where to study and perform research. The *total number* of publications that were awarded four or three stars influences the distribution of funding, which is relevant for the third objective of the REF.

Hence, the objective of establishing a reputational yardstick corresponds to a size-independent perspective, while the objective of funding allocation corresponds to a size-dependent perspective. This means that agreement between metrics and peer review is relevant from both perspectives. We will comment in more detail on the distinction between the two perspectives in Section \[sec:size\_dependent\].

To provide an indication of the importance of the REF 2014, we briefly look at the funding of UK higher education in 2017–2018[^2]. In 2017–2018, REF results based on research output were used by the Higher Education Funding Council for England (HEFCE) to allocate £$685$M to institutions. Although many details are involved (e.g. extra funding for the London region, weighing cost-intensive fields), this was based largely on $4^*$ and $3^*$ publications, which were awarded roughly $80\%$ and $20\%$ of the money, respectively. This amounted to about £$10\,000$ per $4^*$ publication and about £$2\,000$ per $3^*$ publication per year on average[^3]. The total amount of about £$685$M allocated through the evaluation of research output 