NFT Rarity Explained
What is rarity and why is it so important? Once a reveal happens and people on a Discord server can no longer ask ‘Wen reveal?’ a new batch of questions takes over: ‘How to check rarity?’, “Where do you check rarity?’ and so on. So what is rarity and why is it so important?
Simply put, rarity scores are an attempt to capture perceived rarity with mathematical formulae. They’re based on a few common-sense assumptions outlined below. Keep in mind that statistical rarity doesn’t always align with the official rarity of a collection: official rarity can be based on tokens’ utilities which are not always encoded in traits. So how exactly is rarity calculated?
Calculating rarity
At some point creators of a collection make all the metadata public. That metadata is a collection of traits and their values that make a particular token unique (in most cases at least, some collections might release duplicates). There are basically two main choices for rarity ranks:
- official rarity published by collection creators
- statistical ones calculated from mathematical properties of all tokens within a collection
The former is THE rarity to look at if it’s available. If you know about an existing official rarity, but don’t see it live on NFTNerds.ai, feel free to request it on our Discord server in the #reveal-requests channel by providing a link. The latter is best explained with an example, which we’ll provide in a moment.
Rarity on NFTNerds.ai
If there’s no official rarity, NFTNerds.ai will use statistical rank. This is calculated by ranking rarity scores of all tokens in a collection. It’s best explained with an example:
This particular token has 5 traits. Its plain rarity score is:
1/8% + 1/15% + 1/0.23% + 1/15% + 1/12% = 468.95
There are, however, two additional parameters to this algorithm: NORM and COUNT. They can be found at the bottom of the NFTNerds.ai page, next to gas settings. They are toggled on by default, which is a standard preset in other rarity apps as well. Both were turned OFF in the calculation above. Further down, we’ll demonstrate how turning them on will affect the final rarity.
NORM
Normalization is a setting that puts more weight on tokens with rare traits when there is little variety among them. There are 24 ‘Starts’ and only 5 ‘Levels’. So a rare Level should have more of an impact on the overall rarity. Normalization assigns higher weight to less diverse traits. We do that by adding a weight of 1/(count of a trait’s unique values) to every trait’s rarity score. So, to continue our previous example, the final rarity score with NORM ON would be:
1/8% * 1/20 + 1/15% * 1/5 + 1/0.23% * 1/10 + 1/15% * 1/24 + 1/12% * 1/9 = 46.64
COUNT
With COUNT we want to additionally boost the score of tokens with fewer traits, since they are often Genesis, Legendary, etc. To add to our example, let’s say 10% of all tokens have 5 traits and there are 7 possible combinations (some tokens have 4 traits, some have 6, etc.). COUNT basically adds an artificial trait to the equation that treats the number of traits as a trait itself. So our final score would be:
1/8% * 1/20 + 1/15% * 1/5 + 1/0.23% * 1/10 + 1/15% * 1/24 + 1/12% * 1/9 + 1/10% * 1/7 = 48.07
