How rare the extremes are

Under a normal distribution, the population thins out fast as you move away from the mean, and it does so at a predictable, well-documented rate. That rate is worth stating plainly, because online discussion of size runs almost entirely in the tails, which are the thinnest, least populated part of the whole curve.

The standard shares, by standard deviation

Using the erect-length mean and SD reported by Veale et al. (2015) as the concrete example, the standard normal distribution's shares work out roughly like this:

• Within 1 SD of the mean: about two in three men.
• Within 2 SD of the mean: about 19 in 20 men.
• Beyond 2 SD above the mean: roughly 1 in 44 men.
• Beyond 3 SD above the mean: roughly 1 in 741 men.

Each additional standard deviation does not shave off a fixed slice - it cuts the remaining slice sharply, so the population thins faster the further out you go. This is a property of the normal curve's shape, applied directionally here rather than converted into an invented head-count of "how many men" a given figure represents, which the paper's data does not support to that level of specificity.

The same effect, tighter, on girth

Erect circumference has a smaller standard deviation than erect length in Veale et al. (2015) - 1.10 cm against 1.66 cm - which means its curve is more tightly wound around the mean. The same standard-deviation shares apply: about two in three men within 1 SD, about 19 in 20 within 2 SD. But because girth's SD is a smaller number of centimetres, the same statistical rarity - "beyond 2 SD" - corresponds to a narrower band of actual measurements than it does for length. A girth figure that sounds only modestly unusual in centimetre terms can already represent the same underlying rarity as a much larger-sounding length figure, simply because girth's population is packed more tightly to begin with. A couple of centimetres of girth carries the same statistical weight, in tail terms, that several centimetres of length would - a distinction lost on anyone comparing the two measurements by eye rather than against each one's own spread.

Why this matters for anecdote

A forum thread, a comment section, or a claimed figure circulating online is not a random sample of the population - it is a sample of who chose to post, and posting about an unusual figure is, itself, an unusual act. Men near the mean have nothing notable to report and rarely do; men who believe themselves near either tail have a reason to speak up that the crowded middle does not share. The result is a visible sample heavily over-representing exactly the part of the distribution that is, by the arithmetic above, the smallest part of it - the same selection effect that shows up in who agrees to take part in a measured study in the first place.

What this does not claim

This is a statement about shares of a distribution under a normal assumption, not a claim about any individual, and not a precise headcount from the pooled 15,521 men - the paper does not report tail counts to that resolution, and inventing one from the mean and SD alone would overstate what two summary numbers can support. Where the arithmetic for a specific extreme percentile, like the 99th, is worked through properly goes further than this post does; this one only establishes the shape and the direction.

The practical read

If a figure sounds unusual enough to be worth mentioning, the base-rate arithmetic above says it probably is - genuinely rare figures are, definitionally, rare, and the volume of people discussing them online says more about who talks than about how common they are. That gap between what gets talked about and what the distribution actually contains is also the gap between a measured statistic and a subjective impression: a rating from Rate Cock is not drawn from this curve at all, an AI system's photo-based estimate carries none of this population arithmetic behind it, a comparative score built for browsing is answering a different question, and an individual human judge's confident opinion is exactly the kind of anecdote that over-samples the tails in the first place.