Recent research has shown that large language models (LLMs) favor their own outputs when acting as judges, undermining the integrity of automated post-training and evaluation workflows. However, it is difficult to disentangle which evaluation biases are explained by narcissism versus general experimental confounds, distorting measurements of self-preference bias. We discover a core methodological confound which could reduce measurement error by 89.6%. Specifically, LLM evaluators may deliver self-preferring verdicts when the judge responds to queries which they completed incorrectly themselves; this would be true regardless of whether one of their responses is their own. To decouple self-preference signals from noisy outputs on hard problems, we introduce an Evaluator Quality Baseline, which compares the probability that a judge incorrectly votes for itself against the probability that it votes for an incorrect response from another model. Evaluating this simple baseline on 37,448 queries, only 51% of initial findings retain statistical significance. Finally, we turn towards characterizing the entropy of "easy" versus "hard" evaluation votes from LLM judges. Our corrective baseline enables future research on self-preference by eliminating noisy data from potential solutions. More widely, this work contributes to the growing body of work on cataloging and isolating judge-bias effects.