Ranking dynamics in movies and music (2506.21944v1)

Abstract: Ranking systems are widely used to simplify and interpret complex data across diverse domains, from economic indicators and sports scores to online content popularity. While previous studies including the Zipf's law have focused on the static, aggregated properties of ranks, in recent years researchers have begun to uncover generic features in their temporal dynamics. In this work, we introduce and study a series of system-level indices that quantify the compositional changes in ranking lists over time, and also characterize the temporal ranking trajectories of individual items' ranking dynamics. We apply our method to analyze ranking dynamics of movies from the over-the-top services, including Netflix, as well as that of music items in Spotify charts. We find that newly released movies or music items influence most the system-level compositional changes of ranking lists; the highest ranks of items are strongly correlated with their lifetimes in the lists more than their first and last ranks. Our findings offer a novel lens to understand collective ranking dynamics and provide a basis for comparing fluctuation patterns across various ordered systems.