Using real-world study data usually requires contractual agreements where research results may only be published in anonymized form. Requiring formal privacy guarantees, such as differential privacy, could be helpful for data-driven projects to comply with data protection. However, deploying differential privacy in consumer use cases raises the need to explain its underlying mechanisms and the resulting privacy guarantees. In this paper, we thoroughly review and extend an existing privacy metric. We show how to compute this risk metric efficiently for a set of basic statistical queries. Our empirical analysis based on an extensive, real-world scientific data set expands the knowledge on how to compute risks under realistic conditions, while presenting more challenges than solutions.