Estimates of the depth of bombardment-induced amorphization (Ra) are presently available for seven different ions injected into Si (Ar, As, B, Ne, P, Sb and Si) as well as for Kr injected into WO3. These depths can be interpreted in terms of recent damage-distribution theories to yieldFd(Ra), theinitialdisplacement fraction at depthRa. (Here the term ‘initial’ means ‘present before thermal and athermal annealing’.) The resulting values ofFd(Ra) were found to be reasonably constant, such that, depending on which theory was used, they had an average of either 0.7 ±0.2 or 0.4 ±0.2 for Si and either 0.09 ±0.03 or 0.17 ±0.06 for WO3. This approximate constancy is considered to be particularly significant with Si, since the data used encompassed incident masses from 11 to 122, incident energies from 10 to 280 keV, and doses from 3 × 1014to 1 × 1014ions/cm2. It is concluded, in view of the constancy ofFd(Ra), that the amorphization of si and WO3can be self-consistently explained by homogeneous damage accumulation. An alternative category of explanation, based on the random impingement of discrete disordered regions of volumeVais, however, not excluded; in fact, it is argued that the constancy demonstrated here forFd(Ra) is also compatible with discrete disordered regions providedVais proportional to the incident energyE.