Equation 5 · Part 7 · Measuring Claude Code and Agentic Development Tools: Evidence, Benchmarks, and Uncertainty
Numerator: 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.
Full expression→Numerator: hat p (1 - hat p)→Article meaning
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 is . For n = 500 and 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…
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.
Open the illustrated fractions: division written vertically guide →
Sources cited in the article section
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