Electrocatalytic water-splitting hydrogen generation consists of the cathodic hydrogen evolution reaction (HER) and the anodic oxygen evolution reaction (OER), where the four-electron-relevant OER is the rate-determining step. So far, there have been many efforts to substitute for the highly expensive noble-metal electrocatalysts (platinum, ruthenium or rhodium oxides, etc.). Transition-metal oxides based on Co, Ni, Mn, and V have been suggested as such alternatives, due to their low cost, high efficiency, and high stability. Recently, since the compositional diversity can provide a new breakthrough in that area, a high-entropy oxide (HEO) with five transition-metal cations has been suggested as a promising electrocatalyst toward the OER. In our studies, two kinds of HEOs were prepared and their OER activities were investigated. To begin with, for the (Mg0.2Fe0.2Co0.2Ni0.2Cu0.2)O, the effect of constituent cations on the OER activity was unveiled. Furthermore, a core cation driving the high OER activity was found. For it, the medium-entropy oxides (MEOs) with four cations are prepared by subtracting each cation (Mg, Fe, Co, Ni, or Cu) from the HEO, exhibiting homogeneous morphology, equiatomic composition, and single-phase rocksalt structure. As a result, it is found that the highest concentration of Co3+ in the MEO (w/o Cu) leads to the best OER activity, and thus Co3+ is the core ion driving the high OER activity. Furthermore, it is regarded that Cu2+ ions prevent the conversion of Co or Fe cations from 2+ to 3+ in the HEO and MEOs. Accordingly, maximizing the concentration of Co3+ within electrocatalysts is suggested as an effective design strategy for the high-efficiency electrocatalysts based on high or medium entropy materials. Secondly, the relationship between structure and OER activity was elucidated for the (Mg0.2Fe0.2Co0.2Zn0.2Cu0.2)O with a temperature-dependent rocksalt-to-spinel transition.