A new index for measuring scientists’ output

The online SAO/NASA Astrophysics Data System (ADS) has a search mechanism that makes it easy to look up citation statistics for astronomy and physics. The h-index has been proposed for rating individuals’ output. ¹ As examples, Edward Witten currently has an h-index of 125 because he has 125 papers receiving 125 or more citations each, and Albert Einstein has an h-index of only 27. I, by comparison, have an h-index of 46. Any index on which I score higher than Einstein is not optimal!

The h-index is nonlinear and doesn’t proportionately reward individuals for their most important paper, however influential it may be. Furthermore, by using total citations, the h-index unfairly favors people in large collaborations, because it effectively treats all authors in a multiauthor paper as if each had written the entire paper alone. Total citations are fine for ranking papers, but for ranking individuals, citations for a paper must be allocated among its authors. There are two easy ways to do that: Either use citations that acknowledge first-author status (for example, ^Einstein, A.) and thus recognize leadership, or use fractions and split the citations equally among authors (normalized citations).

What if we include both measures and take their average? Still, Einstein does not do that well. It’s not that people are no longer using his papers; rather, he has become so famous that people no longer bother to cite the original references. Can we find those hidden citations? Yes. Einstein’s name is often mentioned in the abstracts and titles of papers. Those name citations, which can also be found on the ADS, are just as important as direct citations to his papers and are arguably even harder to get. Eponymous citations count: If you do something important, people will name things after you—the Einstein ring, the Hubble constant, Feynman diagrams, and the like.

I propose an E-index citation count, proportional to total output. In the E-index, the total count C would equal $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ first-author citations + $\raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.$ normalized citations + last-name citations in abstracts + last-name citations in titles. Using ADS as of 1 January 2010, Einstein has C = 71 444 citations. (If you suspect your candidate shares a last name and is not responsible for all the abstract or title citations, then rank the most recent 3000 of them by citation count to get the most important ones, and look at the top 10. If 8 of the top 10 refer to your candidate, give your candidate 80% of those abstract or title citations.)

A convenient citation unit is the milli-Einstein (mE) = 71.4 citations. Some who did well include Fermi (1277 mE), Einstein (1000), Hubble (815), Landau (657), Witten (641), Anderson (561), Schrödinger (502), Weinberg (457), Heisenberg (417), Planck (374), Hawking (323), and Feynman (313).

Every automatic method of ranking will have a few outliers who do either much better or much worse than expected, but the E-index should be an improvement over the h-index for evaluating 20th- and 21st-century astronomers and physicists.