It is a well known phenomenon that students with a high initial pretest score demonstrate lower learning gains since there is less room for improvement. In this paper we explore a related issue, that of selecting appropriate interventions for students who start out with a high initial competency. We present a mathematical model that makes it possible to project success rates at selecting appropriate intervention based on accuracy at analyzing student performance at a task. This model demonstrates that for high initial competency students, selecting interventions based on any sort of isolated analysis of student performance is doomed to failure even with very high accuracy analysis. We explore an alternative approach to selecting interventions within the context of the WHY2 conceptual physics tutoring system based on prior probabilities of student need.
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