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Published equation contexts

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

Why this formula appears here

That instability is worth making precise rather than gesturing at. If a benchmark of n instances is treated as n independent Bernoulli trials with true resolve probability p , the standard error of the observed proportion p^\hat p is SE(p^)=p^(1−p^)n\mathrm{SE}(\hat p) = \sqrt{\frac{\hat p (1 - \hat p)}{n}}. For n = 500 and p^\hat p near one half, this is on the order of two percentage points — before accounting for the additional variance introduced by sampling temperature, agentic scaffolding, or a different number of retries per problem. A published gap of four or five points between two systems evaluated under different harnesses, different reasoning-effort settings, and different retry budgets is not obviously a capability gap at all; it may be…

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nn

Symbol n

n occurs below the fraction bar. The quantity above the bar is divided by this expression; zero is excluded as a denominator.

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With a fixed numerator, increasing a nonzero denominator reduces the fraction. Read it with the definitions, units, and assumptions supplied by the article.

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Published contexts (1)

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SE(p^)=p^(1−p^)n.\mathrm{SE}(\hat p) = \sqrt{\frac{\hat p (1 - \hat p)}{n}}.

Equation 5 · AI Agents & Systems

Measuring Claude Code and Agentic Development Tools: Evidence, Benchmarks, and Uncertainty

This equation states an equality: the expressions on both sides have the same value under the article’s assumptions.

That instability is worth making precise rather than gesturing at. If a benchmark of n instances is treated as n independent Bernoulli trials with true resolve probability p , the standard error of the observed proportion p^\hat p is SE(p^)=p^(1−p^)n\mathrm{SE}(\hat p) = \sqrt{\frac{\hat p (1 - \hat p)}{n}}. For n = 500 and p^\hat p near one half, this is on the order of two percentage points — before accounting for the additional variance introduced by sampling temperature, agentic scaffolding, or a different number of retries per problem. A published gap of four or five points between two systems evaluated under different harnesses, different reasoning-effort settings, and different retry budgets is not obviously a capability gap at all; it may be…

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