💳 Credit Scoring Model — Scorecard Builder Live

PDO defines how many score points correspond to a doubling of the good:bad odds ratio — for example, if PDO = 20 and a score of 600 corresponds to 50:1 odds, then a score of 620 corresponds to 100:1 odds and a score of 580 corresponds to 25:1 odds. Twenty points per doubling is a long-standing industry convention (used by FICO-style bureau scores) because it produces a scale that spreads scores widely enough to be visually and operationally meaningful across a 300–850 range, without being so steep that small model changes swing scores wildly or so flat that the scale loses discrimination.

A cutoff of 850 (approve almost nobody) drives the default rate among approvals toward zero, but it also rejects thousands of pounds of profitable good accounts, so total profit is low. As the cutoff falls, more marginal-but-still-profitable good accounts get approved, each adding positive expected margin, and profit keeps rising even though the default rate among approvals is creeping up — because losing money on a few extra bad accounts is outweighed by the interest earned on many more good ones. Past some point the marginal accounts being let in are bad often enough that their expected losses exceed the margin earned on the marginal goods, and profit turns down even though the default rate keeps climbing. The profit-maximising cutoff sits at the point where marginal expected margin equals marginal expected loss — a genuinely different criterion from minimising the raw default rate.

Each synthetic applicant's true default outcome is drawn as a Bernoulli trial from a ground-truth logistic function of income, DTI ratio, payment history and utilisation, plus independent random noise — so the population has a genuinely knowable, if hidden, risk relationship that the trained scorecard is trying to recover. Real banks instead observe defaults only among accounts that were actually approved and funded; applicants who were rejected never generate a repayment outcome at all. That gap is called reject inference, and it means production scorecards are always trained on a selectively observed sample, never the full applicant population the way this simulation's ground truth is generated.

Adverse selection describes how the mix of applicants who actually accept a loan offer can shift with price and cutoff — for instance, if a lender raises its interest rate to protect margin at a given cutoff, safer applicants with better outside options may walk away while riskier applicants with fewer alternatives still accept, quietly raising the true default rate of whoever remains. This simulation holds the applicant population fixed and only changes who is approved, which isolates the scorecard mechanics (points, cutoff, approval/default/profit trade-offs) cleanly, but it deliberately does not model applicants declining an offer — a real portfolio manager has to reason about both effects at once, and conflating them would make the core scorecard lesson harder to see.

The model-quality control scales how strongly the four features actually separate good and bad applicants in the ground-truth generator, before any training happens. A higher-quality population has less overlap between the good and bad score distributions, so the same trained scorecard achieves a lower default rate at any given approval rate — the whole profit curve lifts and its peak becomes sharper and more forgiving, because there is more genuine signal for the logistic regression to exploit. A lower-quality population squeezes the good and bad distributions together, so no cutoff can cleanly separate them and every point on the approval/default/profit trade-off gets worse simultaneously — this mirrors how, in practice, richer or cleaner applicant data produces a materially better scorecard, not just a relabelled one.