We extend the early work of Stoner, Mott, Friedel, and Terakura and Kanamori, which relates alloy magnetization to solute valence. We describe the conditions under which the simple formula av=A0-x(10+ZB-ZA) can be expected to apply. In particular, we consider Fe- and Co-metalloid alloys. Here av is the atom-averaged moment, A0 is the host moment, x is the metalloid-atom fraction, and ZB and ZA are the valence of metalloid and transition metal, respectively. We show that the validity of this formula rests on the existence of band gaps in the density of states in the spin-up band. Spin-polarized band-structure calculations do indeed show band gaps in moderately concentrated (x0.25) compounds and indicate that A0 should be somewhat higher for fcc than bcc structures. The theory compares well with data on concentrated amorphous and crystalline alloys of Co with Au, B, Sn, and P, and of Fe with Au, B, Al, Ga, and Si. Our explanation of this large amount of data is far simpler than, and as accurate as, any previous efforts at explanation. © 1984 The American Physical Society.