Citation entropy and research impact estimation

TL;DR

This paper introduces a new real-valued s-index for measuring research impact, compares it with the h-index, and discusses the limitations of single-number metrics in evaluating scientific output.

Contribution

Proposes the s-index as an alternative to the h-index, analyzing its advantages and limitations through citation data with Zipfian distribution.

Findings

The s-index may be as useful as the h-index in certain cases.

The h-index performs surprisingly well despite its known drawbacks.

Single-number metrics for research impact have inherent limitations.

Abstract

A new indicator, a real valued $s$-index, is suggested to characterize a quality and impact of the scientific research output. It is expected to be at least as useful as the notorious $h$-index, at the same time avoiding some its obvious drawbacks. However, surprisingly, the $h$-index is found to be quite a good indicator for majority of real-life citation data with their alleged Zipfian behaviour for which these drawbacks do not show up. The style of the paper was chosen deliberately somewhat frivolous to indicate that any attempt to characterize the scientific output of a researcher by just one number always has an element of a grotesque game in it and should not be taken too seriously. I hope this frivolous style will be perceived as a funny decoration only.