Measuring the Rarity of Non-Fungible Token Collections

Abstract

Rarity is a key determinant of value in non-fungible token markets, yet its measurement remains fragmented, opaque, and theoretically underdeveloped. We analyse the statistical and combinatorial rarity metrics used by major platforms and show that most reduce to transformations of the Pythagorean means. The widely-used OpenRarity metric produces rankings identical to the geometric mean of attribute frequencies and is therefore not a new methodology. However, this approach admits a coherent probabilistic interpretation only under the assumption of trait independence. Alternative arithmetic- and harmonic-mean metrics lack theoretical justification, while the Jaccard distance is structurally biased when metadata omit missing traits. When metadata are standardised appropriately, Jaccard-based rankings are identical to the arithmetic mean ranks. These findings explain pervasive inconsistencies in rarity rankings and help explain the weak empirical relationship between price and rarity. We propose a standardised, theoretically grounded framework for rarity measurement that accommodates dependence structures and corrects metadata bias.