Ranking Rarity: Understanding Rarity Calculation Methods

The Problem

If you look at any collectible NFT item on OpenSea, such as a Bored Ape Yacht Club, you will see that it has many properties (or traits).

Bored Ape Yacht Club #73’s Properties
Bored Ape Yacht Club #9941’s Properties .. is he rarer than #73 above?
We’ll compare the above 2 apes with #9542 here

Trait Rarity Ranking

This refers to comparing NFTs by simply comparing the rarest trait of each NFT. For example, comparing the Apes above:

  • Ape #9941's rarest trait is Bored Unshaven Dagger which 0.28% have
  • Ape #9542’s rarest trait is Bored Unshaven Pizza which 0.26% have
Sorted by Trait Rarity
Example Collection A NFTs

Average Trait Rarity

Another method that is sometimes used is averaging the rarity of traits that exist on the NFT.

  • Ape #9941’s average trait rarity is 6.056%
  • Ape #9542’s average trait rarity is 6.452%
Average Trait Rarity Ranking
Example Collection A: Average trait rarity is calculated and listed at the rightmost column.
Example Collection B: A collection that has 10 NFTs
Example Collection B: With trait rarity percentages listed.
Example Collection B: With Average Trait Rarity on rightmost column.

Statistical Rarity

Now lets look at Statistical Rarity which has become a somewhat popular method and is used very often in community made spreadsheets.

What the calculation looks like in Excel
  • Ape #9941’s statistical rarity is 0.00000056965722%
  • Ape #9542’s statistical rarity is 0.00000044983967%
Statistical Rarity Ranking
Sorted by Trait Rarity
Sorted by Average Trait Rarity
Sorted by Statistical Rarity

Statistical Rarity vs. Example Collection A and B

Now let’s see how Statistical Rarity does with our 2 example collections that we tested Trait Rarity and Average Trait Rarity with.

Example Collection A: With Statistical Rarity
Example Collection B
Example Collection B: With Statistical Rarity

Rarity Score: How is it Calculated?

So, what is Rarity Score? Rarity Score is a method that I (the founder of rarity.tools) came up with.

Rarity Score vs. Example Collection A and B

Let’s go ahead and see how Rarity Score tackles our two problem examples.

Example Collection A: Rarity Score for each Trait Value and Total Rarity Score for each NFT ID

Summary

As noted, Statistical Rarity and Average Rarity have a tendency to over-emphasize the overall level of rarities of all traits in an NFT, while not giving enough emphasis to single rare traits that could be 1 of 1s in the whole collection.

What’s Next?

While the calculation methods are the most core part of calculating the rankings, there are still many additional elements that are used to get the best final result.

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rarity.tools

https://rarity.tools : NFTs ranked and sorted by rarity! See the rarest CryptoPunks, Hashmasks, Waifusions and Chubbies and check how rare a specific ID is.