Abstract. We argue that the effective power of a coalition depends not only on the raw capabilities of its members, but also how much effort they choose to exert. Free-riding and competition between partners mean that a coalition’s power is not merely the sum of its members’ power. We develop a unified model of crisis bargaining and war fighting between military coalitions. Using data on the escalation and outcomes of international disputes, we structurally estimate the model parameters, allowing us to identify determinants of countries’ force multipliers and the degree of prior uncertainty. We find that demographic and economic characteristics are the most important determinants of military effectiveness, with regime type and geopolitical considerations playing lesser roles. The structural model also allows us to simulate counterfactual outcomes in disputes between coalitions. This allows us to test historical claims like that earlier American involvement would have made a substantial difference in both World Wars, even in the face of strategic free-riding by its allies.