We analyse stories in Harry Potter fan fiction published on Archive of Our Own (AO3), using concepts from cultural evolution. In particular, we focus on cumulative cultural evolution, that is, the idea that cultural systems improve with time, drawing on previous innovations. In this study we examine two features of cumulative culture, accumulation and improvement. First, we show that stories in Harry Potter’s fan fiction accumulate cultural traits - unique tags, in our analysis - through time, both globally and at the level of single stories. Second, more recent stories are also liked more by readers than earlier stories. Our research illustrates the potential of the combination of cultural evolution theory and digital literary studies, and it paves the way for the study of the effects of online digital media on cultural cumulation.