Quantify base-rate dilution in CTR

Q: Quantify base-rate dilution in CTR

This question evaluates a candidate's understanding of weighted averages, base-rate (dilution) effects, and algebraic manipulation of proportions when combining differing click-through rates across subpopulations.

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Question

Weighted-Average CTR and Volume Requirements

You are assessing the impact of introducing a new high-CTR event notification into an existing stream of baseline notifications. Overall CTR is the volume-weighted average across notification types.

Baseline (non-event) notification CTR: b = 2.0%
Event notification CTR: e = 20.0%
Baseline volume: N messages
Event volume: k messages

Answer the following:

Write the overall CTR formula.
With N = 9,990 and k = 10, compute the overall CTR and the relative lift vs. baseline. Explain why a 10× CTR on tiny volume yields a negligible overall change.
Derive the minimum share s = k/(N + k) required to achieve at least a 10% relative increase in overall CTR (i.e., C_overall ≥ 1.10·b), in terms of b and e; then plug in b = 2.0%, e = 20.0% to solve for s.
With N fixed at 1,000,000 and a send-budget constraint, solve for the smallest integer k that meets the target from (3).

Quantify base-rate dilution in CTR

Weighted-Average CTR and Volume Requirements

Solution

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Quantify base-rate dilution in CTR

Overview

Weighted-Average CTR and Volume Requirements

Solution

Comments (0)