The drop-weight impact test is an experiment that has been used for nearly 80 years to evaluate handling sensitivity of high explosives. Although the results of this test are known to have large statistical uncertainties, it is one of the most common tests due to its accessibility and modest material requirements. In this paper, we compile a large data set of drop-weight impact sensitivity test results (mainly performed at Los Alamos National Laboratory), along with a compendium of molecular and chemical descriptors for the explosives under test. These data consist of over 500 unique explosives, over 1000 repeat tests, and over 100 descriptors, for a total of about 1500 observations. We use random forest methods to estimate a model of explosive handling sensitivity as a function of chemical and molecular properties of the explosives under test. Our model predicts well across a wide range of explosive types, spanning a broad range of explosive performance and sensitivity. We find that properties related to explosive performance, such as heat of explosion, oxygen balance, and functional group, are highly predictive of explosive handling sensitivity. Yet, models that omit many of these properties still perform well. Our results suggest that there is not one or even several factors that explain explosive handling sensitivity, but that there are many complex, interrelated effects at play.