Sports are spontaneous generators of stories. Through skill and chance, the script of each game is dynamically written in real time by players acting out possible trajectories allowed by a sport's rules. By properly characterizing a given sport's ecology of 'game stories', we are able to capture the sport's capacity for unfolding interesting narratives, in part by contrasting them with random walks. Here, we explore the game story space afforded by a data set of 1,310 Australian Football League (AFL) score lines. We find that AFL games exhibit a continuous spectrum of stories rather than distinct clusters. We show how coarse-graining reveals identifiable motifs ranging from last minute comeback wins to one-sided blowouts. Through an extensive comparison with biased random walks, we show that real AFL games deliver a broader array of motifs than null models, and we provide consequent insights into the narrative appeal of real games.