Analysis of scientific productivity.

(1) Introduction and Results.-Some years ago Shockley' studied the productivity distribution of professional people within large laboratories in government, industry, and universities. A typical productivity distribution is shown by the stepped diagram in Figure 1. Here a measure of productivity has been taken to be the number of papers published within a four-year period. According to this measure, more than a third of the personnel showed no productivity. A major fraction of the papers published came from a very small fraction of the personnel. From the characteristic shape of such productivity distribution curves, Shockley deduced that productivity, as measured by publication rate, can be expressed as the product of several essentially independent factors. The purpose of the present paper is to develop a method of correlating the number of these independent factors with the precise shape of the productivity distribution curves. This correlation is unique provided we assume a given statistical distribution for the individual factors. We here assume that each factor f has a uniform statistical distribution from zero up to a maximum value fma.z The consequences of this simple assumption are deduced in section (2). Figure 2 presents the theoretical statistical distribution of productivity for several values of the number of independent factors. This number, n, will be called the degree of sophistication. The steepness of the statistical distribution is seen to increase rapidly with the increasing degree of sophistication. The area beneath each curve is exactly halved each time we increase by unity the degree of sophistication. Thus