Equation 9 · Part 2 · Measuring AI Agent Reliability: What the Evidence Actually Supports
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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.
Full expression→=→Article meaning
The passage around this formula
That combinatorial form is the unbiased estimator: it uses every one of the n observed outcomes rather than discarding some of them, and it has materially lower variance than the intuitive shortcut of raising a single measured success rate to a power. The paper is explicit that the naive alternative is biased, not merely noisier, so the difference is not a technicality — using the wrong formula changes which system looks better [ 2 ] . With n=100 samples per problem, their Codex model solved 70.2% of HumanEval problems by this best-of-many-samples criterion, against 28.8% at pass@1 [ 2 ] . That gap is not a measurement error. It is the honest size of the difference between “can this model…
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 surrounding passage
These citations provide research context; check each source for the exact claim it supports.