Move the threshold.
See the trade-off.
One fixed population of 100 synthetic records: 20 labelled fraud, 80 labelled legitimate. A score is a ranking signal, not a calibrated probability.
The denominator matters.
Precision = TP / (TP + FP). Recall = TP / (TP + FN). False-positive rate = FP / (FP + TN). Alert rate = (TP + FP) / all records. Undefined ratios are shown as such.
Illustrative cost = FN × missed-fraud cost + FP × legitimate-friction cost + alerts × review cost. This model assumes every alert is reviewed; the other costs exclude review. Flagged fraud is not necessarily prevented fraud. Mature labels for the whole evaluated population are needed to estimate recall.
Primary reference: classification metrics ↗