Even the index for Democratic politicians and cabinet members remains more than twice as high as the benchmark for the population as a whole. In 1990 — the last year for which the Census Bureau published data on first names — Jameses made up 1.6 percent of the population, Johns were an additional 1.6 percent, and Roberts and Williams accounted for another 1.5 and 1.2 percent. The other side of our ratio is the share of women, who were 51.2 percent of the population. Putting these numbers together, the ratio of Jims-Bobs-Jacks-Bills to women is 0.12 to 1.

Other institutions are clearly in transition. For instance, Chief Justice John Roberts is the only John on the Supreme Court, and he is outnumbered by three women, which yields a score of 0.33. But this is a more balanced court than it has historically been, and before Justice Elena Kagan took over from Justice John Paul Stevens, there were as many Justice Johns as women.

Emboldened by this new approach to quantifying the glass ceiling, I felt compelled to also track progress within my own field, which is academic economics. I took a quick count of full professors in the “top six” economics departments — typically thought to include Chicago, Harvard, M.I.T., Princeton, Stanford and Yale — and discovered 1.12 Professors James, Robert, John or William for each female economics professor, suggesting that we are still a substantial distance from gender parity. Indeed, this is a setting where the index probably understates the problem, as economics faculty members are an internationally diverse group, and the index is unmoved by Jaimes, Robertos, Juans or Willems.

The Glass Ceiling Index is a fun but quite imperfect way of measuring the permeability of the glass ceiling. (Especially because in a few decades, the millennial Jacobs, Tylers and Zacharys will outnumber baby boomer Bills and Bobs.) But it does point to an important truth — that in many important decision-making areas of American life, women remain vastly outnumbered.