We present a lithography-free technological strategy that enables fabrication of large area substrates for surface-enhanced Raman spectroscopy (SERS) with excellent performance in the red to NIR spectral range. Our approach takes advantage of metal dewetting as a facile means to create stochastic arrays of circular patterns suitable for subsequent fabrication of plasmonic disc-on-pillar (DOP) structures using a combination of anisotropic reactive ion etching (RIE) and thin film deposition. Consistent with our previous studies of individual DOP structures, pillar height which, in turn, is defined by the RIE processing time, has a dramatic effect on the SERS performance of stochastic arrays of DOP structures. Our computational analysis of model DOP systems confirms the strong effect of the pillar height and also explains the broadband sensitivity of the implemented SERS substrates. Our Raman mapping data combined with SEM structural analysis of the substrates exposed to benzenethiol solutions indicates that clustering of shorter DOP structures and bundling of taller ones is a likely mechanism contributing to higher SERS activity. Nonetheless, bundled DOP structures appeared to be consistently less SERS-active than vertically aligned clusters of DOPs with optimized parameters. The latter are characterized by average SERS enhancement factors above 107.