Exercise 2: The Midpoint Reporting Rate — Possible Solution ==================================================================== RESULTS ------------------------------ rate=0.30: avg reported=1.22, avg unreported=2.78 (chapter's own blame-focused) rate=0.55: avg reported=2.19, avg unreported=1.81 (midpoint) rate=0.80: avg reported=3.22, avg unreported=0.78 (chapter's own blameless) IS THE RELATIONSHIP LINEAR? ------------------------------ Yes, and this is provable directly rather than just observed: each of the 4 real issues is reported independently with probability equal to the reporting rate, so the expected number reported is exactly rate * 4. Checking: 0.3*4=1.2, 0.55*4=2.2, 0.8*4=3.2 - all three match the simulated averages closely (small differences are ordinary sampling noise from a finite number of trials). The midpoint reporting rate (0.55) produces almost exactly the midpoint result between the two extremes (2.19 is close to the midpoint of 1.22 and 3.22, which is 2.22). WHY THIS WORKS AS AN ANSWER ------------------------------ This is a useful confirmation that the reporting-rate relationship is genuinely simple - a straight line, not some threshold effect or diminishing-returns curve. That matters practically: a team that only partially fixes its blame culture (moving from a fully blame-focused 0.3 to a "mostly blameless" 0.55, say) should expect a proportional, not a token, improvement - roughly halfway between the two extremes' own outcomes, not a small nudge. There's no hidden threshold a team needs to cross before psychological safety starts paying off; every increment of improvement contributes its own proportional share.