Where Variance Comes From in LLM Evaluation

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When the same model gets a different score on a second run, the difference is not a mystery. It comes from several identifiable sources, and separating them tells you where to spend your effort.

Question sampling

A benchmark contains only a sample of the questions you could have asked. A different sample of similar questions would give a different score. This is usually the largest source of variance, and it shrinks only by adding more items.

Generation randomness

If the model samples its output with a non-zero temperature, repeated runs on the same prompt can produce different answers. Fixing a random seed makes a run repeatable, but it hides the variability rather than removing it. Running several samples per question and averaging reveals how much of the score is luck.

Prompt and format choices

Small changes to wording, example order, answer format, or whitespace can shift scores. If you only try one prompt, you do not know how sensitive the result is.

Grader noise

Automatic answer matching can misjudge correct answers that are phrased differently. Human raters disagree with each other, and model-based judges add their own inconsistency.

Infrastructure effects

Different hardware, numeric precision, batching, or library versions can change outputs slightly, even with the same settings.

A decomposition mindset

Treat the total variance as a sum of components. Estimate each one with simple experiments: rerun with different seeds, rephrase prompts, and re-grade a subset.

Why it matters

Knowing the dominant source tells you the remedy. More questions reduce sampling variance. Multiple samples reduce generation noise. Better graders reduce measurement noise. Without that diagnosis, extra runs may not help.

Continue with the book

Explore the full treatment, worked examples, and exercises in Statistical Foundations for LLM Development and Evaluation.