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Published equation contexts

Pr⁡(C>τ∣failure)\Pr(C > \tau \mid \text{failure})

Why this formula appears here

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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CC

Symbol C

C is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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τ\tau

Symbol τ

τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.

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Pr⁡\Pr

Probability operator

The probability operator gives the chance of the event named inside its brackets or parentheses.

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Published contexts (1)

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Pr⁡(C>τ∣failure)\Pr(C > \tau \mid \text{failure})

Equation 8 · Model Evaluation

Why Average Success Rate Hides the Failures That Matter Most

This equation states a bound: one expression must stay on the indicated side of the other under the article’s assumptions.

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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