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Equation 14 · Part 6 · How to Actually Compare Frontier AI Models Without Building a Misleading Leaderboard

Numerator: hat p (1-hat p)

SE(p^)≈p^(1−p^)n,\mathrm{SE}(\hat p) \approx \sqrt{\frac{\hat p (1-\hat p)}{n}},
p^(1−p^)\hat p (1-\hat p)

What this part means

The complete quantity above the fraction bar.

Its job in the formula

hat p (1-hat p) occurs above the fraction bar. The numerator is divided by the entire denominator below it.

The passage around this formula

Reported variance, not a bare point estimate. A score computed from n independent trials with an underlying success probability p^\hat p carries a standard error of roughly SE(p^)≈p^(1−p^)n\mathrm{SE}(\hat p) \approx \sqrt{\frac{\hat p (1-\hat p)}{n}}. and two point estimates whose intervals overlap should not be reported as a ranking. Evan Miller’s statistical treatment of language-model evaluation makes this argument in more general form, framing individual evaluation questions as draws from an unseen larger population and deriving the formulas needed to report genuine uncertainty rather than a single noisy number [ 1 ] . Epoch AI’s benchmarking hub applies the same discipline operationally: it runs each model sixteen times on GPQA Diamond and Mock…

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Learn the underlying idea

A fraction a/b means a divided by b. The top number is the numerator; the bottom number is the denominator, and it cannot be zero.

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Sources cited in the surrounding passage

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