Abstract: Humans are storytellers, even in communication scenarios which are assumed to be more rationality-oriented, such as argumentation. Indeed, supporting arguments with narratives or personal experiences (henceforth, stories) is a very natural thing to do -- and yet, this phenomenon is largely unexplored in computational argumentation. Which role do stories play in an argument? Do they make the argument more effective? What are their narrative properties? To address these questions, we collected and annotated StoryARG, a dataset sampled from well-established corpora in computational argumentation (ChangeMyView and RegulationRoom), and the Social Sciences (Europolis), as well as comments to New York Times articles. StoryARG contains 2451 textual spans annotated at two levels. At the argumentative level, we annotate the function of the story (e.g., clarification, disclosure of harm, search for a solution, establishing speaker's authority), as well as its impact on the effectiveness of the argument and its emotional load. At the level of narrative properties, we annotate whether the story has a plot-like development, is factual or hypothetical, and who the protagonist is. What makes a story effective in an argument? Our analysis of the annotations in StoryARG uncover a positive impact on effectiveness for stories which illustrate a solution to a problem, and in general, annotator-specific preferences that we investigate with regression analysis.