We analyze a firm's investment problem when it faces preemption risk and profits are convex in market profitability. In a setup where firms have asymmetric profit convexity, which we relate to firm quality, we show that this has interesting effects on valuation and the order of entry. The interplay between profit convexity and market growth impacts whether a high-quality or a low-quality firm is the first mover. We relate the first-mover advantage to patents; we find that patents expedite investments and increase the incentives for high-quality firms to become first movers. Furthermore, even with a persistent first-mover advantage we show that first-mover advantages in terms of firm value are either over- or underestimated. Thus, our model sheds light on why empirical studies find mixed support for the existence of a first-mover advantage.