Exercise 3: Why Lowering the Threshold Trades Precision for Recall, and Why It's a Business Decision — Possible Solution ==================================================================== WHAT THE THRESHOLD ACTUALLY CONTROLS, PER ml1-5 AND THIS CHAPTER ------------------------------ Per ml1-5, a threshold (commonly 0.5) converts the model's own predicted probability into a Yes/No decision — probability above the threshold predicts "Yes" (will leave), below predicts "No." Lowering the threshold means a SMALLER predicted probability is now enough to trigger a "Yes" (at-risk) prediction than before. WHY LOWERING THE THRESHOLD RAISES RECALL ------------------------------ Per this chapter, "Recall = True Positives ÷ (True Positives + False Negatives)." Lowering the threshold means more employees overall get flagged as "Yes," including some who previously fell just below the old threshold. Among the real, actual leavers, some of those who were previously being missed (predicted "No" because their probability sat between the new, lower threshold and the old, higher one) will now be correctly flagged as "Yes" — directly reducing the number of False Negatives among real leavers, which per the recall formula directly raises recall, since fewer real leavers are being missed. WHY LOWERING THE THRESHOLD LOWERS PRECISION ------------------------------ Per this chapter, "Precision = True Positives ÷ (True Positives + False Positives)." The same threshold change that catches more real leavers also causes more employees who were NEVER actually going to leave to get flagged as "Yes" as well, since the lower bar for a "Yes" prediction doesn't distinguish between genuine at-risk employees and employees who simply happen to have a moderately elevated (but not truly high) predicted probability. This increases the number of False Positives, which per the precision formula directly lowers precision, since a smaller proportion of all "Yes" flags are now genuinely correct. WHY BOTH EFFECTS HAPPEN TOGETHER, MECHANICALLY ------------------------------ Both effects follow from the exact same single change — more employees crossing the "Yes" line overall. Some of those newly-flagged employees are real leavers who were previously missed (helping recall); some are not real leavers at all (hurting precision). There's no way to expand who gets flagged without picking up both kinds of new cases at once, which is precisely why the tradeoff is inherent to adjusting the threshold, not something that can be avoided by choosing the "right" lower value. WHY THE CHAPTER FRAMES THE ACTUAL CHOICE AS A BUSINESS DECISION ------------------------------ Per this chapter, a real deployment "might deliberately lower the threshold below 0.5, accepting more false alarms in exchange for catching more genuine flight risks — a business decision the metrics inform but don't make automatically." The metrics themselves (precision and recall at any given threshold) are purely descriptive — they report what happens at that setting, but choosing WHICH threshold is "correct" requires weighing the real-world cost of a False Negative (a lost employee, per Exercise 2) against the real-world cost of a False Positive (an unnecessary conversation) — a judgment about actual business costs that the model and its metrics can inform but have no way to resolve on their own. WHY THIS WORKS AS AN ANSWER ------------------------------ It traces exactly how lowering the threshold mechanically shifts cases into and out of each confusion-matrix category, explains why this necessarily raises recall while lowering precision at the same time, and explains why the chapter treats picking the specific threshold as a business judgment rather than a metric the model itself determines.