Response times are a simple low-cost indicator of the process of reasoning in strategic games. In this paper, we leverage the dynamic nature of response-time data from repeated strategic interactions to measure the strategic complexity of a situation by how long people think on average when they face that situation (where we categorize situations according to the characteristics of play in the previous round). We find that strategic complexity varies significantly across situations, and we find considerable heterogeneity in how responsive subjects' thinking times are to complexity. We also study how variation in response times at the individual level across rounds affects strategic behavior and success: when a subject thinks for longer than she would normally do in a particular situation, she wins less frequently and earns less. The behavioral mechanism that drives the reduction in performance is a tendency to move away from Nash equilibrium behavior. Finally, cognitive ability and personality have no effect on average response times.