Context

StreamBox uses a binary classification model to predict which subscribers are likely to cancel in the next 30 days. Customers above a score threshold receive a retention offer worth $8, but unnecessary offers reduce margin, so the team wants to tune the decision threshold rather than retrain the model.

Current Performance

Validation set size: 20,000 users. Positive class = churn. Current threshold = 0.50.

The Problem

The marketing lead is asking why the team should change the threshold if the model itself has not changed. They also want to know which threshold best balances churn prevention against offer cost.

Requirements

1. Explain threshold tuning in plain language and why it changes model behavior without retraining.
2. Interpret the precision-recall tradeoff across the three thresholds.
3. Recommend the best threshold for this retention use case and justify it.
4. Use the confusion matrix counts to explain the business impact of false positives vs. false negatives.
5. Describe how you would validate the chosen threshold before full rollout.

Constraints

• Monthly retention budget supports at most 2,500 offers.
• Estimated value of saving a true churner: $45.
• Cost of sending an unnecessary offer: $8.
• The model score is already calibrated well enough for ranking users.