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• The paper investigates whether students' ability relative to their school peers is linked to overclaiming. • Being higher achieving than one's school peers is found to be linked to overclaiming. • Effect sizes are relatively modest at around 0.1 standard deviations. Using the OECD's Programme for International Student Assessment (PISA) study, we investigate whether students' relative ability in mathematics (in comparison to their school peers) is linked to their tendency to overclaim. Although the estimated effect size is modest (around 0.1 standard deviations) we find empirical support that being a big fish in a small pond is linked to overclaiming, with this robust to different analytic approaches and model specifications. Thus, being one of the highest academic achievers within a school may push young people's beliefs in their own abilities too far, straying into overconfidence and making claims about their knowledge and skills that they cannot justify. [ABSTRACT FROM AUTHOR]