When it comes to energy density, all-solid-state batteries are seen as a promising technology for next-generation electrochemical storage devices. Nevertheless, the performance of all-solid-state cells is still very limited. The reasons are manifold, with insufficient ionic and electronic percolation within the composite cathode being a crucial one. In this work, we investigate percolation characteristics by three-dimensional microstructural modeling with the aim to define and understand boundary conditions for well-percolating networks. Utilizing spherical active material particles together with convex polyhedra as the solid electrolyte, ionic and electronic conduction clusters are determined and analyzed by means of percolation theory for varying macroscopic parameters, such as composition, porosity, particle size, and electrode thickness. Small active material particles turn out to enhance the effective electronic conductivity, offering high surface areas and thus more possibilities to connect particles, while porosity crucially affects ionic and electronic conduction capabilities. An impact of electrode thickness on the effective electronic conductivity is observed exclusively in thin electrodes, where percolation effects are suppressed implying favorable electrode properties. From microstructural modeling, ideal compositions are derived and guidelines for electrode design are developed at a given porosity and particle size of active material and solid electrolyte.