How Sensitive Are LLM Leaderboard Claims to Hidden Model Selection?

Ranking LLMs via pairwise human feedback underpins current leaderboards for open-ended tasks, such as creative writing and problem-solving. We analyze ~89K comparisons in 116 languages from 52 LLMs from Arena, and show that the best-fit global Bradley-Terry (BT) ranking is misleading. Nearly 2/3 of the decisive votes cancel out, and even the top 50 models according to the global BT ranking are statistically indistinguishable (pairwise win probabilities are at most 0.53 within the top 50 models). We trace this failure to strong, structured heterogeneity of opinions across language, task, and time. Moreover, we find an important characteristic - language plays a key role. Grouping by language (and families) increases the agreement of votes massively, resulting in two orders of magnitude higher spread in the ELO scores (i.e., very consistent rankings). What appears as global noise is in fact a mixture of coherent but conflicting subpopulations. To address such heterogeneity in supervised machine learning, we introduce the framework of $(λ, ν)$-portfolios, which are small sets of models that achieve a prediction error at most $λ$, "covering" at least a $ν$ fraction of users. We formulate this as a variant of the set cover problem and provide guarantees using the VC dimension of the underlying set system. On the Arena data, our algorithms recover just 5 distinct BT rankings that cover over 96% of votes at a modest $λ$, compared to the 21% coverage by the global ranking. We also provide a portfolio of 6 LLMs that cover twice as many votes as the top-6 LLMs from a global ranking. We further construct portfolios for a classification problem on the COMPAS dataset using an ensemble of fairness-regularized classification models and show that these portfolios can be used to detect blind spots in the data, which might be of independent interest to policymakers.

We report a striking statistical regularity in frontier LLM outputs that enables a CPU-only scoring primitive running at 2.6 microseconds per token, with estimated latency up to 100,000$\times$ (five orders of magnitude) below existing sampling-based detectors. Across six contemporary models from five independent vendors, two generation sizes, and five held-out domains, token rank-frequency distributions converge to the same two-parameter Mandelbrot ranking distribution, with 34 of 36 model-by-domain fits exceeding $R^{2} = 0.94$ and 35 of 36 favoring Mandelbrot over Zipf by AIC. The shared family does not collapse the models into statistical duplicates. Fitted Mandelbrot parameters remain cleanly separable between models: the cross-model spread in $q$ (1.63 to 3.69) exceeds its per-model bootstrap standard deviation (0.03 to 0.10) by more than an order of magnitude, yielding tens of standard deviations of separation per few thousand output tokens. Two capabilities follow. First, statistical model fingerprinting: text from a vendor-delivered LLM can be tested against its claimed model family without cryptographic watermarks or access to model internals, supporting provenance verification and silent-substitution audits. Second, a model-agnostic reference distribution for black-box output assessment, from which we derive a single-pass scoring primitive that composes with model log probabilities when available and degrades to a rank-only mode usable on closed APIs. Pilot results on FRANK, TruthfulQA, and HaluEval map where the primitive helps (lexical anomalies, unsupported entities) and where it structurally cannot (reasoning errors in domain-appropriate vocabulary). We position the primitive as a first-pass triage layer in compound evaluation stacks, not as a replacement for sampling-based or source-conditioned verifiers.

Across two public LLM leaderboards, many displayed pairwise rankings do not meet a conventional paired-test resolution target under the actual paired evaluation design: 11 of 40 Open LLM Leaderboard v1 pairwise comparisons and 4 of 9 MMLU-Pro top-10 adjacent-rank pairs are unresolved at (alpha, 1-beta) = (0.05, 0.8). The MMLU-Pro count rises to 6/9 under real subject-level clustering and stays at 5-6 out of 9 in 99.9% of category-bootstrap resamples. We frame paired LLM evaluation as a hypothesis-testing problem, invert level-alpha, power-(1-beta) tests, and report a per-pair resolution ratio q = N/N* as the primary diagnostic. A sharp small-effect expansion with an explicit second-order constant shows that the widely-used unpaired Cohen-h-plus-(1-rho) shortcut deviates from the correct N* by approximately a factor of two in the close-comparison regime, a deficit that three of five off-the-shelf calculators(Cohen 1988, G*Power, R pwr) silently inherit when the user post-multiplies their per-arm output by (1-rho). The unresolved-pair pattern remains under multiplicity correction and anytime-valid sequential testing.