Reading an LLM judge's verdict from the logits of its first generated token is cheap, requires no generation, and is exactly what constrained decoding and likelihood-scoring evaluation harnesses produce.
We show that this readout distorts position bias in one direction: it overstates it in every condition we test, so figures obtained this way behave as upper bounds.
The mechanism is that judges do not always lead with a verdict token, on 12% to 49% of pairs for three Qwen3 judges and under 3% for Llama-3.1-8B and Phi-3.5-mini, and forcing a read on those pairs returns whichever response was shown first rather than a judgment.
Pooled over the 924 pairs where a judge did not commit, the forced read flips on 89.7% of them when the responses are swapped, against 47.5% read after generation (paired difference +0.422, 95% CI [+0.365, +0.467]).
The distortion is specific to what is measured: it moves position bias by 42 points while moving judge accuracy by under one point in seven of ten conditions, so it misleads whoever audits a judge rather than whoever uses one.
A second, smaller failure occurs even when the judge does lead with a verdict token, since it sometimes opens with one letter and reasons its way to the other, on 0 to 5.5% of pairs at a rate uncorrelated with compliance.
We recommend reporting the rate at which a judge leads with a verdict token, which costs one forward pass and no labels, alongside any position-bias figure.