Computational modelling offers a powerful tool for formalising psychological theories, making them more transparent, testable, and applicable in digital contexts. Yet, the question often remains: how should one computationally model a theory? We provide a demonstration of how formalisms taken from artificial intelligence can offer a fertile starting point. Specifically, we focus on the "need for competence", postulated as a key basic psychological need within Self-Determination Theory (SDT)—arguably the most influential framework for intrinsic motivation (IM) in psychology. Recent research has identified multiple distinct facets of competence in key SDT texts: effectance, skill use, task performance, and capacity growth. We draw on the computational IM literature in reinforcement learning to suggest that different existing formalisms may be appropriate for modelling these different facets. Using these formalisms, we reveal underlying preconditions that SDT fails to make explicit, demonstrating how computational models can improve our understanding of IM. More generally, our work can support a cycle of theory development by inspiring new computational models, which can then be tested empirically to refine the theory. Thus, we provide a foundation for advancing competence-related theory in SDT and motivational psychology more broadly.