Prominent theories propose that commitment problems drive phenomena such as war and democratization. However, existing work disagrees about a basic question: how does a challenger’s coercive strength affect prospects for conflict and/or institutional reform? We establish that the relationship depends on how challenger strength affects the average and maximum probability of winning a conflict in a given period (“threat”). We analyze a formal model with a general distribution of threats, and conceptualize challenger strength as affecting this distribution. If the maximum threat is fixed and stronger challengers pose a higher average threat, then weak challengers will rebel (absent reform) during the rare periods they pose a high threat. However, if stronger challengers pose a greater maximum threat, then they are harder to buy off. Applying these insights advances theoretical and empirical debates about democratization.