Understanding Rarity Rankings

This article analyses the different rarity methods and compares pros vs cons.

# Understanding Rarity Rankings

# Welcome to NFT INSIGHTS, from Rareboard.

With the help of community volunteers, Fab evolved fabboard from the popular vercel app that used to live on fabboard.vercel.app/pancakesquad into rareboard.com

Rareboard’s goal is to become the most trusted tool for analysing the rarity, and potential value, of NFT collections.

Our app gained a huge number of users in its first week (breaking Fab’s data plan more than once) when it quickly became the most credible source for assessing the rarity of the PancakeSquad NFT release.

This article analyses the methods that Fab employed on the original app, and explains the choices for emphasis in the new app.

Our goal is to help you get ahead of the market by presenting reliable live data and research in order to make informed decisions on which NFTs you want to add to your collection.

The rarity methods we use are objective in their own way, but it is a subjective choice for you as a collector to decide how to benefit from the data we present. Please be familiar with the terms of usage of the ranking methodologies and do your own research and due diligence check. In the descriptions of the rarity ranking types, we have used an example of the same NFT to show how different methodologies generate different rank numbers for the same token.

As NFT collecting matures, so will the methods that rareboard.com presents. We are an open group that is able to iterate extremely fast, based on community feedback and needs. This document itself will evolve over time, and experts will be invited and encouraged to add to our library of research on articles.rareboard.com.

# Sets - A Brief Interlude

Before we share our research into the common rarity methods for NFTs, we would like to mention the concept of Sets.

Sets are an established method of assessing the potential impact of combinations of attributes within an NFT collection. With the Bored Ape Yacht Club, this matching of attributes became to be known as a Theme Match, and within Rareboard we call these matches Sets.

The most famous Sets in the PancakeSquad is the None Club, where the rarest Set contains four None attributes. Taking Sets into account has a significant impact on the potential rarity of NFTs, and we will be sharing a full Rareboard Research article on this topic in the near future.

In order to include Sets in any of the rarity methods on Rareboard, simply select + Sets from your chosen Scoring Method.

# Rareboard’s Scoring Methods

# Rarity Score (RS)

Rarity Score is a rarity ranking method developed and popularised by the founders of rarity.tools. It is thus promoted as the default ranking method for most collectors of NFTs.

It was originally implemented in April 2021 on WFBrowser by Crazy4NFTs and is now the method used on the rarity.tools platform.

The method uses the formula:

[Rarity Score for a Trait Value] = 1 / ([Number of Items with that Trait Value] / [Total Number of Items in Collection])

The total Rarity Score for an NFT is the sum of the Rarity Score of all of it’s trait values.

The intention of the Rarity Score method is to find a way to emphasise single rare traits, whilst still including the overall trait rarities as part of its calculation.

Note on normalisation of traits: Depending on the design and combinations inherent in an NFT population, it is pertinent to normalise the trait score before computation is made for the Rarity Score. Normalisation is a process of ensuring that the right weighting is applied to a trait taking into consideration that the trait may belong to a subclass of attributes (or variants) of that trait. Where there are subclasses of trait, it is thus important to ensure that the subclasses distribution is taken into consideration for computation. Normalisation has a bigger impact on the ranking based on the Rarity Score method.

# Pros

The method is popular and therefore may influence market decisions The method matches some human expectations as people seem to be able to process single rare traits intuitively, in a way they cannot immediately process true statistical rarity The method accounts for single rare traits, which may be an indication of desirability

# Con

The method in itself is not based on known statistical methods for computation.

For further reading about this method, we recommend the link below: https://raritytools.medium.com/ranking-rarity-understanding-rarity-calculation-methods-86ceaeb9b98c

# Statistical Rarity (SR)

Statistical rarity is an objective method that accounts for the rarity of all of the NFT’s attributes in order to arrive at an overall rarity rank. Although it is perhaps the most robust mathematically, it is not as popular as Rarity Score, in the current NFT space.

For the nerds, the Statistical Rarity method obeys the theorem of probability. It solves the problem of determining the rarity of an NFT by considering the weighted combination of all the attributes.

Each rarity attribute is presented as a percentage. The statistical approach combines all the attributes by multiplication to arrive at a combined ranking based on Statistical Rarity.

Statistical Rarity ignores subjectivity and as such may become more useful over time as a good measure of objective ranking.

[Statistical Rarity Score] = [Attribute Trait Value 1] * [Attribute Trait Value 2]... [Attribute Trait Value N]*

# Pros

Removes subjectivity and obeys the theorem of probability which is widely adopted in the world of statistics. The strength of this method is that it is a blank canvas of ranking before subjectivity is introduced. Statistics is the science of decision making under uncertainty, which must be based on facts not on rumours, personal opinion, nor on belief1.

# Cons

It removes the element of judgement, guesswork and intuition which can be useful in determining the value of an NFT. Statistical Rarity is currently less popular than the Rarity Score method, and may therefore influence short term trading less heavily than Rarity Score.

For further reading about this method, we recommend the links below: https://achekroud.substack.com/p/d8f13e0a-ae26-40e4-bff2-beacb2916ff0 http://home.ubalt.edu/ntsbarsh/stat-data/Topics.htm#rbfcl

# Average Rarity

Average rarity method also takes into account all the trait attributes to arrive at a rarity rank. However, it does it by an average of all the rarity attributes, which is less mathematically robust than Statistical Rarity. Whilst the average rarity method uses all the available attribute data, it is simplistic in its approach by using an arithmetic average. It is calculated by the sum of attribute values divided by the number of attributes.

[Average Rarity Score] = ([Attribute Trait Value 1] + [Attribute Trait Value 2]...+ [Attribute Trait Value N])/N

# Pro

The average rarity method considers all attributes available in a class.

# Con

The value can be skewed to higher attributes and hence provides a distorted rank which may give a confusing result.

# Trait Rarity

Trait rarity is a simple method that ranks NFTs by their rarest trait. It does not seem to offer a satisfying result either mathematically or subjectively.

# Pro

It is a very simple method for judging rarity. It can be very useful for a quick decision about an NFT as the rarest trait immediately translates to the score or rank.

# Con

Can be deceptive in ranking the rarity of NFTs. For example, all NFTs with the same lowest trait score are ranked the same regardless of any other rarity trait score.

Neither Average Rarity or Trait Rarity are particularly satisfying either mathematically or subjectively and neither are popular in the NFT space. For this reason these ranking methods have less emphasis on the board, so that it is easier for users to try to estimate the value of their NFTs.