Methodology of "RR" and "RS"

When browsing through Yumi you will mainly be confronted with one value for the rarity of an NFT but have the option to also view two more.

1. Rarity Ranking (RR) is the ranking of an NFT within a collection. It starts at 1 and goes up to the number of NFTs in a collection. The lower the ranking, the higher the rarity.

2. Rarity Score (RS) is the actual rarity score of the NFT according to the calculation described below. For more tech-interested users, this can be used to validate the rarity score of an NFT. The NFTs are sorted according to the rarity score (RS) to give the rarity ranking (RR).

3. Relative Rarity Ranking is the percentage rarity ranking of an NFT to give a quick metric to evaluate the rarity of your NFT. It’s the Rarity Ranking (RR) divided by the number of NFTs in that collection times 100. The NFTs are grouped into five categories

   • Top 0.1%

   • Top 1%

   • Top 5%

   • Top 20%

   • Common (= all others)

Example of the rarity values shown on Yumi. Left side shows the display on the overview page and the right side shows the display on the NFT detail page, including the tooltip.

Rarity Ranking is the score that you see on all NFTs by default. When hovering above the Rarity Ranking field, you see a tooltip that shows the Rarity Score and the Relative Rarity Ranking.

Methodology of "RS"

The Rarity Score is a method of quantifying the rarity of an NFT that was developed by OpenRarity and is currently being used on collections on Opensea. The formula for calculating the Rarity Score of an individual NFT is as follows:

Formula for Rarity Score.

In this equation, (R) is the Rarity Score of a specific NFT, P(trait) is the probability of an NFT having a certain trait, and (N) is the total number of properties of the NFT.

We chose to use the Rarity Score method for several reasons. Firstly, it provides a realistic representation of an NFT’s rarity, allowing users to accurately gauge its value. The method involves multiplying the probability of each trait to determine the probability of an NFT possessing all of its traits. This is then transformed into a numerical value using a base 2 logarithm, which allows for easy interpretation of the score. An increase of 1 of the numerical value of the score means that the NFT is twice as rare. For example, an NFT with a score of 21 is twice as rare as an NFT with a score of 20. This makes it easy to compare the rarity of different NFTs and make informed investment decisions.

To help users make informed decisions about which NFT to invest in, we added the above mentioned metrics Rarity Ranking and Relative Rarity Ranking. This allows users to quickly and easily compare the rarity of different NFTs within a collection.