Calculator Inputs
Provide labels and one score column for each class.
Formula Used
True Positive Rate
TPR = TP ÷ (TP + FN)
TPR measures correctly detected positives for each selected class.
False Positive Rate
FPR = FP ÷ (FP + TN)
FPR measures negative samples incorrectly assigned to that class.
Trapezoidal AUC
AUC = Σ (FPRᵢ − FPRᵢ₋₁)(TPRᵢ + TPRᵢ₋₁) ÷ 2
AUC summarizes ranking performance across all evaluated thresholds.
Macro Average
Macro AUC = Σ AUCₖ ÷ K
Every class contributes equally, regardless of support.
Weighted Average
Weighted AUC = Σ (nₖ ÷ N)AUCₖ
Class support controls each score's contribution.
Youden Threshold
J = TPR − FPR
The reported threshold maximizes this separation statistic.
How to Use This Calculator
- Enter class names in the exact score-column order.
- Paste one actual label for every evaluated sample.
- Paste one score row for every actual label.
- Select normalization when rows contain logits or unscaled scores.
- Choose threshold, pairwise, and confidence interval options.
- Press the calculation button to display results above.
- Inspect weak classes, thresholds, curves, and average AUC values.
- Download the summary for reporting or model comparisons.
Understanding Multiclass ROC Analysis
Core Evaluation Concepts
Multiclass ROC analysis carefully extends binary evaluation across several target classes. Each class temporarily becomes positive while all remaining classes become negative. This approach creates one meaningful comparable curve for every label.
A ROC curve directly links sensitivity with false positive behavior. Threshold changes gradually move predictions across different operating points. Strong curves usually stay near the upper-left plot corner.
Area under the curve summarizes overall ranking quality across thresholds. An AUC near one generally indicates excellent class separation. Values near one-half often resemble random ranking behavior.
Understanding Average Scores
Micro averaging combines every individual one-versus-rest decision before calculating performance. Large classes therefore usually influence the result more strongly. This score reflects broad overall prediction behavior across all samples.
Macro averaging deliberately gives every class equal importance during aggregation. Rare classes therefore still affect the final score meaningfully. Use macro results when balanced treatment matters most.
Weighted averaging uses class support while combining individual class scores. Frequent labels receive proportionally greater influence. This measure balances class detail with dataset composition.
Curves and Threshold Decisions
Class curves can reveal weaknesses hidden by one summary score. Similar averages may conceal very different label performance. Inspect every curve before accepting deployment readiness.
Threshold inspection supports practical decisions beyond simple model ranking. Some applications demand higher sensitivity for selected classes. Others prioritize fewer false alarms and steadier precision.
Probability normalization can repair rows that do not sum correctly. Simple division preserves relative scores within each sample. Softmax converts arbitrary logits into positive probability distributions.
Stable Comparison Practices
Interpolation aligns curves on a shared false positive grid. This alignment enables stable macro curve construction. More grid points produce smoother visual summaries.
Reliable interpretation also requires enough examples per class. Tiny classes can produce unstable curves and misleading AUC values. Confidence improves when evaluation data represents expected production traffic.
Use exported tables for reviews, reports, and comparison studies. Recalculate after changing preprocessing, labels, or model versions. Consistent evaluation helps teams detect meaningful performance shifts quickly.
Advanced Interpretation
Pairwise analysis compares classes directly when confusion patterns need deeper investigation. It removes unrelated classes from each comparison. However, many pairwise curves can become difficult to review.
A useful operating threshold depends on business costs and error consequences. No universal cutoff serves every class equally. Review threshold tables beside domain requirements and capacity limits.
Model comparison should use identical samples, labels, and preprocessing rules. Otherwise, apparent gains may come from evaluation differences. Controlled testing makes important AUC changes easier to trust.
Frequently Asked Questions
1. What does multiclass ROC measure?
It measures class ranking quality across many decision thresholds. Each label is evaluated against all remaining labels. The curves expose sensitivity and false positive tradeoffs.
2. Should score rows total one?
Probabilities commonly total one, but raw scores may not. Select sum normalization for positive unscaled values. Select softmax when the matrix contains model logits.
3. What is micro-average AUC?
Micro averaging pools every class decision before curve calculation. Larger classes create more pooled decisions. The result emphasizes overall sample-level discrimination.
4. What is macro-average AUC?
Macro averaging calculates equal influence across all classes. A rare class matters as much as a common class. This approach highlights balanced class treatment.
5. Why use weighted AUC?
Weighted AUC respects the observed support of each class. Common labels influence the result more strongly. It reflects performance under the current class distribution.
6. What does pairwise AUC show?
Pairwise AUC evaluates two classes without unrelated samples. It reveals specific class pairs that confuse the model. Many classes can produce numerous pair combinations.
7. How is the best threshold selected?
The calculator maximizes Youden's J statistic for each class. That statistic subtracts FPR from TPR. Operational costs may still require another threshold.
8. What do bootstrap intervals mean?
Bootstrap intervals estimate AUC uncertainty through repeated resampling. Wider intervals suggest less stable evaluation results. Small classes often create wider intervals.
9. Can AUC replace confusion matrices?
No single metric answers every evaluation question. AUC evaluates ranking across thresholds. Confusion matrices describe errors at one chosen threshold.