Conventional horizontal evolutionary prototyping for small-data system development is inadequate and too expensive for identifying, analyzing, and mitigating risks in big data system development. RASP (Risk-Based, Architecture-Centric Strategic Prototyping) is a model for cost-effective, systematic risk management in agile big data system development. It uses prototyping strategically and only in areas that architecture analysis can't sufficiently address. Developers use less costly vertical evolutionary prototypes instead of blindly building full-scale prototypes. An embedded multiple-case study of nine big data projects at a global outsourcing firm validated RASP. A decision flowchart and guidelines distilled from lessons learned can help architects decide whether, when, and how to do strategic prototyping. This article is part of a special issue on Software Engineering for Big Data Systems.