There is growing interest in using measures of teacher applicant quality to improve hiring decisions, but the statistical properties of such measures are not well understood. We use unique data on structured ratings solicited from the references of teacher applicants to explore the dimensionality of measures of teacher applicant quality and the inter-rater reliability of the reference ratings. Despite questions about applicants designed to capture multiple dimensions of quality, factor analysis suggests that the reference ratings only capture one underlying dimension. Point estimates of inter-rater reliability range between 0.23 and 0.31 and are significantly lower for novice applicants. It is difficult to judge whether these levels of reliability are high or low in the current context given so little evidence on applicant assessment tools. [This paper was published in "Economics of Education Review" v83 Aug 2021.]