Three dimensions of scientific impact

The growing popularity of bibliometric indexes (whose most famous example is the h index by J. E. Hirsch [J. E. Hirsch, Proc. Natl. Acad. Sci. U.S.A. 102, 16569–16572 (2005)]) is opposed by those claiming that one’s scientific impact cannot be reduced to a single number. Some even believe that our complex reality fails to submit to any quantitative description. We argue that neither of the two controversial extremes is true. By assuming that some citations are distributed according to the rich get richer rule (success breeds success, preferential attachment) while some others are assigned totally at random (all in all, a paper needs a bibliography), we have crafted a model that accurately summarizes citation records with merely three easily interpretable parameters: productivity, total impact, and how lucky an author has been so far.