Disordered fiber mats made of glass microfibers (GMF) were studied using small-angle light scattering (SALS), ultrasmall-angle X-ray scattering (USAXS), SEM, and optical microscopy. The morphological scaling of these materials in the micron scale was very similar to that of polymers in the nanometer scale. In some fiber mats, such as GMF, the structure is randomized at the time of formation, leading to a statistical analogy with the thermal randomization that occurs in nanometer-scale, high polymers. Analogues for the coil radius-of-gyration, persistence unit, and scaling regimes exist in such fiber mats and may be a useful feature both for modeling thermally equilibrated polymeric systems, as well as furthering the understanding of the physical properties of fiber mats through analogy with the theoretical understanding of thermally equilibrated polymeric systems.