Non-Rarity Metrics for Personal Profile Profile Pictures

There appear to be many different metrics for measuring the rarity of a bored ape or a cryptopunk, or for an PFP in the public domain, but in fact there are only four -- and all of them are incorrect!

A non-fungible token (NFT) is a digital asset that is generated in a large collection of similar but non-identical tokens, where the only limit on the total quantity supplied is that each must be unique. Personal picture profile (PFP) collections are images, some of which are already associated with avatars in the metaverse, and most also confer real-world benefits on token holders. Like Pokemon cards, the value of a collection depends in part on its scarcity. But the relative value of a token within a PFP collection depends on its rarity.

Tokens with many commonly-found attributes are typically perceived as less valuable than those with several rare attributes. The problem is that, even though numerous rarity metrics have been proposed, until now nobody knows how to measure rarity in a mathematically rigorous manner. And, using identical metadata from the token minting onto a blockchain, different metrics can give vastly different results -- ranking some tokens as very rare according to one metric but very common according to another.