Credit Scorecard: Weight-of-Evidence & ROC Discrimination (2D)

Test Applicant

Annual income $45,000

Debt-to-income ratio 28%

Payment history score 78/100

Approval cutoff 50% default-risk

APPROVE

Feature Weights (manual)

Income weight 1.00×

DTI weight 1.00×

Payment history weight 1.00×

Model Discrimination

Applicants

Base default rate

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ROC AUC

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Gini coefficient

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Applicant P(default)

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Applicant score

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How it works

Real credit bureaus often build scorecards from weight of evidence (WOE) rather than a trained classifier: each feature is cut into bins, and every bin gets a fixed WOE = ln( %good in bin / %bad in bin ), computed once from a labelled population.

Income, DTI and payment history are each split into 5 population-quantile bins; every bin's WOE is recomputed whenever you regenerate the population.
Feature weights here are set by hand, not fit by gradient descent — a scorecard analyst overriding a feature's statistical weight based on policy or regulation. At weight = 1.0× for every feature the score is the maximum-likelihood-consistent sum of WOE (assuming independent features), which is the mathematically optimal combination.
Pushing any weight away from 1.0× necessarily throws away some of the population's real separating signal — watch the ROC AUC and Gini coefficient fall as you detune the weights, even though the underlying data hasn't changed at all.

The applicant's score is score = Σ weight_f × WOE_f(bin), converted to a default probability with P(default) = 1 / (1 + odds_prior · e^score), where odds_prior is the population's good:bad base rate. The ROC curve sweeps every possible score cutoff over the whole synthetic population, plotting the true-positive rate (goods correctly approved) against the false-positive rate (bads incorrectly approved) — the area under that curve is the AUC, and Gini = 2·AUC − 1 is the same discrimination measure banks quote in scorecard validation reports.