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The recently born expression "analytic narratives" refers to studies that have appeared at the boundaries of history, political science and economics. These studies purport to explain specific historical events by combining the usual narrative way of historians with the analytic tools that economists and political scientists find in rational choice theory. Game theory is prominent among these tools. The paper explains what analytic narratives are by sampling from the eponymous book Analytic Narratives by Bates, Greif, Levi, Rosenthal and Weingast and covering one outside study by Mongin (2008). It first evaluates the explanatory performance of the new genre, using some philosophy of historical explanation, and then checks its discursive consistency, using some narratology. The paper concludes that analytic narratives can usefully complement standard narratives in historical explanation, provided they specialize in the gaps that these narratives reveal, and that they are discursively consistent, despite the tension that combining a formal model with a narration creates. Two expository modes, called alternation and local supplementation, emerge from the discussion as the most appropriate ones to resolve this tension.