The Judge Knows When It Knows: Calibrated Abstention for LLM-Based A/B-Test Prediction

Abstract

Can a multimodal LLM predict which version of a web page will win a real A/B test from screenshots alone? We report the most complete answer we are aware of, from six weeks of pre-registered experiments on real conversion tests: mostly no -- and the exceptions are identifiable in advance. On 330 real A/B tests a Gemini 3 Flash judge reaches Cohen's kappa = 0.14, but on the trustworthy (statistically significant) half of the labels the evidence is inconclusive (kappa = 0.11, CI includes zero). We show that 44% of the "ground-truth" labels in a leading CRO agency's catalog come from non-significant tests, and that the judge agrees more with the unreliable labels than the reliable ones -- a shared prior between labeler and model, not prediction. Every standard improvement lever (a 2.8x more expensive frontier model, prompt redesign, stimulus fidelity, change-type priors) fails its pre-registered gate. The judge's confident calls are different: a vote-margin gate isolates a subset (49% coverage) reaching kappa = 0.31 on significant labels. We measure the mechanism directly -- judges differing in model or prompt agree with each other at kappa = 0.74-0.88 while agreeing with real outcomes at only ~0.2, so a 16-vote panel carries about 2 effective independent votes -- and we reproduce it in humans: 15 CRO experts agree with each other (inter-rater kappa = 0.53) but score at chance against real outcomes (kappa ~ 0). Consensus, human or model, is reproducible, persuasive, and not evidence. We release our pre-registrations, locked gates, negative results, statistical harness, human responses, and a claims ledger in which every number carries an evidence tier.