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It Won Every Part, Then Lost the Total

🏥 Two hospitals' surgery success rates. For mild cases it is A 93% against B 87%; for severe cases A 73% against B 69% — split, A leads in both. Pool them and it becomes A 77%, B 83%: the ranking flips. Not one of the four success rates was touched. All that changed is «who took more of which patients». 🔀 Second, the reason. Severe cases succeed less at either hospital, and 80% of A's patients are severe against only 20% of B's. The pooled number shows that gap, not skill. Set the two shares equal and it can «never» flip — what flips it is not the rates but the mix. 🔍 Third, the judgement. If you are a severe case, read the number for «your own group», not the total. This app was made with code too · Remix it with different shares.