A retention offer costs $50 and, if given to a true churner, saves a customer worth $600 (net of the offer). Given to a loyal customer it is wasted. The model's probability for a customer is p.
At what probability threshold does contacting a customer break even?
Why did you pick that answer? Two or three sentences. The act of articulating it is what builds the judgment — not the click that follows.
Expected value of contacting = p × 600 − (1 − p) × 50. Setting it to zero: 600p = 50 − 50p → 650p = 50 → p ≈ 0.077. Because a saved customer is worth 12 times the offer, it pays to contact anyone with even an 8% chance of leaving. The 0.5 default would leave most of the profit on the table — this is the whole point of tuning the threshold to the cost matrix.
0.5 is only break-even when both mistakes cost the same. Here a missed churner costs 12× a wasted offer.
That reasoning fits when the offer is expensive relative to the save. Here the save dwarfs the offer, so the bar drops, not rises.
There is no reason to multiply the break-even by 0.5. The equation p × 600 = (1 − p) × 50 has a single solution.