According to the Language Familiarity Effect (LFE), people are better at discriminating between speakers of their native language. Although this cognitive effect was largely studied in the literature, experiments have only been conducted on a limited number of language pairs and their results only show the presence of the effect without yielding a gradual measure that may vary across language pairs. In this work, we show that the computational model of LFE introduced by Thorburn, Feldman, and Schatz (2019) can address these two limitations. In a first experiment, we attest to this model's capacity to obtain a gradual measure of the LFE by replicating behavioural findings on native and accented speech. In a second experiment, we evaluate LFE on a large number of language pairs, including many which have never been tested on humans. We show that the effect is replicated across a wide array of languages, providing further evidence of its universality. Building on the gradual measure of LFE, we also show that languages belonging to the same family yield smaller scores, supporting the idea of an effect of language distance on LFE.