Are democracies better at winning wars and militarized disputes? Is there an advantage associated with initiating a war or dispute? Noting that pairwise contest data are the norm in applied research, we motivate a straightforward Bradley–Terry statistical model for these problems from first principles, which will allow for a closer integration of theoretical and statistical practice for scholars of international relations. The essence of this approach is that we learn about the latent abilities of states from observing conflict outcomes between them. We demonstrate the novelty and appeal of this setup with reference to previous attempts to capture estimands of interest and show that for many questions of concern—especially regarding "democratic effectiveness" and "initiation effects"—our approach may be preferred on theoretical and statistical grounds. The evidence we find only partially supports the ideas of "democratic triumphalists": democracy aids effectiveness, but only in certain contexts (while in others it actually impairs fighting ability). We also provide estimates of possible "initiation effects," and show that moving first seems to carry little advantage in interstate wars, but a substantial one in lower-level disputes.