Evaluation processes are critical in science and innovation, determining which innovative ideas receive crucial resources. We estimate whether “luck,” or random factors unrelated to idea quality, can bias selection in such processes. We analyze 16,278 evaluations of 2,813 innovation-driven startups by 1,052 judges in a pitch competition for admission to one of the world’s largest entrepreneurship accelerators (2013–2021). Human relational elements of luck, particularly contrast effects between sequentially evaluated competitors and drawing strict or lenient judges, have large effects, with moderate variation impacting a startup’s likelihood of admission by 25%. Timing-based elements of luck, such as time of day and weather, has negligible effect. These findings show that luck can distort resource allocation and indicate that evaluation processes should be designed to minimize this bias. We also discuss implications for evaluation process design.