Randomly acquired characteristics (RACs), also known as accidental marks, are random markings on a shoe sole, such as scratches or holes, that are used by forensic experts to compare a suspect's shoe with a print found at the crime scene. This article investigates the relationships among three features of a RAC: its location, shape type and orientation. If these features, as well as the RACs, are independent of each other, a simple probabilistic calculation could be used to evaluate the rarity of a RAC and hence the evidential value of the shoe and print comparison, whereas a correlation among the features would complicate the analysis. Using a data set of about 380 shoes, it is found that RACs and their features are not independent, and moreover, are not independent of the shoe sole pattern. It is argued that some of the dependencies found are caused by the elements of the sole. The results have important implications for the way forensic experts should evaluate the degree of rarity of a combination of RACs.