This paper discusses the problem of testing the performance of the adaptation layer in a self-adaptive system. The problem is notoriously hard, due to the high degree of uncertainty and variability inherent in an adaptive software application. In particular, providing any type of formal guarantee for this problem is extremely difficult. In this paper we propose the use of a rigorous probabilistic approach to overcome the mentioned difficulties and provide probabilistic guarantees on the software performance. We describe the set up needed for the application of a probabilistic approach. We then discuss the traditional tools from statistics that could be applied to analyse the results, highlighting their limitations and motivating why they are unsuitable for the given problem. We propose the use of a novel tool – \emph{the scenario theory} – to overcome said limitations. We conclude the paper with a thorough empirical evaluation of the proposed approach, using two adaptive software applications: the Tele-Assistance Service and the Self-Adaptive Video Encoder. With the first, we empirically expose the trade-off between data collection and confidence in the testing campaign. With the second, we demonstrate how to compare different adaptation strategies.