What is a decision threshold in classification?

A decision threshold is the cutoff used to convert a binary classifier's predicted probability or decision score into a class label. The classifier estimates *how likely* an event is; the threshold determines *when to label it positive*.

How does it work?

Suppose a fraud detector estimates the probability p that a transaction is fraudulent. If we choose a threshold of 0.70, the rule is:

Predicted Fraud       if p >= 0.70
Predicted Legitimate  if p <  0.70

Practical example

For three transactions:

• Transaction A: fraud probability 0.12 → Legitimate.
• Transaction B: fraud probability 0.58 → Legitimate.
• Transaction C: fraud probability 0.91 → Fraud.

At this chosen 0.70 cutoff, only C is flagged. With a 0.50 cutoff, B would also be flagged. The underlying probability estimates have not changed; only the final decisions have.

Why isn't 0.50 always best?

A 0.50 probability cutoff is a common default, but its suitability depends on the consequences of mistakes:

• Lower threshold: typically catches more actual positives (higher recall), but may flag more negatives incorrectly (more false positives).
• Higher threshold: typically flags fewer cases, often reducing false positives but missing more positives (more false negatives).

For fraud detection, missed fraud and unnecessary transaction blocks carry different costs. Choose the rule based on those costs rather than assuming 0.50 is optimal.

How should the threshold be selected?

1. Define the positive class and what false positives and false negatives cost.
2. Compare candidate thresholds using validation data with metrics such as precision, recall, F1-score, or an explicit business-cost function.
3. Fix the chosen threshold before assessing results on a held-out test set. Avoid selecting it using test labels.

Important: Some classifiers output decision scores instead of probabilities; their thresholds may be on a different scale (such as 0 for a decision function). A probability between 0 and 1 does not automatically guarantee good calibration.

In short: a decision threshold converts model scores into actions, letting you align classification behavior with practical costs and requirements.

References

• scikit-learn: Tuning the decision threshold for class prediction
• scikit-learn: Precision-recall curve