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Tune the Blend Weight Between Proxy and Long-Term Value
A team implements $r_{\text{blend}} = \alpha \cdot \hat r_{\text{click}}
- (1-\alpha) \cdot \hat V_{\text{LTV}}$ for a content feed, with both terms rescaled to a comparable 0-100 index. They run an experiment sweeping \alpha \in \{1.0, 0.8, 0.6, 0.4\} across five equal-sized user segments over a 90-day window (one segment held at \alpha=1.0 as the current-production baseline), and observe:
| α | Week-1 CTR index | Month-3 retention |
|---|---|---|
| 1.0 (baseline) | 100 (reference) | 71.0% |
| 0.8 | 97 | 72.4% |
| 0.6 | 93 | 73.6% |
| 0.4 | 86 | 73.8% |
- Describe the shape of this trade-off curve and identify roughly where diminishing returns set in.
- Suppose the product's finance team estimates that each point of month-3 retention is worth $340,000 in aggregate 12-month LTV, and each point of week-1 CTR index below 100 costs an estimated $95,000 in near-term ad/sponsorship revenue (a business that depends partly on click volume). Using these figures, which α would you recommend, and show the math.
- What would make you distrust this experiment's conclusion, and what would you check before committing to the recommended α long-term?
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