My name is supervocalic

So it was pointed out to me yesterday that my name (“Michael Lugo”) has each of the five vowels (a, e, i, o, u) exactly once. Such a word is called supervocalic.
What are the chances of that?

A quick calculation: assume that letters have the frequencies given in the Wikipedia article for English. In particular the frequencies of A, E, I, O, and U are 8.167%, 12.702%, 6.966%, 7.507%, 2.758%. The frequency of all other letters combined is 61.900%; call this q. Call the product of these c; the value of c is about 1.50 \times 10^{-6}.

Now assume that names are created by picking letters independently at random. To construct a string in which each vowel appears exactly once, we must:

  • decide where the vowels will appear. We can do this in n(n-1)(n-2)(n-3)(n-4) = n!/(n-5)! ways; here order matters.
  • put A, E, I, O, U in those five pre-chosen positions, and consonants in the others; the probability of this is C q^{n-5}.

So a string of length n has probability {n! \over (n-5)!} C q^{n-5} of having each vowel occur exactly once. For n = 6, 7, \ldots, 20 I give those probabilities in the following table:

6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
0.0007 0.0014 0.0024 0.0033 0.0041 0.0047 0.0050 0.0050 0.0048 0.0045 0.0040 0.0035 0.0030 0.0025 0.0021

For example, a name of length 11 (like mine) has probability about 0.0047 of containing each vowel exactly once. The string length which is most likely to be supervocalic is 13; that makes sense, as a typical string is thirty-eight percent vowels, and five is about thirty-eight percent of thirteen. It’s hard to go much further with this, though, because I don’t have the distribution of lengths of names. But whatever the distribution of name lengths, the proportion of supervocalic names is bounded above by one in two hundred. Special, but not that special. (My instinct is that supervocalic names are probably a bit more likely than this, because the distribution of the number of vowels in a name of length n is probably more tightly concentrated than a binomial.)

Ken Jennings has a list of sets that contain exactly one such word, many of which contain less than a couple hundred elements, but it’s hard to say what that means in this context. For more words with this property, see the message boards; in particular there are some nine-letter examples. Getting much shorter than that seems to interfere with euphony, which my model doesn’t take into account. There have been 250 major league baseball players who have each vowel at least once; many have each vowel exactly once. Many of them are named Charlie; few, it seems, are named Michael, because your typical baseball player is more likely to go by Mike.

5 thoughts on “My name is supervocalic

  1. Inspired by this post, I did some searching for supervocalic people in the movie industry (which was mentioned in the Ken Jennings message board, but no-one had the tools to do the search).

    The person with the shortest supervocalic name is Biao Yuen, who manages to squeeze five vowels + Y into an eight letter name. He (she?) was in Shanghai Noon. If you’re looking for a Western name, Len Cariou and Paul Fiore score five vowels in nine letter names.

    Full list here:

    Quite a few people have the five vowels in order, but only two, Charles Kimbrough and Matthew Kimbrough have them without repeats. (Yahoo Serious could have managed it if he’d only thought to call himself Yah Serious.)

    Full list here:

    Finally, there are quite a lot of examples of supervocalic people in supervocalic movies. Tetta Sugimoto in Autoreiji does it in fewest letters, but Linus Roache in Pandaemonium is the shortest Western example.

    (There are some magnificently inefficient examples towards the bottom of that list: Gabourey Sidibe in Precious (Based on the Novel Push by Sapphire), Hugo Weaving in The Adventures of Priscilla, Queen of the Desert etc.) (But that’s probably more than you ever wanted to know about this topic…)

    Bruce Nash (not supervocalic, but no repeated letters)

    PS Full disclosure: I own OpusData and The Numbers, which were used to compile these results.

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