Bibliometric indicators: the origin of their log-normal distribution and why they are not a reliable proxy for an individual scholar’s talent

There is now compelling evidence that the statistical distributions of extensive individual bibliometric indicators collected by a scholar, such as the number of publications or the total number of citations, are well represented by a Log-Normal function when homogeneous samples are considered. A Log-Normal distribution function is the normal distribution for the logarithm of the variable. In linear scale it is a highly skewed distribution with a long tail in the high productivity side. We are still lacking a detailed and convincingab-initiomodel able to explain observed Log-Normal distributions—this is the gap this paper sets out to fill. Here, we propose a general explanation of the observed evidence by developing a straightforward model based on the following simple assumptions: (1) the materialist principle of the natural equality of human intelligence, (2) thesuccess breeds successeffect, also known as Merton effect, which can be traced back to the Gospel parables about the Talents (Matthew) and Minas (Luke), and, (3) therecognitionandreputationmechanism. Building on these assumptions we propose a distribution function that, although mathematically not identical to a Log-Normal distribution, shares with it all its main features. Our model well reproduces the empirical distributions, so the hypotheses at the basis of the model arenot falsified. Therefore the distributions of the bibliometric parameters observedmightbe the result of chance and noise (chaos) related to multiplicative phenomena connected to apublish or perishinflationary mechanism, led by scholars’ recognition and reputations. In short, being a scholar in the right tail or in the left tail of the distribution could have very little connection to her/his merit and achievements. This interpretationmightcast some doubts on the use of the number of papers and/or citations as a measure of scientific achievements. A tricky issue seems to emerge, that is:what then do bibliometric indicators really measure? This issue calls for deeper investigations into the meaning of bibliometric indicators. This is an interesting and intriguing topic for further research to be carried out within a wider interdisciplinary investigation of the science of science, which may include elements and investigation tools from philosophy, psychology and sociology.