Diagnose profit drop via mix decomposition

Quick Overview

The question evaluates a data scientist's competency in profit decomposition, attribution, experiment design, and diagnostic dashboarding within the Analytics & Experimentation domain.

Diagnose profit drop via mix decomposition

Company: Capital One

Role: Data Scientist

Category: Analytics & Experimentation

Difficulty: hard

Interview Round: Technical Screen

Using the scenarios from the previous question, profit falls in the mixed day despite more tables (25 vs 20) and higher average spend ($36 vs $30). 1) Decompose the change in daily profit into volume effect, spend effect, and mix effect. Use a stepwise counterfactual: (a) Start from baseline (20 tables, $30, no coupons), (b) change only tables to 25, (c) change only spend to $36, (d) finally apply the observed mix (10/25 coupon tables). Quantify each step’s contribution and verify the final profit difference. 2) Attribute the loss primarily to which factor(s) and justify with numbers. 3) Design an experiment to measure cannibalization and long-term value of coupon customers: specify randomization unit (e.g., day-of-week or ZIP-level holdout), treatment(s) (discount depth, commission, minimum spend), primary metric (daily contribution margin), guardrails (utilization, service time), and sample-size or duration assumptions. 4) Propose a diagnostic dashboard: which daily KPIs and derived ratios would you track to prevent this surprise in the future?

Quick Answer: The question evaluates a data scientist's competency in profit decomposition, attribution, experiment design, and diagnostic dashboarding within the Analytics & Experimentation domain.

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Capital One
Oct 13, 2025, 9:49 PM
hardData ScientistTechnical ScreenAnalytics & Experimentation
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Profit Decomposition, Attribution, Experiment Design, and Diagnostics

Context and Assumptions (to make the task self-contained)

We analyze why daily profit fell on a “mixed” coupon day even though the restaurant had more tables and higher average spend per table. We define daily profit as contribution margin = net revenue after discounts/commissions minus variable costs, ignoring fixed costs.

Assumptions (typical coupon economics; adjust if your prior scenario differs):

  • Variable cost rate (food + variable labor) = 40% of gross spend.
  • Non-coupon table revenue = 100% of gross spend.
  • Coupon economics: customer receives 50% off; the platform takes 20% commission on the discounted amount. Net to the restaurant = 0.5 × (1 − 0.20) = 40% of gross spend.
  • Baseline day: 20 tables, average gross spend $30, no coupons.
  • Mixed day: 25 tables, average gross spend $36, with 10/25 coupon tables.

Tasks

  1. Decompose the change in daily profit into volume effect, spend effect, and mix effect using a stepwise counterfactual:
    • (a) Baseline: 20 tables, $30, no coupons
    • (b) Change only tables to 25 (keep $30, no coupons)
    • (c) Change only spend to $36 (25 tables, no coupons)
    • (d) Apply observed mix: 10/25 coupon tables at $36 Quantify each step’s contribution and verify the final profit difference.
  2. Attribute the loss primarily to which factor(s) with numeric justification.
  3. Design an experiment to measure cannibalization and long-term value of coupon customers. Specify:
    • Randomization unit (e.g., day-of-week within store, ZIP-level or DMA holdout)
    • Treatments (e.g., discount depth, commission share, minimum spend, new-customer-only)
    • Primary metric (e.g., daily contribution margin), guardrails (e.g., utilization, service time), and sample-size/duration assumptions.
  4. Propose a diagnostic dashboard: daily KPIs and derived ratios to catch issues early and prevent future surprises.
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