A benchmark score looks like a fact about a model. Statistically, it is an estimate of an underlying quantity, and treating it that way changes how you read results.
What a score actually measures
Suppose a model answers 78 of 100 questions correctly. The number 78% is not the model's true ability. It is the result of one sample of questions, one set of prompts, and one run of a sampling process. A different sample would likely produce a different number.
The quantity of interest
Define what you want to know: the model's expected accuracy over a population of tasks you care about. The benchmark is a finite sample from that population, and the score is an estimator of the population mean.
Sources of uncertainty
- Which questions were chosen.
- Randomness in generation, such as sampling temperature and seed.
- Prompt wording and formatting.
- Grader noise, whether from humans or automated judges.
Why it matters
Two models scoring 78% and 80% may be statistically indistinguishable. Treating small differences as real can lead to wrong decisions about which model to ship or which training change helped.
A good first habit
Whenever you report a score, report the number of items and some measure of uncertainty, and say what population you are trying to generalize to. That single step makes evaluation claims far more honest.
Continue with the book
Explore the full treatment, worked examples, and exercises in Statistical Foundations for LLM Development and Evaluation.
Adapted from Statistical Foundations for LLM Development and Evaluation, published by Choral Software. Article text and original examples © 2026 Choral Software. All rights reserved.