Many face recognition studies use average faces as a theoretical concept (e.g., face norm) and/or a research tool (e.g., for face morphing), nonetheless, how the averaging process—using an increasing number of faces to create an average face—changes the resulting averaged faces and how our visual system perceives these faces remain unclear. Here we aimed to address these questions by combining 3D-face averaging, eye movement tracking, and the computation of image-based face similarity. Our results show that average faces created with an increasing number of “parent” faces become increasingly more similar to each other. Participants’ ability to discriminate between two average faces dropped from near-ceiling level (when comparing two average faces created each from two-parent faces) to chance level (when the faces to compare were created out of 80 faces each). The non-linear relation between face similarity and participants’ face discrimination performance was captured nearly perfectly with an exponential function. This finding suggests that the relationship between physical and perceived face similarity follows a Fechner law. Eye-tracking revealed that when the comparison task became more challenging, participants performed more fixations onto the faces. Nonetheless, the distribution of fixations across core facial features (eyes, nose, mouth, and center area of a face) remained unchanged, irrespective of task difficulty. These results not only provide a long-needed benchmark for the theoretical characterization and empirical use of average faces, but also set new constraints on the understanding of how faces are encoded, stored, categorized and identified using a modernized face space metaphor.