High Entropy Alloys are inherently complex and span a vast composition space, making their research and discovery challenging. Developing quantitative predictions of their phase selection requires a large quantity of consistently determined experimental data. Here, we use combinatorial methods to fabricate and characterize 2478 quinary alloys based on Al and transition metals. All data are publicly available at http://materialsatlasproject.org/. Phase selection can be predicted for considered alloys when combining the content of FCC/BCC elements and the constituents’ atomic size difference. Mining our data reveals that High Entropy Alloys with increasing atomic size difference prefer BCC structure over FCC. This preference is typically overshadowed by other selection motifs, which dominate during close-to-equilibrium processing. Not suggested by the Hume-Rothery rules, this preference originates from the ability of the BCC structure to accommodate a large atomic size difference with lower strain energy penalty which can be practically only realized in High Entropy Alloys. Display omitted