The potential of tasks to foster mathematical learning and understanding is an important aspect of instruction and their implementation in teaching is thus often viewed to be positively related to the quality of instruction. Both the selection of tasks as well as their implementation in the classroom depend on many factors, with teachers' knowledge and skills as one of the most important ones. The present study aims to analyze the relations between different aspects of task potential, the quality of instruction, and teachers' competence in order to investigate whether task potential can be seen as an indicator for teaching quality, for teacher competence, or as an independent construct in models of educational effectiveness. To this end, we draw on data from the TEDS-Validate study, namely tests of mathematics teachers' competence (n = 31) observations in their classrooms (n = 60), and an in-depth analysis of all tasks used in the respective lessons (n = 2490). Multiple regression analysis suggests that while some facets of task potential are related to either teaching quality or teacher competence, the potential of tasks emerges as an independent construct with some characteristics predicting the teaching quality of the respective lessons. Implications of these results for the role of tasks in educational effectiveness research are discussed.