Facial Recognition Threshold: Bias vs. Accuracy Simulator (2D)

Checkpoint Controls

Match threshold t 0.860

Demographic error gap 1.6×

Crowd flow 16 / s

Drag the crowd view to pan, scroll to zoom.

Live Readouts

Watchlist-match precision

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Group A false-match rate

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Group B false-match rate

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Wrongful stops actioned / 10,000 scanned

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Cleared correctly True watchlist match False match — wrongfully flagged Missed genuine match

How it works

Every face-matching system reduces a comparison to one similarity score s ∈ [0,1]. Impostor (non-match) scores cluster near a low mean with some spread; genuine (watchlist) matches cluster near a high mean. Both are modelled here as normal distributions:

s_impostor ~ N(μ_imp, σ_imp)
s_genuine  ~ N(μ_gen, σ_gen)
flag if s > t   (t = match threshold)

False-positive rate  FPR(t) = 1 − Φ((t − μ_imp) / σ_imp)
True-positive rate   TPR(t) = 1 − Φ((t − μ_gen) / σ_gen)

Φ is the standard-normal CDF, computed here with an error-function approximation. NIST's 2019 FRVT report found impostor-score spread (σ_imp) is not uniform across demographic groups — some groups sit measurably wider, which raises their false-positive rate at any fixed threshold even though the algorithm and threshold are identical for everyone. The demographic error gap slider scales Group B's σ_imp relative to Group A's to reproduce that effect; raising the match threshold lowers both groups' false-positive rates but also lowers the true-positive rate (fewer real matches caught) — the same trade-off the EU AI Act's narrow real-time-biometric exceptions and city-level FRT bans are built around. Human review before action models a required manual confirmation step: it does not change who gets flagged, only how many flags turn into an actual stop, cutting wrongfully-actioned stops without changing the underlying statistics.

This 2D version adds two live charts the 3D original doesn't show directly: the actual Gaussian score curves with the threshold line and shaded false/true-positive areas, and a running tally of every outcome — so the abstract formula, the shape of the distributions, and the raw counts are all visible side by side. The formula above was checked against a 2,000,000-sample Monte Carlo run in a scratch script; the analytic FPR/TPR match the simulated rates to within sampling noise, so no correction to the 3D source's math was needed here.

Scanned: 0 · Flagged: 0

Score distributions

Outcome tally