The relationship between psychological pressure and performance outcomes has been studied across a variety of sporting contexts. As an extension and complement to recent empirical studies, we construct a formal model of soccer penalty shoot-outs to determine the links between psychological pressure and first-mover advantage (FMA). Our approach indicates that even seemingly simple competitive interactions may include a rich, complex set of effects. We demonstrate that psychological pressure leads to FMA in shoot-outs; however, we show that this relationship can vary depending on a variety of different factors, such as the nature of the pressure, the magnitude of the pressure, and the specific rules governing the shoot-out. Overall, our work clarifies and extends knowledge of the operation of FMA and of how psychological pressure impacts performance outcomes in competitive interactions.