ReasonBENCH: Benchmarking the (In)Stability of LLM Reasoning

Abstract

Benchmark scores for LLM reasoning systems are reported as single numbers, yet the same model, strategy, and task can produce meaningfully different answers and costs across repeated executions, even under greedy decoding (T = 0). This variance is not a statistical nuisance: the highest-performing strategy wins only 77% of head-to-head runs against its nearest competitor, meaning a single observed score can silently misrank systems. We introduce ReasonBench, a benchmark suite recording 30 independent trials across 10 reasoning strategies, 12 models, and 6 tasks, treating quality and cost as distributions rather than point estimates. We find that this variance is structured rather than random: a two-component taxonomy -- Global Noise, capturing cross-benchmark unevenness, and Run Noise, capturing within-benchmark stochasticity -- reveals that strategy architecture predicts stability profiles, while models and strategies shift orthogonal aspects of the distribution. A hierarchical decomposition attributes three-quarters of score variance to benchmark, system, and item structure, with a persistent residual that single-run evaluation silently absorbs. Finally, cost and quality decouple asymmetrically: cheap methods are structurally immune to joint cost-quality failure, while expensive methods remain exposed regardless of their accuracy. These findings establish instability as an inherent property of reasoning systems and motivate distribution-aware evaluation as standard practice.