Do Repetitions Matter? Strengthening Reliability in LLM Evaluations

LLM leaderboards often rely on single stochastic runs, but how many repetitions are required for reliable conclusions remains unclear. We re-evaluate eight state-of-the-art models on the AI4Math Benchmark with three independent runs per setting. Using mixed-effects logistic regression, domain-level marginal means, rank-instability analysis, and run-to-run reliability, we assessed the value of additional repetitions. Our findings shows that Single-run leaderboards are brittle: 10/12 slices (83%) invert at least one pairwise rank relative to the three-run majority, despite a zero sign-flip rate for pairwise significance and moderate overall interclass correlation. Averaging runs yields modest SE shrinkage (~5% from one to three) but large ranking gains; two runs remove ~83% of single-run inversions. We provide cost-aware guidance for practitioners: treat evaluation as an experiment, report uncertainty, and use ≥ 2 repetitions under stochastic decoding. These practices improve robustness while remaining feasible for small teams and help align model comparisons with real-world reliability.