Using a combination of auto‐ethnographic and narrative analysis, this paper sheds light on stories by wheelchair basketball players about their disabilities. Narrative is a means through which people recall experiences and place them into a meaningful series of events. In contrast to critiques of disabled athletes’ narratives emphasizing ‘overcoming’ disability and ‘passing’ as able‐bodied, I argue that wheelchair basketball players construct narratives of competence, which contrast with common stereotypes of disability. In doing so, they construct a shared sense of identity. I suggest that ‘narratives of competence’ are a more productive theoretical framework for understanding the stories of disabled athletes than ‘overcoming narratives’ because the storytellers are not attempting to pass as able‐bodied. Rather, they are presenting themselves as capable people, who are not trapped in liminal space due to their disabilities. In addition to arguing against previous accounts that describe disabled athletes as passing, this article contributes to the growing emphasis in anthropology to de‐medicalize disability.