Beyond cumulative impact: the he-index and a volume-normalized efficiency metric for research evaluation

Traditional bibliometric indicators such as the h-index emphasize cumulative citation impact but provide limited insight into the efficiency and concentration of that impact across a researcher's publication portfolio. This study introduces the he-index as an interpretable indicator of the proportion of publications represented by the h-index core, relative to the researcher's total publication output. Using publicly accessible Scopus data from 54 researchers across engineering, medicine, and social sciences in the United States, China, and Australia, we examine the behavior of the he-index in relation to publication volume, career stage, and disciplinary context. As expected for a ratio-based indicator, the he-index exhibits a strong negative association with total publications (Spearman ρ = -0.77, p < 0.001), which may reflect structural sensitivity to publication volume. To improve cross-volume interpretability, we further propose a volume-normalized efficiency metric (he ^* = h/ĥ), where the expected h-index is estimated using a power-law scaling model (ĥ = 1.02N ^0.7, R ² ≈ 0.87). The normalized metric shows no significant dependence on publication volume (ρ = 0.064, p = 0.645) and exhibits weaker career-stage sensitivity, while discipline-level differences remain non-significant. External validation using field-weighted citation impact (FWCI) available for a subset of researchers provides additional support for the normalized metric, with he ^* positively associated with FWCI (ρ = 0.419, p = 0.003), whereas the raw he-index shows no significant association. Overall, the findings indicate that impact concentration and volume-normalized citation efficiency offer complementary perspectives to cumulative impact metrics, supporting more nuanced and multidimensional research evaluation.