A resilient mat system where a mat has overall mat thickness T, and the mat has an upper layer with an upper layer thickness t, and a plurality of supporting resilient substructure columns, each column having a relatively uniform height h, such that T=t+h, wherein the ratio of h:t>3.5 for values of T>about 0.9 inch. Each column has a frusto-conical column wall, a central void, and a column bottom. The frusto-conical column has its smaller diameter end at the column bottom, a plurality of the columns optionally further have a vertical stiffening rib along a portion of the upper zone of the column wall.