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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%
  1. Describe the shape of this trade-off curve and identify roughly where diminishing returns set in.
  2. 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.
  3. 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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