Breaking Bad Names: A Mathematical Analysis

I was binge re-watching Breaking Bad when I started thinking about the opening credits. Each name has a chemical element symbol highlighted in green — Vince Gilligan’s name highlights V for Vanadium, for example.

I wondered: out of 118 identified elements, how common is it that we can find at least one element symbol inside a random name?

The data

I found a list of 5,163 unique first names and 88,799 unique last names and wrote a Python script to count how many element symbols could be inserted into each name.

I expected it to be rare to find a name with no possible insertions. I had no idea how rare.

Results

For first names, only 0.81% had no possible symbol insertions. The complete list of elementless first names includes names like ada, dee, emma, jade, mel, and zelda — 42 names total.

The most common number of possible insertions was 4, and the maximum was 11. One of the 11-insertion names was Catherine — despite having only 9 characters:

  • Catherine (Carbon)
  • Catherine (Calcium)
  • CAtherine (Astatine)
  • CaTherine (Thorium)
  • CatHerine (Hydrogen)
  • CatHerine (Helium)
  • CathErine (Erbium)
  • CatherIne (Iodine)
  • CatherIne (Indium)
  • CatheriNe (Nitrogen)
  • CatheriNee (Neon)

For last names, just 0.18% had no insertions — there are roughly 160 such names.

Full names

For full names we can combine the distributions. If $P_{first}(i)$ is the probability of $i$ insertions in the first name and $P_{last}(j)$ is the same for the last name, then:

$$P(n) = \sum_{i=0}^{n} P_{first}(i) \cdot P_{last}(n - i)$$

The chance that a full name has zero possible element insertions: 0.0015%.

Full names show a distribution shifted even further right, with a tail extending to 25 possible insertions. An example: Catherine Bernasconi, only 19 characters, has 25 possible element symbol placements.

For my own name — Andy Bohn — there are 8:

  • ANdy Bohn (Nitrogen)
  • ANdy Bohn (Neodymium)
  • AnDy Bohn (Dysprosium)
  • AndY Bohn (Yttrium)
  • Andy Bohn (Boron)
  • Andy BOhn (Oxygen)
  • Andy BoHn (Hydrogen)
  • Andy BohN (Nitrogen)

Note: I didn’t consider elements that span the first and last name boundary.