This paper develops a measure of the influence of individual arguments in abstract argumentation frameworks. By applying ideas from power indices in coalitional game theory, the proposed measure—called admissibility impact value—quantifies the impact that individual arguments have on the set of admissible extensions of a given argumentation framework. It improves on existing impact measures in that it is more fine-grained and sensitive to small differences in the attack relations of argumentation frameworks. Special consideration is given to well-founded frameworks, where the improvements are particularly pronounced.