How critical are individual members perceived to be for their group's performance? In this paper, we show that judgments of criticality are intimately linked to considering responsibility. Prospective responsibility attributions in groups are relevant across many domains and situations, and have the potential to influence motivation, performance, and allocations of resources. We develop various models that differ in how the relationship between criticality and responsibility is conceptualized. To test our models, we experimentally vary the task structure (disjunctive, conjunctive, and mixed) and the abilities of the group members (which affects their probability of success). We show that both factors influence criticality judgments, and that a model which construes criticality as anticipated credit best explains participants' judgments. Unlike prior work that has defined criticality as anticipated responsibility for both success and failures, our results suggest that people only consider the possible outcomes in which an individual contributed to a group success, but disregard group failure.