Equation 28 · Part 3 · Why Average Success Rate Hides the Failures That Matter Most
superscript
superscript
What this part means
A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.
Its job in the formula
A raised mark can be a power or an index. Its position and the surrounding notation determine which.
Full expression→superscript→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 exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.
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Sources cited in the surrounding passage
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