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Equation 5 · Part 2 · A Practitioner's Map of Agent Evaluation Frameworks

=

p^=0.5\hat p = 0.5
=

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

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 fifty-task set — close to the size of tau-bench’s original airline domain or GAIA’s seventy-five-question Level 3 tier — versus roughly ±\pm 4.4 points on SWE-bench Verified’s five hundred tasks, or ±\pm 5.1 points on OSWorld’s 369. A three- or four-point difference between two systems on a fifty- or seventy-five-task slice is, on this generous accounting, close to noise; the…

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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

These citations provide research context; check each source for the exact claim it supports.