We report a successful first-principles calculation of the correlation between crystal structure and $d$-electron-to-atom ratio in the transition-metal Laves alloys. The existence of a Hume-Rothery-type rule is related to geometrical similarities of the structures. The $d$-band binding is the main determinant of structure, and the common-band model is well obeyed, with a deviation whose physical interpretation we discuss. An experimental test is suggested.