Transition-metal alloyed nanoparticles with core-shell features (shell enrichment by one of the metals) are becoming ubiquitous, from (electro-)catalysis to biomedical applications, due to their size control, performance, biocompatibility, and cost. We investigate 132 binary-alloyed nanoparticle systems (groups 8 to 11 in the Periodic Table) using density functional theory (DFT) and systematically explore their segregation energies to determine core-shell preferences. We find that core-shell preferences are generally described by two independent factors: (1) cohesive energy (related to vapor pressure) and (2) atomic size (quantified by the Wigner-Seitz radius), and the interplay between them. These independent factors are shown to provide general trends for the surface segregation preference for atoms in nanoparticles, as well as semi-infinite surfaces, and give a simple correlation (a "design map") for the alloying and catalytic behavior. Finally, we provide a universal description of core-shell preference via tight-binding theory (band-energy differences) that (i) quantitatively reproduces the DFT segregation energies and (ii) confirms the electronic origins and correlations for core-shell behavior.