It’s been a while since I posted to this personal blog — so long, in fact, that I have had a child! We named him “Phineas Charles Ball”. (Photos are on Flickr.) “Phineas” is a fairly unusual name — although it’s become more familiar lately — and this post is my exploration on how “weird” this name actually is, and how name uniqueness trends have been developing over time.

As many of you already know, one of the most useful sources for analyzing baby name trends in the United States is the baby name data published by the Social Security Administration. These data have become especially high quality as social security numbers have become ubiquitous (at this point almost all children acquire one at birth). What you might not have realized is that some great raw data files are also available that go beyond what the website provides — the only limitation in these is that names used less than five times in a given year are not reported (for privacy reasons).

The first thing I wanted to plot was what most of us have noticed — qualitatively if not quantitatively — names have been becoming more unique. First I calculated the diversity as Shannon entropy. (I did a bit of a hack though: because I was limited to names seen 5 or more times, I only calculated the entropy of the most common 90% of names in a given year. This was close to the maximum possible — by 2011 nearly 1 in 10 girls has a name seen less than five times!)

Another way to slice this data is to try to answer this question: “How many names are needed to cover half the population?” (Or 10%. Or 90%.)

In 1950 you could cover half the male population with just 24 names — in 2010 you needed 139. As a child I remember sadly eyeing prelabeled personalized souvenirs, knowing I wouldn’t find my name among the items. (This is especially true because my first name isn’t the most common spelling.) Selling this sort of prelabeled paraphernalia has become a lot more difficult — many more names are needed to cover the same fraction of the population!

Some observations…

1. Name uniqueness hasn’t been increasing monotonically. Names seem to have become slightly less unique between 1910 and 1950. After 1950 uniqueness increased, and really took off in the mid-1980s.
2. Girl names are more unique than boy names (you probably already noticed this). It may be interesting to note that boy names today are as unique as girl names were in the early 1990s.
3. You should take the early data with a grain of salt: the total applicant data shows that not all US citizens received social security numbers (SSNs); especially few that were born before 1910. The program was created in 1935 and the legal uses of SSNs expanded gradually.

So Phineas’s name occurs in a context of increasing uniqueness: to have a rare name now is more common than it was when I was born, and much more common than when my parents were born. This particular name also happens to have become more popular lately. When we slice the data we find that in the latest years the uniqueness of “Phineas” is near 80th percentile — one in five boys has a rarer name. It’s a bit unusual, but it’s not a dramatic outlier.

I’ll close with a list of famous Phineas’s: Phineas Gage (a famous case of frontal brain damage), Finny in “A Separate Piece“, P.T. Barnum (P. = Phineas!), and Phineas Flynn from the cartoon “Phineas and Ferb“. Also oft misremembered as Phineas: Phileas Fogg in Jules Verne’s “Around the World in Eighty Days“. Chris’s favorite find is Phineas Ball (1824-1894), waterworks engineer and mayor of Worcester, MA.