  Established frameworks to understand problems with reproducibility in science
begin with the relationship between our understanding of the prior probability
of a claim and the statistical certainty that should be demanded of it, and
explore the ways in which independent investigations, biases in study design
and publication bias interact with these considerations.
  We propose a complementary perspective; namely, that to improve
reproducibility in science, our interpretation of the persuasiveness of
evidence (e.g., statistical significance thresholds) should be responsive to
our understanding of the effort that would be required to improve that
evidence. We will quantify this notion in some formal settings. Indeed, we will
demonstrate that even simplistic models of evidence publication can exhibit an
improvable evidence paradox, where the publication of easily improvable
evidence in favor of a claim can best seen as evidence the claim is false.
