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There is little question that the distribution and numbers of large mammals have been altered by human activities. In North America, native ungulates have declined substantially since the mid-1800s. There is no baseline, however, against which to measure the magnitude of changes aside from anecdotal accounts or published information derived from a single location at a single point in time and extrapolated to derive a continent-wide population estimate. One example is bighorn sheep (Ovis canadensis), which were estimated to number from 1.5 to 2.0 million individuals in 1850. The literature is replete with references to those numbers, yet the derivation of that ‘estimate’ has not been formally questioned; bighorn sheep, which are endemic to North America, currently number approximately 85,000 individuals. We combined basic math and logic to develop a simple model of population density at differing scales and examined results reductio ad absurdum to question the estimate of 1.5 million bighorn sheep and the magnitude of the hypothesized decline that followed. We evaluated the plausibility of bighorn sheep population densities that must have existed at four spatial scales if there were ≥1.5 million individuals and argue that such numbers likely never existed. Continued use of 1.5 million bighorn sheep as a baseline against which to assess the magnitude of anthropogenic impacts is unwise, inappropriate, and apt to become problematic in the context of the conservation of habitat, populations, or restoration to historical ranges. Credibility matters in science, management, and conservation.