Present-day automatic optimization relies on powerful static (i.e., compile-time) analysis and transformation methods. One popular platform for automatic optimization is the polyhedron model. Yet, after several decades of development, there remains a lack of empirical evidence of the model's benefits for real-world software systems. We report on an empirical study in which we analyzed a set of popular software systems, distributed across various application domains. We found that polyhedral analysis at compile time often lacks the information necessary to exploit the potential for optimization of a program's execution. However, when conducted also at run time, polyhedral analysis shows greater relevance for real-world applications. On average, the share of the execution time amenable to polyhedral optimization is increased by a factor of nearly 3. Based on our experimental results, we discuss the merits and potential of polyhedral optimization at compile time and run time.