In the so-called rare type match problem, the discrete characteristics of a crime stain have not been observed in the set of background material. To assess the strength of evidence, two competing statistical hypotheses need to be considered. The formulation of the hypotheses depends on whichidentification of source question is of interest (Ommen, 2017, Approximate statistical solutions tothe forensic identification of source problem. (Phd thesis). South Dakota State University). Assuming that the evidence has been generated according to the beta-binomial model, two quantifications of the value of evidence can be found in the literature, but no clear indication is given when to use either of these. When the likelihood ratio is used to quantify the value of evidence, an estimateis needed for the frequency of the discrete characteristics. The central discussion is about whether or not one of the traces needs to be added to the background material when determining this estimate. In this article it is shown, using fully Bayesian methods, that one of the values of evidence from the literature corresponds to the so-called 'identification of common source' problem and the other to the 'identification of specific source' problem (Ommen, 2017, Approximate statistical solutions to the forensic identification of source problem. (Phd thesis). South Dakota State University). This means that the question whether or not one of the traces needs to be added to the background material reduces to the question whether a common source or specific source problem is under consideration. The distinction between the two values is especially important for the rare type match problem, since the values of evidence differ most in this situation.