In this paper a new use case for legal argumentation support tools is considered: supporting discussions about analyses of complex criminal cases with the help of Bayesian probability theory. By way of a case study, two actual discussions between experts in court cases are analysed on their argumentation structure. In this study the usefulness of several recognised argument schemes is confirmed, a new argument scheme for arguments from statistics are proposed, and an analysis is given of debates between experts about (...) the validity of their arguments. From a practical point of view the case study yields insights into the design of support software for discussions about Bayesian analyses of complex criminal cases. (shrink)