Data-driven design is a proven success factor that more and more digital businesses embrace. At the same time, academics and practitioners alike warn that when virtually everything must be tested and proven with numbers, that can stifle creativity and innovation. This article argues that Taleb's Black Swan theory can solve this dilemma. It shows that online experimentation, and therefore digital design, are fat-tailed phenomena and, hence, prone to Black Swans. It introduces the notion of Black Swan designs -- "crazy" designs that make sense only in hindsight -- along with four specific criteria. To ensure incremental improvements and their potential for innovation, businesses should apply Taleb's barbell strategy: Invest 85-90% of resources into data-driven approaches and 10-15% into potential Black Swans.