As a definiton, ranking is « having a specified rank in a hierarchy. » or « give (someone or something) a rank or place within a grading system. » or again to rank is « to assign something a status or position to distinguish it from others in a group »…

So they are several ways to rank objects. For an NFT collection, some of theses methods are very used and are useful for a community or an holder to know differences between NFTs. One of these formulas is a method used by rarity.tool on Ethereum (opensea) and it is called simply « rarity score« .

This formula is nothing less than a formula so it’s impossible to know exactly the valor of an NFT in the futur. It’s only point of vue, with various choices y criterias. Sometimes, a community or project leaders want to accentuate the weight of some traits (or reduce it). We can then adapt our rarity calculation to match with these requirements.

Here is some elements to explain the method usually used by Web4Crypto to calculate rarity scores and ranking:

We’ll take an example. The #PancaSquad number 2694 which is ranked 203: ## The Rarity score For each trait, the rarity score is given by this formula: 1 / (trait pourcentage/100)

If we take this example above, considering Mouth trait :

• there is 5.27% of the NFTs with a Mustache
• the rarity score is then for this trait (mouth): 1/(5.27/100) = 1/0.0527 = 18.97

We can make the same calcul for all traits:

• Background: 1/0.07 = 14.28
• Bunny: 1/0.0926 = 10.80
• Clothes: 1/0.0596 = 16.78
• Eyes: 1/0.0772 = 12.95
• Mouth: 1/0.0527 = 18.97
• Ear: 1/0.0175 = 57.14
• Hat: 1/0.0024 = 416.67
• Traits count: 1/0.3502 = 2.85

Adding all these individual rarity score, you’ll get NFT’s « Total Rarity Score »

Total Rarity score = 14.28 + 10.80 + 16.78 + 12.95 +  18.97 + 57.14 +  416.67 + 2.85 = 550.44

NB:

• Decimals number can make a little variation in this result (if you take all decimals or only 2 like in this example)
• Traits count is a factor which is usually used in rarity score. So rarity score is the additon of all « individual rarity score » (here we have 6 traits including background) and of traits count.
• Attribute « none » is an attribute like other ones. We can have « none » in various traits (like hat, eyes, ear…)
• We can see here the Holo (hat trait) make increase consequently rarity score
• For PancakeSquad collection, the best rarity score is 70003.26 (for the 12 ex-aequo irst NFTs) and the lower is 90.63 (for the number 9679 which is 10 000/10 000) – see here

To established, final ranking, we have to calculate this result for all NFTs! Then we sort these results by Rarity Score (descending order).

The upper is number 1, the last one is ranked 10 000.

So ourPancakeSquad Number #2694 is ranked 203 compared to rarity scores of others PancakeSquad.

## Other formulas, other ranking

There are several probability ways to determine a ranking (Average Rarity, Statistical rarity, Trait rarity…). Most used formula in a domain is not necessary the same in another domain. For example, we’ll use others way to calculate real object rarity (collecton objects) for example with object datation. If you see others ranking on others website, it means the used formula is different. The website owner will have then obligation to inform you the way he has ranked NFTs of a collection.

« Rarity score » is now a standard for ranking NFT but sometimes, specificities can make big ranking variations. It depends creators choice, community choice or project goals… and your own opinion about an NFTs project…

Before a ranking is official (determined by the creator himself), we give you our ranking, based on known and most used formulas. Our ranking make sens but… is only a vision. Make yours by yourself!

If tou want to have more information about rarity methods, you can read these excellent posts from rarity.tools (here and here) who have settled first, rarity calculation methods in NFTs world.