So - was my estimate right?

Way back when (May 2015), I estimated the number of great-aunts/uncles and 1st cousins N times removed there'd be in the tree based upon a calculated average of 5.8 children per family.

What I came up with was 1,673 aunts/uncles (when I started the project).   It ended up being 2,184.

Why the difference?   Some thoughts:

1. The estimate was based on my mother's side of the family only.  Now while my father's branch of the family tree is meager in comparison, it does add a few dozen people.
   
2. The estimate was based only on generations 3 through 10.   I actually ended up working out to generation 13 (although far from complete). 
   

So - now that I've done the 1st cousins N times removed (8,245 of them) - that ends up being short of the expected 9,760.   Why is that?

Two things, I think.   First in the estimate going from direct ancestors to aunts/uncles, we KNOW that each of them were married (they're grandparents, after all) whereas there's no guarantee that every child who is an aunt/uncle will also have children (some die early, others never marry, etc.).   Another effect is that single-marriage families might have children over a period of 20 years or more, multiple marriage families have a shorter window, which means fewer children per family.

Without looking at every aunt/uncle and removing all the cases where there are no children (code which I could write I suppose), getting an accurate measurement from the aunts/uncles to 1st cousins to estimate the family size for 2nd cousins would be difficult.

In any case, the ratio of 1st cousins to aunt/uncles is 3.8 instead of 5.8 which is essentially an "effective" family size (i.e., counting non-married people in as a family size of zero).

So - I suppose to zeroth-order, the estimate number of 2nd cousins (the C:X,3's on the tree) should be about 31,000 people.  Given that I seem to be able to add about 10K people/year,  I guess we should expect the next report on this to happen in Spring 2021.   :-)