This study sets out to shed light on those infrastructures underlying the ubiquitous, yet contested nature of governing by numbers. Investigating the 30-year long emergence of Germany’s “external quality assurance system” for hospitals, the authors show how methods for quantifying quality align with broader institutional and ideational shifts to form a calculative infrastructure for governance. Our study focuses on three phases of infrastructural development wherein methods for calculating quality, institutions for coordinating data and reform ideals converge with one another. The authors argue that the succession of these phases represents a gradual layering process, whereby old ways of enacting quality governance are not replaced, but augmented by new sets of calculative practices, institutions and ideas. Thinking about infrastructures as multi-layered complexes allows us to explore how they construct possibilities for control, remain stable over time and transform the fields in which they are embedded. Rather than governance being enacted according to a singular goal or value, we see an infrastructure that is flexible enough to support multiple modalities of control, including selective intervention, quality-based competition and automatized budgeting. Infrastructural change, instead of revolving around crises in measurement, is shaped by incubation periods – times of relative calm when political actors, medical practitioners, mathematicians, and many others explore and reflect past experiences, rather than follow erratic reforms fads. Finally, analysing infrastructures as multi-layered constructs underlines how they produce multiple images of care quality, which not only shift existing power relations, but also change the ways we understand and make sense of public services.