Equation 28 · Part 2 · Why Average Success Rate Hides the Failures That Matter Most
=
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What this part means
The expressions on both sides represent the same quantity under the stated assumptions.
Its job in the formula
The equals sign connects the complete expression on the left with the complete expression on the right. Both sides must have compatible units.
Full expression→=→Article meaning
The passage around this formula
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 sample size is inversely proportional to the rate itself. At = 10^{-3} , getting even a rough twenty-event estimate needs on the order of twenty thousand trials. At = 10^{-5} —…
Learn the underlying idea
An equals sign says that the expression on its left and the expression on its right have the same value under the stated definitions and assumptions.
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Sources cited in the surrounding passage
These citations provide research context; check each source for the exact claim it supports.