Many critical questions involving the causes and consequences of formal military alliances are related to differences between various alliances in terms of the scope of the formal obligations, the depth of the commitment between signatories, and the potential military capacity of the alliance. Studying the causes and consequences of such variation is difficult because while we possess many indicators of various features of an alliance agreement that are thought to be related to the broader theoretical concepts of interest, it is unclear how to use the multitude of observable measures to characterize these broader underlying concepts. We show how a Bayesian measurement model can be used to provide parsimonious estimates of the scope, depth, and potential military capacity of formal military alliances signed between 1816 and 2000. We use the resulting estimates to explore some core intuitions that were previously difficult to verify regarding the formation of the formal alliance agreement, and we check the validity of the measures against known cases in alliances as well as by exploring common expectations regarding historical alliances.