Quality Research Follows the Power Law

Research output can be evaluated with productivity and impact, which are quantified by the numbers of publications and citations, respectively. The H-index unifies both factors. However, as an extensive variable, it grows with quantity of research output and favors senior researchers over juniors. In this report, by analyzing the data of the world top 2% scientists (n = 179,597) from an online database, we found that H-index follows power laws with both impact and productivity in a minimalist fitting with only one free parameter. We propose intensive indices (QN and QC) to measure quality research by comparing the actual H-index of a researcher with the power-law fitted H-indices from the top 2% scientists with the same numbers of publications and citations respectively. We further calculated a dynamic research quality (Q1=QN/QC) and a reduced index (Q2=(QNQC)0.5) to evaluate research quality over time. We rationalized that the power law dependency of quality research is due to its heterogeneous production pathways that require extra effort with respect to "regular” research output. A major advantage of these indices is that they are relative to the academic peers with similar accomplishments in publications and citations, and therefore, are independent of career stages. Another advantage is that the average indices are close to 1.0, giving an easily comprehensible physical significance of the indices.