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Equation 8 · Part 3 · Why Average Success Rate Hides the Failures That Matter Most

Probability operator

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

What this part means

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

Its job in the formula

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

The passage around this formula

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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Learn the underlying idea

Probability assigns a number from 0 to 1 to an event under a stated model. Zero means impossible within that model; one means certain.

Open the illustrated probability: a quantified chance guide →

Sources cited in the article section

These citations provide research context; check each source for the exact claim it supports.