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What it is and what it's for

Evaluates a binary classifier (predicts yes/no, 1/0). The model doesn't return a verdict but a score from 0 to 1 —the probability of being class 1— and you decide where to cut. This tool generates example data and shows you live how it is evaluated: score histogram, confusion matrix, metrics and the ROC and PR curves. Everything recomputes instantly in your browser; nothing needs training.

The controls: a toy dataset

The data is synthetic so you can experiment without bringing your own:

• Quality — how good the classifier is: 0 = chance (positive and negative scores overlap), 1 = almost perfect (they separate cleanly).
• Balance — the fraction of examples that are positive; lower it to simulate imbalanced classes.
• Samples — how many examples to generate (100–1000).
• Regenerate — re-draws the data with another seed while keeping the settings, to see the variability.

The threshold decides everything

The threshold is the cut-off line: score ≥ threshold → predicted positive. In the histogram, the bars are the scores of the negatives (0) and the positives (1); the vertical line is your threshold. Move it and watch: lowering it captures more real positives (more recall) but lets in more false alarms (less precision); raising it does the opposite. There is no perfect threshold: it depends on which error costs you more.

The confusion matrix, cell by cell

It crosses the actual label (rows) with the predicted one (columns) at the current threshold:

• TP (true positive) — it was 1 and you got 1: a positive well caught.
• FN (false negative) — it was 1 and you said 0: a positive that slips past you.
• FP (false positive) — it was 0 and you said 1: a false alarm.
• TN (true negative) — it was 0 and you got 0: a negative well discarded.

The diagonal TP + TN (green) are the hits; off it FP + FN (red) are the errors. The color intensifies with the count.

The metrics and what each one means

They are computed from the four cells:

• Accuracy = (TP+TN)/total — percentage of hits. Misleading if the classes are imbalanced.
• Precision = TP/(TP+FP) — of what you flag as positive, how much is right.
• Recall (TPR or sensitivity) = TP/(TP+FN) — of the real positives, how many you catch.
• Specificity = TN/(TN+FP) — of the real negatives, how many you discard.
• F1 = harmonic mean of precision and recall 2·P·R/(P+R) — a single number that rewards the balance between the two.

ROC and AUC

The ROC curve sweeps through ALL thresholds at once, pitting hits (TPR = recall) against false alarms (FPR = FP/(FP+TN)). The marked point is your current threshold and the diagonal is chance. The AUC (area under the curve) summarizes quality independently of the threshold: 1 = perfect, 0.5 = chance. It equals the probability that a random positive scores higher than a random negative.

PR, AP and imbalance

The PR curve pits precision against recall across the thresholds; its summary is the AP (average precision). The horizontal baseline is the fraction of positives: what a random classifier would get. With heavily imbalanced classes that line sinks and truly beating it is hard —which is why PR is more honest than accuracy when positives are few—. Lower the “Balance” and check it.

ROC or PR? when to use each

• Use ROC/AUC when the classes are balanced or you care equally about hits and false alarms; it is robust and easy to compare across models.
• Use PR/AP when positives are rare (fraud, disease, spam) and what matters is getting them right: ROC can look great while the real precision is poor.

Tip: lower the “Quality” and you'll see the ROC hug the diagonal; lower the “Balance” and you'll see accuracy lie while AP does not.

Confusion matrix, ROC and PR

Evaluate a binary classifier: move the threshold and watch metrics and curves live

Quality

0.600

Balance

50.0%

Samples

500

Model scores

Negatives (0)Positives (1)← Threshold 0.500 →

Confusion matrix

	Prediction
Actual	1	0
1	220TP	26FN
0	29FP	225TN

Accuracy89.0%

Precision88.4%

Recall (TPR)89.4%

Specificity88.6%

F10.889

ROC · AUC = 0.960

FPR (false alarms)↑ TPR (hits)

PR · AP = 0.959

Recall↑ Precision

Choosing the threshold and reading these curves is everyday work when evaluating a model. Try: lower the "quality" and watch the ROC hug the diagonal; lower the "balance" and see how accuracy lies but AP doesn't. Related: Hypothesis testing and Neural network.