicts positive, how often is it right? | False positives are especially costly. | Can be unstable when few positives are predicted. |
| Recall (sensitivity) | Of the real positives, how many did the model find? | False negatives are especially costly. | Can rise while false alarms increase. |
| F1 | How well are precision and recall balanced? | You need one summary focused on the positive class. | Does not directly include true negatives. |
| AUC | How well does the model rank positives above negatives across thresholds? | You want to compare ranking ability before choosing a threshold. | Does not identify the best operating threshold. |
How the alternative metrics work
Balanced accuracy for imbalanced classes
For a binary classifier, balanced accuracy is the average of sensitivity (the true-positive rate) and specificity (the true-negative rate): 0.5 × [TP/(TP + FN) + TN/(TN + FP)]. It gives each class equal weight rather than letting the more frequent class dominate. Scikit-learn describes its balanced_accuracy_score as a way to avoid inflated performance estimates on imbalanced datasets. Check sensitivity and specificity separately as well, since their average can hide a weak result for one class.
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Precision when false alarms matter
Precision is TP/(TP + FP): among cases predicted positive, it measures the share that truly are positive. Prioritize it when acting on a false alarm is costly. Precision alone does not say how many actual positives the classifier missed.
Recall when missed positives matter
Recall, also called sensitivity, is TP/(TP + FN): among all actual positives, it measures the share the classifier finds. It is useful when missing a positive case is costly, but increasing recall may also mean accepting more false positives.
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F1 when you need one precision–recall summary
F1 is the harmonic mean of precision and recall: 2TP/(2TP + FP + FN). Scikit-learn explains that it can be interpreted as the harmonic mean of those two measures in its f1_score documentation. F1 provides a single positive-class-focused summary, but it does not directly account for true negatives.
AUC for ranking across thresholds
AUC summarizes how well a model ranks positive cases above negative cases across possible thresholds. It answers a different question from accuracy: AUC describes ranking performance across thresholds, while accuracy evaluates the final positive/negative decisions at one chosen threshold. AUC does not tell you which threshold is suitable for your application.
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Why the decision threshold matters
Many classifiers produce a score or probability, then label a case positive if it meets a chosen threshold. Changing that threshold changes the resulting predictions—and therefore fixed-threshold measures such as accuracy, precision, and recall. When publishing or comparing these metrics, state the threshold used. Use AUC separately when the aim is to compare ranking before selecting an operating threshold.
Quick Recap
A practical way to report classifier performance
- Describe the class distribution. State how many positive and negative cases are in the evaluation set so readers can judge whether accuracy may be dominated by one class.
- Identify the costly error. Decide whether false positives, false negatives, or both carry the greater consequence.
- Report the confusion matrix. Show TP, FP, FN, and TN, or provide enough information for readers to understand the error pattern.
- Choose complementary metrics. Include accuracy for overall correctness; add precision or recall to address the relevant error cost, and balanced accuracy when class imbalance matters.
- State the threshold. Specify the decision threshold for fixed-threshold metrics. If comparing score-ranking ability across thresholds, report AUC as a separate measure.
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