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Equation 3 · Part 8 · How to Evaluate Codex Beyond SWE-bench and Vendor Scores

superscript

p^=1n∑i=1nYi\hat p=\frac{1}{n}\sum_{i=1}^{n}Y_i
superscript

What this part means

A raised number can be a power. When it is a label or bound, it selects a case or the upper limit of a sum; the formula’s structure distinguishes these uses.

Its job in the formula

A raised mark can be a power or an index. Its position and the surrounding notation determine which.

The passage around this formula

Let YiY_i∈\in\{0,1\} indicate whether evaluation task i is resolved. The familiar score p^=1n∑i=1nYi\hat p=\frac{1}{n}\sum_{i=1}^{n}Y_i. is an estimate of success probability only for a distribution represented by those n instances and the evaluated system. The system is not just a model. It includes context retrieval, tools, prompts, retries, execution limits, and candidate selection. The evaluation distribution is not “software engineering.” It is a constructed sample with inclusion criteria, repository mix, languages, issue styles, and executable tests.

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Learn the underlying idea

An exponent tells how a base is used in multiplication. In x³, x is the base and 3 is the exponent: x³ = x × x × x.

Open the illustrated exponents: repeated multiplication and powers guide →

The article lists its research sources here.