Ask Which, Not How Good: Sizing Benchmarks Scored by an LLM

Benchmarks scored by an LLM judge routinely adjudicate differences of a tenth of a point, but the resolution of those benchmarks has never been measured. Existing sample-complexity work covers accuracy benchmarks and leaves the judged case open. Treating the system as the object of measurement, we decompose 373,019 judgments into system, item, judge and interaction components using generalizability theory. The central result is structural: under a single judge, generalizability asymptotes to sigma2_s/(sigma2_s+sigma2_sj) regardless of item count, because the system-by-judge term carries no n_i. Items saturate; judges do not. The item cost of a target diverges as the target nears that ceiling. The ceiling is a property of pointwise rubric scoring, not of LLM judging. Run as a pairwise preference in both presentation orders, sigma2_sj falls two orders of magnitude below sigma2_s and the ceiling rises to 0.986 (bootstrap [0.934, 1.000] on 11 systems), so one judge suffices. Pairwise buys a different problem: a system presented first wins 8.6 percentage points more often than the same system presented second, a bias 1.23x the median improvement claimed in the 53 published win-rate comparisons we recovered. Protocol design dominates panel size. Measured floors are 0.41-1.24 points on a 0-5 scale at native item counts, against a median reported improvement of 0.28 points; on the one benchmark recurring often enough for an exactly matched comparison, all 17 recovered MT-Bench improvements fall below MT-Bench's own floor, and 70% of the win-rate claims fall below the pairwise floor. An audit of 628 arXiv papers, double-coded by two independent models and validated against blind human coding (kappa=0.73), finds fewer than one paper in four states whether its evaluation was run more than once, and only 46-67% report uncertainty of any kind.