The need for improved functionalities in extreme environments is fueling interest in high-entropy ceramics. Except for the computational discovery of high-entropy carbides, performed with the entropy-forming-ability formalism, most innovation has been slowly driven by experimental means. Here, we introduce DEED, a descriptor that captures the interplay between entropy gains and enthalpy costs, allowing the correct classification of synthesizability of multi-component ceramics, regardless of chemistry and structure. DEED guided the experimental discovery of new single-phase high-entropy carbonitrides and borides. This descriptor, integrated into the AFLOW computational ecosystem, provides a panoply of potential novel candidates, ripe for experimental discovery.