Forming a molecular candidate set that contains a wide range of potentially effective compounds is crucial to the success of drug discovery. While many aim to optimize particular chemical properties, there is limited literature on how to properly measure and encourage the exploration of the chemical space when generating drug candidates. This problem is challenging due to the lack of formal criteria to select good exploration measures. We propose a novel framework to systematically evaluate exploration measures for drug candidate generation. The procedure is built upon three formal analyses: an axiomatic analysis that validates the potential measures analytically, an empirical analysis that compares the correlations of the measures to a proxy gold standard, and a practical analysis that benchmarks the effectiveness of the measures in an optimization procedure of molecular generation. We are able to evaluate a wide range of potential exploration measures under this framework and make recommendations on existing and novel exploration measures that are suitable for the task of drug discovery.