Equation 29 · Why Average Success Rate Hides the Failures That Matter Most
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.
Read it piece by piece
Symbol n
n is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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 q_τ
q_τ is a part of this expression. Its role is fixed by the surrounding article and by the operations shown in the formula.
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
State the sample size the claim actually requires. If a system is being represented as safe at a given tail probability, report the number of trials run and compare it explicitly against the n k/ threshold needed to have observed the claimed rate with any precision, rather than letting a comfortable-sounding trial count stand in for a rate that would in fact require orders of magnitude more observations.
Sources cited in the article section
- [8] LLM06:2025 Excessive Agency ↗
- [2] Rigorous Agent Evaluation: An Adversarial Approach to Uncover Catastrophic Failures ↗
- [9] Artificial Intelligence Risk Management Framework: Generative Artificial Intelligence Profile (NIST AI 600-1) ↗
These citations give research context. Read each source to check which claims it supports.
Return to Why Average Success Rate Hides the Failures That Matter Most