Face recognition has been widely accepted as a means of identification in applications ranging from border control to security in the banking sector. Surprisingly, while widely accepted, we still lack the understanding of the uniqueness or distinctiveness of face as a biometric characteristic. In this work, we study the impact of factors such as image resolution, feature representation, database size, age and gender on uniqueness denoted by the Kullback-Leibler divergence between genuine and impostor distributions. Towards understanding the impact, we present experimental results on the datasets AT&T, LFW, IMDb-Face, as well as ND-TWINS, with the feature extraction algorithms VGGFace, VGG16, ResNet50, InceptionV3, MobileNet and DenseNet121, that reveal the quantitative impact of the named factors. While these are early results, our findings indicate the need for a better understanding of the concept of biometric uniqueness and its implication on face recognition.