During adolescence, what is more important for educational achievement, well-being, and the formation of positive social relationships: being competent, having positive thoughts about oneself, or a complex relationship between the two? There has been a long-standing debate in psychology on the effects of accurate and biased self-perceptions, and sophisticated ways of modeling the effects of self-perception, competence, and their interplay have recently been suggested. But recent research has focused on adults and has not taken reference effects into account. The present preregistered study used a large German sample of students (N = 6,086 students in 559 classes) in Grade 5 (mean age = 10.55 years, SD = 0.64) with data from the National Educational Panel Study (NEPS). We tested the effects of academic self-concept and competence in math and reading on outcomes pertaining to achievement, well-being, and social relationships up to 4 years later and identified the best fitting hypotheses through a model fit comparison. In contrast to previous studies, we took the frame of reference for students’ self-concept into account by controlling for class-level effects of self-concept and competence in a multilevel analysis. Results showed that educational achievement was best explained by the complex interplay of self-concept and competence, where competence was the stronger predictor. By contrast, self-concept was a stronger predictor of well-being than competence was. For social relationships, results were less clear and differed by the specific outcome variables that were used. Overall, in the school context, self-concept and competence per se seem to be more predictive of future outcomes than their fit or misfit.