Recent literature results have highlighted the role of small transition metal and intermetallic nanoparticles supported on graphene as catalysts for many key applications in energy and commodity chemicals industries. Specifically, metal nanoparticle catalysts down to sizes of 4 and even 1 (single atom catalysts) on graphene have been studied for the Oxygen Reduction Reaction (ORR). A recent study showed that 4-atom transition metal intermetallic nanoparticles (NP) on graphene (metal-decorated graphene (MDG)) even generate a predictive Volcano Plot for ORR activity. Initial results from that study were not completely explained, and an expanded analysis and discussion built from that work is presented in this manuscript. Specifically, in this new work, the original Volcano Plot for 4-atom MDG NP catalysts for the ORR is analyzed for its counter-intuitive thermodynamic inversion between the rate limiting steps of O* hydrogenation and OH* hydrogenation. The Volcano Plot is then further studied for dependence on solvent correction energy, system pH, and with an initial probe on the sensitivity of descriptor values on doping of the graphene support via B and N atoms. Recommendations for optimum 4-atom MDG NP catalyst operation for the ORR are provided, and directions for future work and study are provided.