question:
What is the average CTR lift from our recommendations?

datasets:
- shaped_events_daily.csv (300 rows): Daily A/B test metrics with event_date, customer_id, variant (shaped/control), raw_impressions, raw_clicks, clean_impressions, clean_clicks
- shaped_customers.csv (5 rows): Customer master with customer_id, customer_name, vertical, catalog_size, avg_daily_events, onboarding_date

expected answer:
Average CTR lift across all customers: +31.0% (impression-weighted). CTR must be computed from clean_clicks/clean_impressions (NOT raw metrics which include bot traffic). Lift = (shaped_ctr - control_ctr) / control_ctr.

CTR lift by vertical: E-Commerce +34.2% (top performer), Media +27.1%, Marketplace +22.6%.

Why E-Commerce outperforms: E-Commerce has significantly larger catalog size (avg 500K items vs 78.5K for Media and 45K for Marketplace) and higher data volume (avg 145K daily events vs 91.5K for Media and 52K for Marketplace). More data enables better personalization.

Baseline CTR per vertical (control variant): E-Commerce 2.15%, Media 1.77%, Marketplace 1.49%.

Excluding top performer (E-Commerce): Average lift is +26.3% across Media and Marketplace verticals.
