Oxidative doping of extended g-conjugated polymers and oligomers produces dramatic changes in optical and electrical properties, arising from polaron and soliton-derived midgap states. Despite the great importance of such changes for materials properties, far less is known about the cationic polaron states than about the neutral, semiconducting or insulating, undoped materials. The systematic, multifactor computational analysis of oligoheterocycles such as oligothiophenes, oligofurans, and oligopyrroles presented here affords qualitative and quantitative understanding of the interplay among skeletal substitution pattern, electronic structure, and the effective band gap reduction on p-doping. A simple linear relation is derived for predicting p-doped oligomer and polymer effective band gaps based on those of the neutral oligomers; this relationship confirms the effectiveness of a "fixed band" approximation and explains the counterintuitive increase of the effective band gap on p-doping of many small band gap oligomers. The present analysis also suggests new candidates for transparent conductive polymers and predicts limiting behavior of ionization potential, electron affinity, and other properties for various polyheterocyclic systems. The results yield insight into materials constraints in electrochromic polymers as well as on p- and n-type conductors and semiconductors.