Presidential birth year cohort clustering

Looking at a list of where each of our presidents was born, I noticed an oddity. It has no significance, I don't think, but there is an anomalous pattern.

Given that presidents are elected every four years, you would expect that, on average, there would be about four years between birthdates of presidents. In fact, given the frequency of two term presidents, you would expect the average difference in birth years to be something more like six years.

It is in fact a lot lumpier than that, and that lumpiness changes over time. This only has significance, and I am not sure that it has significance, depends on the weight you assign to generational cohort shaping. For example, we think of the Great Generation as having been forged first by the Great Depression and then by their shared experience of World War II. I think there is some assignable cohort attributes arising from shared experiences but I am not confident how determinative those shared experiences might be.

Of the thirteen presidents born in the 18th century, the average difference in birth years is 5.25 years. The maximum difference was nine years (between William Harrison, 1773 and Martin Van Buren, 1782). The minimum gap was zero. We had two presidents in the nineteenth century who were born in the same year, Andrew Jackson and John Quincy Adams were both born in 1767 and one followed the other in sequence of presidents.

Of the twenty presidents born in the nineteenth century, the average age gap shrank by half a year to 4.75 years. The maximum age gap was 13 years which occurred on two occasions. The first time was between William Mckinley and Woodrow Wilson (two presidents apart from one another in sequence of presidents). The second time was between Abraham Lincoln and Ulysses S. Grant (one president apart from one another in sequence.) On the other hand, again, there was only one occasion in that century when two presidents were born in the same year as one another. Ulysses S. Grant and Rutherford B. Hayes were both born in 1822 and followed one another in sequence as presidents.

Of the eleven presidents born in the 20th century, the average age gap shrank again, down to 4.3 years apart. The maximum age gap among all presidents was in this century, with an eighteen birth year gap between Lyndon B. Johnson and Dwight D. Eisenhower (one president apart in sequence.) However, there have been three occasions when presidents shared the same birth year. Richard Nixon and Gerald Ford were both born in 1913, one following the other in the sequence of their presidencies. Jimmy Carter and George H. W. Bush were both born in 1924 (one president apart in sequence.) Finally, Donald Trump, George W. Bush and Bill Clinton were all born in the same year, 1946. Bush following Clinton in sequence and Trump and Bush separated by one president in sequence.

The lowering of the average in birth year difference from 5.25 to 4.3 implies that there is a generational cohort smoothing going on. On the other hand, the number of occasions where presidents are born in the same year implies greater cohort clustering.

I don't think it has great significance because I don't think shared cohort experiences are all that determinative. Bush, Clinton and Trump shared the same cohort experiences from all being born in the same year but the difference in familial circumstances (traditional patrician, wrong-side-of-the-tracks familial dysfunction, and driven immigrant mogul family) far outweigh the shaping influence of cohort. But it is still striking how much more birth year clustering there is among our recent presidents.