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Equation 5 · Part 3 · Measuring Claude Code and Agentic Development Tools: Evidence, Benchmarks, and Uncertainty

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

The passage around this formula

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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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 article section

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