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Equation 26 · Part 2 · Why Average Success Rate Hides the Failures That Matter Most

Symbol k

n≈kqτn \approx \frac{k}{q_\tau}
kk

What this part means

k occurs above the fraction bar. The numerator is divided by the entire denominator below it.

Its job in the formula

k occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

​ , so getting a usably precise estimate — a relative error in the neighbourhood of 20 to 25 percent, comparable to observing on the order of twenty events — requires n≈kqτn \approx \frac{k}{q_\tau}. trials in total. This is where the arithmetic becomes unforgiving in a way the mean-difference case never does. Detecting a fixed three-percentage-point difference between two average success rates takes roughly the same, bounded number of trials — on the order of a thousand — regardless of how good either system actually is, because that calculation is about the spread of a difference, not the rarity of an event. Bounding or estimating a rare catastrophic-failure rate is different in kind: the required…

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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 surrounding passage

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