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Equation 11 · Why Average Success Rate Hides the Failures That Matter Most

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pp

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the success rate. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.

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pp

Symbol p

the success rate.

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The success rate p says nothing at all about the second factor. Two agents can share an identical p of 0.99 while their conditional severity distributions, Pr⁡(C>τ∣failure)\Pr(C > \tau \mid \text{failure}) , differ by orders of magnitude — one agent’s failures cluster near the harmless end of C , the other’s failures put meaningful mass past τ\tau . A leaderboard built entirely on p ranks these two agents identically. An operator who deploys the higher-severity one because its accuracy number looked the same has made a real decision without the information that decision required.

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