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Equation 3 · Part 6 · A Practitioner's Map of Agent Evaluation Frameworks

subscript

p^  ±  zα/2p^(1−p^)n,\hat p \; \pm \; z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}},
subscript

What this part means

The lower label selects a particular version, component, or indexed member of the quantity. For example, x₀ and xₜ can be values at different positions.

Its job in the formula

A subscript distinguishes a version, component, step, or member of a quantity. It does not automatically mean multiplication.

The passage around this formula

The second argument is about how much any one number can actually tell you, independent of harness effects, purely from how many tasks produced it. Treat a benchmark’s headline pass rate as an estimate p^\hat p of a task-set success probability, drawn from n roughly independent trials. The familiar normal approximation to a binomial confidence interval, p^  ±  zα/2p^(1−p^)n\hat p \; \pm \; z_{\alpha/2}\sqrt{\frac{\hat p (1-\hat p)}{n}}. gives a rough sense of how much noise sits under a given n , even granting the generous and almost certainly false assumption that every task in the set is an equally difficult coin flip. At the widest plausible spread, p^\hat p = 0.5 , a 95% interval ( zα/2z_{\alpha/2} ≈\approx 1.96 ) works out to roughly ±\pm 13.9 points on a…

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Learn the underlying idea

A subscript is a label attached below a symbol. It often selects a time step, component, category, or member of a sequence.

Open the illustrated subscripts: which member of a family? guide →

Sources cited in the article section

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