Recent empirical work has shown that many scientific results may not be reproducible. By itself, this does not entail that there is a problem. However, I argue that there is a problem: the reward structure of science incentivizes scientists to focus on speed and impact at the expense of the reproducibility of their work. I illustrate this using a well-known failure of reproducibility: Fleischmann and Pons' work on cold fusion. I then use a rational choice model to identify a set of sufficient conditions for this problem to arise, and I argue that these conditions plausibly apply to a wide range of research situations. In the conclusion I consider possible solutions and implications for how Fleischmann and Pons' work should be evaluated.