Like its 2008 predecessor, the, 2014 Research Excellence Framework was a high-stakes exercise. For universities and their constituent departments, it had zero-sum implications for league table position in a way that the 2001 exercise did not, and "post facto" it is having a significant effect on investment and disinvestment as departments vie with each other internally for dwindling estate and staffing resources. Yet there has never been an analysis of how different Units of Assessment compare with each other in terms of their competitiveness, and how the percentage of staff submitted in each discipline affects the competition space. The purpose of this paper is twofold: to introduce the Herfindahl Index, currently used as the basis for antitrust regulation in the US, to an educational setting; and to apply the Index to the 2008 and 2014 research assessment exercises to gauge the competitiveness of individual disciplines. It finds that competition in the UK research sector is exceptionally tough, but that competitiveness in some subjects, especially Education, is hugely increased when the metric used as base is the total number of staff "eligible," rather than the total number of staff submitted, which suggests a very concentrated market in terms of quality.