Museum collection strategies are governed by a variety of factors, including topical focus, acquisition funds, availability of works in the art market, donations and specific coincidental opportunities. Yet, it remains unclear if more fundamental collection patterns emerge, exist, and are shared between museums, which could for example allow an established artist to estimate when a contemporary art museum would acquire their works. Here we collect and analyze data from 12 European contemporary art museums, taking into account artwork creation dates, collection acquisition dates, and the associated artist age at both points in time. From this simple quantitative construct we are able to reveal a striking gradient of museum profiles at the aggregate level. This lag can function to constitute a macroeconomic index of "mean museum collection lag", ranging from 3 years in the most dynamic cases (Kiasma) to 33 years in the most established institutions (Reina Sofia). Meanwhile, on the granular level, plotting artist age over collection year, and using artist-age vs artwork-collection matrices, a detailed picture becomes evident, where individual museums are characterized by shared patterns and a rich heterogeneity of ideographic details. Regularities include continuous acquisitions, systematic acquisition of older materials over time, and brief bursts, where whole oeuvres of individual artists join specific collections. Hence, we are able to shed light on the detailed collection history of museums, transcending the anecdotal nature of art historical storytelling via the provision of a quantitative context. Our approach of cultural data analysis combines expertise in art, art history, computational social science, and computer science. Our joint perspective builds a bridge between and serves an audience of museum professionals, art market actors, collectors, and individual artists alike.