Overcoming NFT pricing challenge by 1/1 information-based pricing & Rarity function.
What’s the challenge?
Lately, we have been studying pricing problems across collectible NFTs(Non-Fungible Token) and we propose a new technique for pricing 1/1 collectible NFTs.It’s a critical problem for most startups and consumers. this challenge has different aspects from “how to price NFTs or any non-fungible asset fairly?”, “how to differentiate between every item based on their rarity?”, “How to price a non-fungible item proportional with respect to other members in the collectible group?”, to “How the average price should change over time?”.
How rare is an item in a collectible group?
One of the key challenges is to answer “which items are rare and how rare are they?”. Every member of a collectible group has a set of attributes that may or may not accrue in an item. for example, CryptoPunks Attributes have a known number of occurrences in the group. Beanie accrued only 44 times over 10,000 CryptoPunk so the probability of a punk having a beanie is 0.44% and if we compute self-information for occurrence of Beanie attribute, it’s equal to:
Probability of having a Beanie:
Self-information(Shannon information) of having a beanie is:
So for computing the rarity of punk (if attributes are mutually independent) we could compute total information of all attributes for each punk by sum of all self-information for all attribute of all punks and get Total information vector:
*We could say it’s the third axiom of information theory
Now we can make a rarity scale of all punks by their sum of self-information (total information). we can make a rarity function by rescaling the Total information of all punks via Min-max feature scaling and make a rarity function for the collectible group.
Rarity function:
Now we have a rarity score of all punks ranged from 0 to 1.
*R = 1 means it’s the rarest.
*Min-Max feature scaling is just a linear transformation that normalizes data to be 0 < R ≤1.
*R is unique for a collectible group.
By utilizing the rarity function we computed the rarity score for all XmasBook episodes (what is XmasBook?).
*TLDR:(XmasBook is a collectible NFT that act as Xmas tree substitute featuring all kind of crazy characters and it’s fun to read, learn more)
And here is the graph for all 2021 items and how rare they are.
You can see the rarity of all 2021 XmasBook and their distribution across the index of tokens.
As you can see rarer items are distributed homogenously through the collection.
How to price?
As we write this article we only minted 100 tokens from the 2021 tokens that we designed.
And we believe in making a price that is fair for everyone. (let’s investigate some pricing technique)
The first case(uniform pricing): If we price every item the same(let’s say X) and releasing them simultaneously some people are going to get hyper rare items for the price of X and other people are going the get a simpler item for the same price X. and this may lead to consumer dissatisfaction because the price is not proportional to the rarity of the items that they have got.
The second case(introducing uncertainty): if we price items and not revealing what item consumers are going to get, after purchase is completed if a consumer not desire all of the items in the collectible group, then some of them are going to stuck with the item that they may not desire and some people are not going to risk the purchase.
Our case(1/1 pricing): after we drove the rarity score we needed a price function that addresses some of the issues that we got introduced.
What was our goal:
● Differentiating items
● Proportional pricing
● Removing uncertainty
● Fair price distribution
● Increasing the price as the network of people owning XmasBook is growing greater.
We chose a price function that forces the price to be under the curve of a function that it would be accessible for almost everyone on the network at every sub collections we are going to release.
Here’s the price function:
Max price curve:
Max price function is showing the price if the rarest item is released at that index.
By enveloping (multiplying to functions) the max price function and rarity score we got the following prices in Ethereum.
Results:
We made a wide range of prices proportional to the rarity score of an item and the number of released items at the time of sale and there is no uncertainty in which NFT you are going to get.
*another byproduct of this method is that all of our items have a unique and 1/1 price.
Here is the list of price points for XmasBook.
First 100 items(let’s call it the first century):
5% of the first 100 items are below 0.06343884192458042 eth
15% of the first 100 items are below 0.0912036715792409 eth
25% of the first 100 items are below 0.1061309917907132 eth
50% of the first 100 items are below 0.13764066611196069 eth
75% of the first 100 items are below 0.16313128706892646 eth
95% of the first 100 items are below 1.095611143296953 eth
All of 2021 items:
5% of all 2021 items are below 0.19527977150195455 eth
15% of all 2021 items are below 0.41387851396084996 eth
25% of all 2021 items are below 0.6857224085204267 eth
50% of all 2021 items are below 1.708159388575348 eth
75% of all 2021 items are below 3.453451487357393 eth
95% of all 2021 items are below 15.941282532763895 eth
We put our first 100 NFTs for sale using this technique.
You can check the sale at this https://opensea.io/collection/xmastree
We would be really happy if anybody else uses this method for pricing their NFTs or anything else.
If you use this function or have a similar experience leave a comment below.
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