We provide a comprehensive approach to a methodology to evaluate the performance of lithium-ion batteries and related intercalation systems at the single-particle level, by constructing diagrammatic representations. The idea that underlies these methodologies is using two dimensionless/scaling parameters, which allow the evaluation of a series of experimental parameters and making predictions in a simple, fast and visual way. In both cases, the model considers the finite diffusion of ions in materials and the charge transfer at the electrode/electrolyte interface. The present work also aims to bring experimental single-particle measurements and single-particle models closer, providing the theoretical background necessary to deduce these scalable parameters, and may inspire more sophisticated theoretical developments in the future, considering other aspects of the nature of the composites. While revisiting relevant work in the area, the present work presents the following novel features: 1- It introduces new scaling kinetic parameter, which makes the diagrams independent of particle geometry. 2- It defines a new metric to evaluate the performance of electrode materials comparatively in terms of their diffusional and charge transfer properties. 3- It derives analytic limits to the behaviour of the model that are universal, in the sense that they do not depend on the intercalation isotherm of the material. 4- It applies artificial intelligence using a deep neural network trained to approximate the results of physics-based simulations, replicating the theoretical state of charge maps with excellent accuracy.