Recent advances in deep learning have brought attention to the possibility of creating advanced, general AI systems that outperform humans across many tasks. However, if these systems pursue unintended goals, there could be catastrophic consequences. A key prerequisite for AI systems pursuing unintended goals is whether they will behave in a coherent and goal-directed manner in the first place, optimizing for some unknown goal; there exists significant research trying to evaluate systems for said behaviors. However, the most rigorous definitions of goal-directedness we currently have are difficult to compute in real-world settings. Drawing upon this previous literature, we explore policy goal-directedness within reinforcement learning (RL) environments. In our findings, we propose a different family of definitions of the goal-directedness of a policy that analyze whether it is well-modeled as near-optimal for many (sparse) reward functions. We operationalize this preliminary definition of goal-directedness and test it in toy Markov decision process (MDP) environments. Furthermore, we explore how goal-directedness could be measured in frontier large-language models (LLMs). Our contribution is a definition of goal-directedness that is simpler and more easily computable in order to approach the question of whether AI systems could pursue dangerous goals. We recommend further exploration of measuring coherence and goal-directedness, based on our findings.