An Agentic AI Workflow (AAW), also known as an LLM-based multi-agent system, is an autonomous system that assembles several LLM-based agents to work collaboratively towards a shared goal. The high autonomy, widespread adoption, and growing interest in such AAWs highlight the need for a deeper understanding of their operations, from both quality and security aspects. To this day, there are no existing methods to assess the influence of each agent on the AAW's final output. Adopting techniques from related fields is not feasible since existing methods perform only static structural analysis, which is unsuitable for inference time execution. We present Counterfactual-based Agent Influence Ranker (CAIR) - the first method for assessing the influence level of each agent on the AAW's output and determining which agents are the most influential. By performing counterfactual analysis, CAIR provides a task-agnostic analysis that can be used both offline and at inference time. We evaluate CAIR using an AAWs dataset of our creation, containing 30 different use cases with 230 different functionalities. Our evaluation showed that CAIR produces consistent rankings, outperforms baseline methods, and can easily enhance the effectiveness and relevancy of downstream tasks.