Ok, so this isn't actually a distribution of pussy, its a distribution fatherhood. But I think that "The Boltzmann distribution of Pussy" sounds better.

Statistical mechanics is a branch of physics that deals with how macroscopic variables such as Energy and Entropy relate to microscopic variables, usually the properties of individual particles within a gas. One of the first, if not the first result of Statistical Mechanics was the distribution of Energy across particles in a gas, the Boltzmann distribution. The requirements for this distribution to be present are astonishingly simple - that some conserved quantity is randomly distributed among particles(not quite, but it will do for now). For gases, energy is distributed among particles. This distribution even applies economics, money distributed across people(see Yakovenko's work for a further explanation). Let's apply the scientific method and see what results it gives for the sexual marketplace.

The number of pregnancies is randomly distributed across all men. Therefore the number of pregnancies a man has caused out of all the pregnancies in any instant should be Boltzmann distributed => PDF(p) = m/T*e^(-p/T), and where p is pregnant women, where T is ratio of pregnancies to men, and M is the number of men.

Main results:

  • The number of men who are the father of less than p pregnancies is CDF(p)=m-m e^(-p/T).
  • The number of pregnancies fathered by men who are the father of less than p pregnancies is mT-m(T+p)exp(-p/t)
  • The bottom 20% of men are the father of less than 0.223*T pregnancies and father 2.14% of all pregnancies
  • The bottom 50% of men are the father of less than 0.693*T pregnancies and father 15.3% of all pregnancies
  • The top 20% of men are the father of 1.61*T number of pregnancies and father 52.2% of all pregnancies

This distribution does not necessarily reflect fatherhood in modern society since contraceptives and relationships(although not for TRP) are an integral part of society. I'd wager that it reflects the distribution found for the thousands of years before we developed civilizations. It does not also take into effect female hypergamy, so the distribution should be even more skewed for the top % of men than it already is.

This distribution cannot be applied to sexual partners itself, because sex is not conserved. However, I believe this distribution was imprinted onto the human mind through hundreds of thousands of years of evolution and it necessarily reflect how women decide to fuck men. Inverting it, we find that if a woman believes she is in the bottom 2%, she will mate with men below the 20% mark. Women between the 2% and 15% mark will mate with men between the 20% and 50% mark. Women between the 15% and 50 % mark will mate with men between the 50% mark and the 80% mark. The top 50% of women will mate with 20% of the men. This distribution is not quite as extreme as the 80-20 rule, but its still very telling.

There is a problem with the distribution. At any point in time there are clearly less pregnancies than men, therefore T must be less than one. I'd guess high that T is approximately 0.2, so the top 20% of men would father 0.332 pregnancies. The men who have fathered more than one pregnancy is 0.674%. Although both of these statement are ridiculous, we have to keep in mind this T value is the instantaneous in time pregnancies, not total number of pregnancies over time. Over a womans lifetime she usually has 2.5 children, so over a whole generation, T is approximately 2.5. This number was even higher in the past, therefore making this distribution sensible again.