Large Language Model judges are widely used to rank texts and text-generating systems through pairwise comparison, and their reliability is typically assessed via three proxies: position bias, transitivity, and pairwise agreement (self- or human-labeled).
Because these proxies drive judge selection and benchmarking, a substantial literature reporting that judges perform poorly on them risks steering practitioners away from otherwise capable evaluators.
We argue this assessment is misleading.
Under the Bradley--Terry geometry underlying pairwise aggregation, each proxy is dominated by close-rank-gap pairs, where inconsistency is information-theoretically expected and individual verdicts contribute little to the aggregate ranking; far-gap pairs carry the ranking signal but barely move the proxies.
We formalize this argument and validate it in a controlled simulation and on two human-rated corpora: the proxies correlate only weakly with ranking accuracy against gold, and their predictive component concentrates in the far-gap regime.
Judges should therefore be assessed on rank-gap-conditional metrics, ideally against human rankings.