The Atypical Principle was formulated to explain the presence of Paragons. It deals with a higher incidence of abnormal results when dealing with large populations.
In order to understand the Atypical Principle, you must first understand probability distribution.
In any random distribution of elements, most will be clustered around the average.
The farther from the average you get, the less likely it is you will have an element with that probability.
so if you can get random number,s and 0 is average, you will have a 50% chance of getting at least a 0.
you might then have a 25% chance of getting at least a 1
and a 12.5% chance of getting at least a 2
only one in a 1000 will have a 10
only one in a million will have a 20
If you only have 12 numbers chosen, the chance of having one greater than 5 is only 30%.
If you choose 100, there is more than a 95% chance you will have one over 5.
if you choose 1 billion, you have a 60% chance of having at least one 30.
In more general terms, the larger your population, the more likely extreme elements become. This applies on both sides of the bell curve.
The human race has become a very large population. While the majority of people hover around 0 in most aspects, some extraordinary people exist from sheer probability. The one in a billion. The one in a trillion. Shining examples of humanity. Even after the events of ALICE II, the number of humans surviving in the colonies was enough to produce these extraordinary people.
Such Atypical individuals also occur on the low end of the spectrum, but they rarely survive.
Due to their extraordinary qualities, they tend to become successful, popular, rich, and well-known. Because of this, nearly every atypical get a spotlight, and their apparent number is much greater due to this increased visibility. They also tend to be healthier, and live longer, so their density increases past what you would otherwise expect from probability alone. A surprising percentage also survived ALICE II, since they were adventurous enough to leave earth beforehand.
Such individuals also tend to produce extraordinary offspring, further increasing their relative rate of incidence.
All off these factors combine to explain the existence of Paragons.