The element Vanadium (V) appears unique among alloying elements for providing high strengthening in both the fcc Co-Cr-Fe-Mn-Ni-V and bcc Cr-Mo-Nb-Ta-V-W-Hf-Ti-Zr high-entropy alloy families. The origin of Vanadium's special role is its atomic volume: large in the fcc alloys and small in the bcc alloys, and thus having a large misfit volume in both crystalline structures. A parameter-free theory applicable to both fcc and bcc HEAs rationalizes this finding, with predictions of strength across a range of fcc and bcc alloys in quantitative and qualitative agreement with experiments. In the fcc class, the analysis demonstrates why the newly-discovered NiCoV and Ni0.632V0.368 alloys have far higher strength than any other fcc alloy and are predicted to be the highest attainable. In the bcc class, the analysis demonstrates that the addition of V always increases the strength relative to the same alloys without V. The optimization of complex alloys for high strength should thus center around the inclusion of V as a primary element at concentration levels of around 25 at.% (C) 2020 Acta Materialia Inc. Published by Elsevier Ltd. All rights reserved.