Finding similar words with the help of word embedding models has yielded meaningful results in many cases. However, the no-tion of similarity has remained ambiguous. In this paper, we examine when exactly similarity values in word embedding mod-els are meaningful. To do so, we analyze the statistical distribu-tion of similarity values systematically, in two series of experi-ments. The first one examines how the distribution of similarity values depends on the different embedding-model algorithms and parameters. The second one starts by showing that intuitive simi-larity thresholds do not exist. We then propose a method stating which similarity values actually are meaningful for a given em-bedding model. In more abstract terms, our insights should give way to a better understanding of the notion of similarity in em-bedding models and to more reliable evaluations of such models.