How many children does an average Eph have? My current guess is at least 1.5, and probably more.

Consider a not-so-randomly selected first-year entry from the mid 1980s. Those Ephs are now into their 50s with, presumably, most of their reproduction complete. The entry had 24 students, 12 men and 12 women. It has produced at least 36 children. Three of the women and (I think) three of the men had no offspring. The remaining 18 averaged exactly two children each. Comments:

1) This is a minimum. If I only relied on the Alumni Directory, I would only have found 32 children. One (male) alum, with 4 children, had not recorded any of them in the directory. I may have missed others.

I am especially suspicious of two other male alums with no children listed. I think — opinions welcome! — that male alums are much less likely to be childless than female alums, and that male alums are less likely to have accurate entries in the directory. Or is that an unfair stereotype?

2) Perhaps some (older!) readers could report the data for their own freshmen entries? Although entries are small, they are (very?) random, so just counting all the children from a single entry probably provides a not-unreasonable estimate.

3) Given that I sampled 24 students out of a class of 500, what is the confidence interval for my 1.5 estimate? I probably should have kept track of the 24 individual values and done a bootstrap . . .

4) This is relevant for our discussions about legacy admissions. If 1.5 is accurate then, for the class of 2024, applying this fall, there are 750 or so high school seniors with an Eph parent (and hundreds more with an Eph grandparent). Around 75 of them will become students at Williams. Is is hard to believe that the top 10% of the distribution of Williams children might be academically equivalent to the other 475 members of the class of 2024? Not at all.

5) A rigorous way of exploring this conclusion would be to calculate the expected regression to the mean of children in terms of the academic abilities of their parents. Smart people have smart children, but generally not children as smart as them. So, the average child of an Eph would not be smart enough to get into Williams. But the top 10%? I bet yes. (Readers are welcome to provide their own calculations in the comments.)