Public debates are a common platform for presenting and juxtaposing diverging views on important issues. In this work we propose a methodology for tracking how ideas flow between participants throughout a debate. We use this approach in a case study of Oxford-style debates—a competitive format where the winner is determined by audience votes—and show how the outcome of a debate depends on aspects of conversational flow. In particular, we find that winners tend to make better use of a debate’s interactive component than losers, by actively pursuing their opponents’ points rather than promoting their own ideas over the course of the conversation.