Churn-Risk Segmentation to Maximize Expected 90-Day Revenue

You must segment 500,000 users into three contiguous groups along a churn-risk score, ordered from least risky (Q1) to most risky (Q4). Segments must be contiguous along this order and labeled Low (least risky), Medium, High (most risky). The Low segment must include at least 20% of users.

Assumptions

• Users are evenly distributed across quartiles (125,000 per quartile).
• Expected 90-day revenue per user = 3 × Avg_Monthly_Spend × (1 − 90d_Churn_Prob).
• Contiguous means each segment is a consecutive block of quartiles in the order Q1 → Q4.

Data summary by quartile

• Q1 (least risky): Users=125,000; Avg_Monthly_Spend=$40; 90d_Churn_Prob=0.05
• Q2: Users=125,000; Avg_Monthly_Spend=$35; 90d_Churn_Prob=0.10
• Q3: Users=125,000; Avg_Monthly_Spend=$25; 90d_Churn_Prob=0.20
• Q4 (most risky): Users=125,000; Avg_Monthly_Spend=$15; 90d_Churn_Prob=0.40

Tasks

1. Compute the expected 90-day revenue contributed by each quartile.
2. Enumerate all feasible contiguous 3-way partitions (Low, Medium, High) that satisfy Low ≥ 20%, and pick the one that maximizes total expected 90-day revenue in High + Medium (show brief calculations).
3. For your chosen segmentation, report users and expected revenue in each segment and overall.
4. Recommend actions for each segment (offers, experimentation plan), and explain how you would monitor drift that could change optimal cut points.