Equation 10 · How Benchmark Contamination Actually Works in Agentic Evaluation
What does this equation mean?
Read the formula alongside the article passage below. Each part has a deeper page with its role in the equation, the supporting passage and nearby citations.
This equation gives an approximation: it relates the quantities while allowing an approximation. Read the equation part by part below; each part has a contextual explanation and a link to its mathematical background.
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Symbol k
k is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
Symbol p^k
is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
superscript
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.
See an illustrated explanation →How to interpret it
Its accuracy depends on the assumptions and range of use described in the article.
What the article says around this equation
averaged over tasks to produce the benchmark’s headline number. The metric is designed to punish an agent whose competence is real but inconsistent across resampled trials — a stochastic policy with true per-trial success probability p has , which falls quickly as k grows. But a policy whose output on a given task is deterministic — an empty response, always, regardless of sampling — produces the identical transcript on every trial, so
Sources cited in the article section
- [8] Establishing Best Practices for Building Rigorous Agentic Benchmarks ↗
- [7] τ-bench: A Benchmark for Tool-Agent-User Interaction in Real-World Domains ↗
- [9] Saving SWE-Bench: A Benchmark Mutation Approach for Realistic Agent Evaluation ↗
These citations give research context. Read each source to check which claims it supports.
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