Already during my lifetime we’ve had one president (George W. Bush) who hailed from the immediate family of another (George H. W. Bush), and there’s a good chance we’ll be repeating theÂ phenomenonÂ with our next president.

In total, we’ve had five presidents (11.6%) who were at least secondÂ cousinÂ¹ to a previous president:

- John Quincy Adams was John Adams’ son
- Zachary Taylor was James Madison’s second cousin
- Benjamin Harrison was William Henry Harrison’s grandson
- Franklin Delano Roosevelt was both Theodore Roosevelt’s fifth cousin and his nephew
- George W. Bush is George H. W. Bush’s son

Four of themÂ (9.3%) shared the last name of their familial predecessor: Adams, Harrison, Roosevelt, and Bush.

If Hillary Clinton is elected to the 45th presidencyÂ², it will bump those two stats up to 13.6% and 11.4%, respectively.

My question to the sociologically-minded statisticians of the world is: What numbers would we expect if we lived in a true meritocracy, rather than the oligarchy we evidently live in?

Put another way: **Given what we know about the genetic makeup of the US population, how often would we expect a president to be at least secondÂ cousin to another president sheerly by chance?**

Â¹Â If we want to roll super deep with this, it appears that 42 out of our 43 presidents so far have all been related to the British King John Lackland who signed the Magna Carta in 1215.

Â²Â Thanks to Grover Cleveland serving two non-consecutive terms, we’ve so far had 44 presidencies but only 43 presidents.

Soon after I postedÂ this to Facebook, my cousin-in-law Daniel Roston came forward withÂ exactly the sort of math I was seeking:

soâ€¦i think i can put an upper limit at around [a snowballâ€™s chance in hell] that it would happen by random chance.

assuming an average family size of 4 offspring (high for now, but maybe less high for 1790), and including the presidentsâ€™ and their [partnerâ€™s] families, i get 256 people with the level of relation of 2nd cousin (i.e., either the president or their partner shares at least as much DNA as a second cousin). Letâ€™s assume all people live at the same time and there are 10^8 people eligible for the presidency.

Then letâ€™s calculate the total number of family members to choose from, since there could be overlap there. The probability that some family member of some president will be among the 256 family members of some other president is 256/10^8. So the probability that they wonâ€™t be is 1-256/10^8. We can calculate the probability that none of the family members will be the same person by multiplying together all the individual probabilities that they wonâ€™t be the same: (1-256/10^8)^(256*43)=0.972. So removing the family members we expect to be the same person, the total number to choose from is .972*43*256=10,700.

Then the probability that a randomly chosen president will not be among those people is 1-10,700/10^8 and the probability that all 43 will not be is (1-10,700/10^8)^43=0.9954.

So the probability that one of our presidents would have been so closely related is 0.0046 and the probability that it would have happened 5 times isâ€¦0.0046^5 = 2 x 10^-12.