Statistics of statisticians: Critical mass of statistics and operational research groups in the UK

TL;DR

This paper models the relationship between research group size and quality in UK statistics and operational research using a physics-inspired approach, identifying critical mass thresholds for optimal group size.

Contribution

It introduces a mean field theory-inspired model to quantify how research quality depends on group size and estimates critical mass thresholds for these disciplines.

Findings

Lower critical mass estimated at 9 ± 3 researchers.

Upper critical mass approximately twice the lower, around 18 researchers.

Research quality linearly depends on group size up to the upper critical mass.

Abstract

Using a recently developed model, inspired by mean field theory in statistical physics, and data from the UK's Research Assessment Exercise, we analyse the relationship between the quality of statistics and operational research groups and the quantity researchers in them. Similar to other academic disciplines, we provide evidence for a linear dependency of quality on quantity up to an upper critical mass, which is interpreted as the average maximum number of colleagues with whom a researcher can communicate meaningfully within a research group. The model also predicts a lower critical mass, which research groups should strive to achieve to avoid extinction. For statistics and operational research, the lower critical mass is estimated to be 9 $\pm$ 3. The upper critical mass, beyond which research quality does not significantly depend on group size, is about twice this value.