Decision Threshold Profit Optimizer

Decision Threshold

Classify "positive" above score 0.50

Cost / Benefit Matrix

Benefit of a caught true positive $100

Cost of a false positive (wasted action) $20

Cost of a missed positive (false negative) $80

Live Readouts

Expected profit / case

$0.00

Optimal threshold

0.50

Precision

Positive class (e.g. churners) score distribution Negative class score distribution Threshold plane — right side flagged "positive" Expected-profit curve vs. threshold

How it works

A classifier never outputs a hard yes/no — it outputs a score, and a business chooses where to cut it. Here two populations (e.g. "will churn" vs. "won't churn") each produce a roughly Gaussian score, overlapping in the middle. For a threshold t:

TP-rate(t) = 1 − Φ((t−μ₁)/σ₁)     [catch positives above t]
FP-rate(t) = 1 − Φ((t−μ₀)/σ₀)     [wrongly flag negatives above t]
Expected profit(t) = p·TPrate(t)·Benefit
                    − (1−p)·FPrate(t)·CostFP
                    − p·(1−TPrate(t))·CostFN

where Φ is the normal CDF and p is the base rate of the positive class (fixed here at 30%, a typical churn/fraud prevalence). The threshold that maximizes this expression is not 0.5 unless the costs happen to be symmetric — a cheap intervention with an expensive miss pushes the optimum down; an expensive, disruptive intervention pushes it up. This is the exact expected-value framework used in real churn-prevention, fraud-review and credit-approval systems (Provost & Fawcett's "Data Science for Business" calls it cost-sensitive decision making).

Threshold slider — moves the green plane; everything to its right is classified "positive" and acted on.
Benefit / cost sliders — the payoff matrix a real business would plug in (customer value saved, review-team cost, lost-customer cost…).
Jump to Optimal Threshold — scans the profit curve and snaps to its true maximum for the current costs.
The gold curve floating above the histograms is expected profit re-computed at every possible threshold; its peak moves the moment you change a cost slider.

Decision threshold Optimal point

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