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Optimal Classification Threshold Finder

Find the cut-off that best balances true positives and false positives.

Try:
Format: score,label with label 1 (positive) or 0 (negative). A header line is fine.
Curve shown

Scores at or above the threshold are predicted positive.

Area under the ROC curve (AUC)

0.5253

An AUC of 0.525 means a randomly chosen positive gets a higher score than a randomly chosen negative 52.5% of the time (ties count half): no better than a coin flip.

Average precision
0.5615
base rate 0.45
Positives
9
Negatives
11
Best threshold
0.8
Youden J 0.131

ROC curve

Confusion matrix at threshold 0.8

Actual \ PredictedPositiveNegative
Positive27
Negative110
Accuracy
0.6
Precision
0.6667
Recall (TPR)
0.2222
False positive rate
0.0909
F1
0.3333
MCC
0.183

How the numbers are computed

AUC, trapezoid rule

AUC=∑i(FPRi−FPRi−1)(TPRi+TPRi−1)2\mathrm{AUC} = \sum_i \frac{(\mathrm{FPR}_i-\mathrm{FPR}_{i-1})(\mathrm{TPR}_i+\mathrm{TPR}_{i-1})}{2}AUC=∑i​2(FPRi​−FPRi−1​)(TPRi​+TPRi−1​)​

Average precision

AP=∑n(Rn−Rn−1) Pn\mathrm{AP} = \sum_n (R_n - R_{n-1})\,P_nAP=∑n​(Rn​−Rn−1​)Pn​

Scores are sorted from high to low. Each distinct score is a threshold; tied scores move together, so a tie between a positive and a negative cuts a diagonal step and counts half.

Curve points

ThresholdFPRTPR (recall)Precision
0.900.11111
0.850.09090.11110.5
0.80.09090.22220.6667
0.750.18180.22220.5
0.70.27270.22220.4
0.660.27270.33330.5
0.620.36360.33330.4286
0.580.36360.44440.5
0.550.45450.44440.4444
0.50.45450.55560.5
0.470.54550.55560.4545
0.440.54550.66670.5
0.40.63640.66670.4615
0.350.72730.66670.4286
0.30.72730.77780.4667
0.260.81820.77780.4375
0.20.81820.88890.4706
0.150.90910.88890.4444
0.110.88890.4211
0.05110.45
  1. Tools
  2. Machine Learning
  3. ROC Curve and AUC Calculator
  4. Optimal Classification Threshold Finder

About Optimal Classification Threshold Finder

This optimal threshold finder searches every cut-off of your scores for the one that maximises Youden's J, and shows the confusion matrix and metrics at that point. It is free, needs no sign-up and runs in your browser, so nothing you enter is uploaded.

Youden's J is the true positive rate minus the false positive rate, so it is the vertical distance from the ROC curve up to the chance diagonal. Its peak is the cut-off that balances the two rates, and it is a sensible default when a miss and a false alarm cost about the same.

If they do not cost the same, move the slider. A screening test might accept more false alarms for a higher true positive rate; an automated action might demand high precision. The page opens at the best threshold for a weak model.

How to use Optimal Classification Threshold Finder

  1. 1Paste your data as score,label lines. A label is 1 for the positive class and 0 for the negative class; true and false also work.
  2. 2Or tap an example to load a good model, a weak model, an imbalanced set or the classic four-point example.
  3. 3Read the AUC and average precision in the result card.
  4. 4Switch between the ROC curve and the precision-recall curve.
  5. 5Move the threshold slider, or press the best-threshold button, to see the confusion matrix and metrics at that cut-off.
  6. 6Open the curve points table to see every threshold, false positive rate, true positive rate and precision.

Features

  • ROC curve with the chance diagonal, shaded area and a marker for your chosen threshold.
  • AUC by the trapezoid rule, with ties between a positive and a negative counted as half.
  • Precision-recall curve with the no-skill baseline, and average precision.
  • A threshold slider with the live confusion matrix, accuracy, precision, recall, false positive rate, F1 and MCC.
  • The best threshold by Youden's J statistic in one tap.
  • Up to 20,000 rows, with a table of the curve points.
  • A plain-English reading of what the AUC means for your model.

Youden's J statistic

The threshold with the largest J is chosen; the first one wins a tie.

J = sensitivity + specificity - 1 = TPR - FPR

Worked examples

  • The weak-model sample → gives best threshold 0.8, J 0.131

    A small J confirms that no threshold separates the classes well.

Privacy: how it works

  • Your scores and labels are processed by code running in your browser tab. They are never sent to Ulkaa or anyone else.

Tips

  • Scores need not be probabilities. Any number where higher means more likely positive works, because only the ranking matters.
  • The AUC depends only on the order of the scores. Multiplying all scores by a constant changes nothing.
  • Tied scores are handled as one step. A tie between a positive and a negative cuts a diagonal and counts half.
  • Both classes must appear in the data, or the rates are undefined and the tool asks for more.

Frequently asked questions

Is it really free?

Yes. There is no price, no trial and no credit card. Ulkaa Tool does the work with your own device, so there is no server bill to pass on to you.

Do I need an account?

No. There is no sign-up and no login. Open the page and use it. An Ulkaa account is not needed for anything on this tool.

Does it run in my browser?

Yes. Your scores and labels are processed by code running in your browser tab, on your own device.

Is my data uploaded?

No. Your scores and labels are never sent to Ulkaa or to anyone else. You can check this yourself by watching the Network tab in your browser developer tools while you use the tool.

What is Youden's J statistic?

The sum of sensitivity and specificity minus 1. It is the largest vertical gap between the ROC curve and the diagonal.

Is the Youden threshold always the best?

No. It assumes false positives and false negatives cost the same. Choose another cut-off when they do not.

More ROC Curve and AUC Calculator pages

  • ROC Curve and AUC CalculatorPaste model scores and true labels to draw the ROC curve, find the AUC and explore thresholds.
  • ROC Curve CalculatorPaste scores and labels to plot the ROC curve and move along it with a threshold slider.
  • AUC CalculatorPaste scores and labels and get the area under the ROC curve.
  • Precision-Recall Curve CalculatorSee precision against recall for every threshold, and compare it with the no-skill line.
  • Average Precision CalculatorGet the average precision of a ranked list of predictions.
  • ROC AUC for Imbalanced DataCheck what a ROC AUC means when only a few cases are positive.

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