Various imagined criminal law cases provoke the intuition that there is something wanting with statistical evidence in the courtroom. The cases are extreme in that they involve “naked statistical proof”, where the proposed guilty verdict rests more or less entirely on a single statistical finding. The intuition is that there is something missing in these cases, high as the probability of guilt may be, such that legal proof of guilt is not achieved. Here we contribute to the considerable debate about how this “anti-statistics” intuition is best vindicated, or otherwise explained. We offer a new proposal: We claim that naked statistical proofs are rejected because they are perceived to be based on less than the total available evidence, in a subjective sense that we make precise. So the evidence is inadequate, but not because, as a body, it fails to meet some quantity- or diversity-of-evidence requirement, nor because individual pieces of evidence are somehow deficient (being general/unsafe/insensitive or the like), such that, some further important epistemic requirement is not met, despite the evidence yielding high probability of guilt. It is merely that there is apparently more evidence available upon which to base the probability of guilt. While this may sound deflationary, we claim that it is the superior account of the naked statistical proof intuitions, not just because it reinstates the powerful probabilist orthodoxy, but also because it has interesting implications for other, more subtle cases, that do not, yet perhaps should, raise our intuitive alarm bells.