Scarcity is easy to assert and hard to prove — except where the grading houses publish their census. A population report records how many copies of a title each house has graded at each grade, and reading it turns vague rarity into a specific, priceable fact: this is how many better copies exist, and this is why the next grade up costs what it does.
A population report answers the question that sets the price: how many copies exist at this grade or better? A copy near the top of a thin population is genuinely scarce and prices accordingly; the same grade on a title with a deep population is ordinary. The report converts a grade from an abstract quality into a rank within a known field — and rank within the field is what the top of the market pays for.
The shape of the population matters as much as any single figure. A title with copies bunched at mid-grades and almost none at the top has a steep price curve near the ceiling; a title with a flatter distribution prices more gently. Reading the curve tells you where the scarcity — and the money — actually sits, which is often a grade or two below the theoretical maximum, at the point where the population thins fast.
A population report counts graded copies, not all copies. Ungraded survivors, copies graded by other houses, and copies not yet graded all sit outside it — so the census is a floor on how many exist, not a ceiling, and it grows over time as more copies are submitted. Read it as strong evidence of relative scarcity, not as a fixed count, and re-check it before a major purchase because the numbers move.