Accuracy tells you what fraction of predictions were correct, but not which errors a classifier made, whether it found the less common class, or whether its predicted probabilities are trustworthy. Start with the confusion matrix, define which mistakes matter, then choose metrics that match the decision you need to make.
Why is accuracy not enough?
Accuracy is the share of predictions that match the true labels. It is useful when classes and error costs are reasonably balanced, but it can conceal poor performance on a less common class. It also treats false positives and false negatives alike, even when their practical consequences differ.
Begin with a confusion matrix: it counts true positives, false positives, true negatives, and false negatives. Define which label is the positive class and what each error means in your application. The scikit-learn metrics documentation lists accuracy alongside measures that reveal other aspects of classification quality.
Which metric should I use for imbalanced classification?
Balanced accuracy
Balanced accuracy is the average of recall across classes. In binary classification, it is the arithmetic mean of sensitivity (true-positive rate) and specificity (true-negative rate). Unlike ordinary accuracy, it gives each class equal weight, reducing the dominance of the majority class in the overall score.
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Pair it with per-class results and class support—the number of actual examples in each class—so readers can see both performance and prevalence. The scikit-learn explanation of balanced accuracy describes its rationale and definition.
Per-class precision and recall
For imbalanced problems, report precision and recall for each class rather than relying on a single overall score. In multiclass settings, if you also report a macro, micro, or weighted average, state which averaging convention you used: they summarize class results differently.
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What is the difference between precision and recall?
Precision asks: of the examples the model predicted as positive, how many were actually positive? Recall asks: of all actual positives, how many did the model find? Name the positive class explicitly; reversing that choice changes the interpretation.
- Use precision when false alarms are costly. A higher precision target may mean accepting lower recall, so fewer actual positives are found.
- Use recall when missing positives is costly. Raising recall can also produce more false positives.
These measures answer different questions; neither is universally better. Report both when their trade-off matters.
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When should I use F1 or F-beta?
F1 is the harmonic mean of precision and recall. It provides a compact summary when you want to balance the two, but it does not make false positives and false negatives equally costly in your application. Include the component precision and recall values so the combined score does not hide how the model performs.
F-beta lets you weight recall more or less heavily than precision by choosing beta. Use it when that emphasis reflects the task, and state the chosen beta. In scikit-learn’s multiclass metrics, micro averaging across all labels makes precision, recall, and F identical to accuracy; that aggregate can therefore obscure class-level performance. See the scikit-learn documentation on precision, recall, and F-measures.
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When should I use ROC AUC or a precision-recall curve?
Precision, recall, and F1 describe decisions made at a particular threshold. ROC and precision-recall (PR) curves instead show how performance changes across thresholds when a model supplies scores. ROC plots true-positive rate against false-positive rate; a PR curve plots precision against recall.
Use these curves when comparing ranking behavior or choosing a threshold. A curve summary such as AUC does not select a deployment threshold for you: choose an operating point based on the real cost of errors or an operational constraint. Report the class prevalence and why you chose ROC or PR analysis; the scikit-learn guide to ROC metrics and its precision-recall metrics section describe these threshold-based measures.
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How do I evaluate whether predicted probabilities are calibrated?
Label quality and probability quality are different. If decisions downstream use predicted probabilities, inspect a calibration (reliability) curve: group predictions into probability bins and compare each bin’s average predicted probability with its observed positive frequency. A well-calibrated model’s predicted probabilities correspond closely to observed frequencies across the bins.
Log loss and Brier score are proper scoring rules for probabilistic predictions, but neither is a pure calibration measure. Brier score combines calibration, discrimination or resolution, and uncertainty; a lower Brier loss alone does not prove better calibration, because stronger discrimination can lower the loss even when calibration is worse. Use a calibration curve alongside a proper loss when probability quality matters. The scikit-learn probability calibration guide explains these distinctions.
What other measures can summarize classification performance?
Matthews correlation coefficient
Matthews correlation coefficient (MCC) is a useful single summary for a binary confusion matrix. Treat it as a complement to, not a replacement for, the class-wise error picture: a scalar cannot show which specific errors matter in your application.
Choose measures by the question
| Evaluation question | Useful measures | Interpretation to preserve |
|---|---|---|
| Which errors is the model making? | Confusion matrix; class-level precision and recall | Name the positive class and define each error in context. |
| How can false alarms be limited? | Precision; threshold analysis | A high precision target can trade away recall. |
| How many actual positives can be found? | Recall or sensitivity; threshold analysis | Higher recall can create more false positives. |
| How can precision and recall be summarized together? | F1 or F-beta | Show component values; F1 weights precision and recall symmetrically. |
| How does a classifier perform across imbalanced classes? | Balanced accuracy; per-class recall | Include class support or prevalence and class-level results. |
| How does ranking change across thresholds? | ROC curve/AUC or PR curve | Use score outputs and select the operating threshold separately. |
| Are predicted probabilities useful? | Log loss, Brier loss, and a calibration curve | Brier loss is not a pure measure of calibration. |
| What is one broad summary of a binary confusion matrix? | MCC | Keep the underlying class-wise error picture in view. |
How should you compare and report classifiers?
Compare models on the same held-out evaluation data, with the same label definitions. Match the measures to the errors that matter, and report class prevalence, per-class performance, threshold or ranking behavior, and probability calibration when probabilities drive decisions.
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- Include the confusion matrix and per-class precision, recall, and support.
- Add a task-matched summary, such as balanced accuracy for class-balanced comparison or F1 for a compact precision-recall summary.
- Show a threshold curve when ranking or threshold selection matters, and identify whether each reported measure uses hard labels, scores, or probabilities.
- When probabilities guide decisions, include a calibration view or proper loss.
- Do not compare values produced with different positive classes, thresholds, or averaging conventions as if they were directly equivalent.
No single evaluation metric proves a classifier is ready for deployment; the relevant evidence depends on the decision, error costs, and inputs used by each measure.
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