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Equation 5 · Part 2 · Why Average Success Rate Hides the Failures That Matter Most

Symbol τ

qτ=Pr⁡(failure and severity>τ)=(1−p)⋅Pr⁡(C>τ∣failure)q_\tau = \Pr(\text{failure and severity} > \tau) = (1-p)\cdot \Pr(C > \tau \mid \text{failure})
τ\tau

What this part means

τ is part of the quantity the equation computes from the expression on the right.

Its job in the formula

τ is part of the quantity the equation computes from the expression on the right.

The passage around this formula

…be a random quantity C ≥\geq 0 describing how bad a given failure turns out to be, conditional on failure occurring. The probability that a given run produces a failure whose severity clears some consequential threshold τ\tau — a deleted database rather than a clumsy sentence — is qτ=Pr⁡(failure and severity>τ)=(1−p)⋅Pr⁡(C>τ∣failure)q_\tau = \Pr(\text{failure and severity} > \tau) = (1-p)\cdot \Pr(C > \tau \mid \text{failure}). 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…

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Learn the underlying idea

A variable is a named place for a value. Its letter is a local label: x can mean position in one formula and a data point in another.

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Sources cited in the article section

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