As a quick recap of the project — Avastars are tokenized avatars which exist on the Ethereum blockchain, and notably they store all of the artwork on the blockchain itself. So compared to other projects where the art sits on a server somewhere, while the token is only a reference ID, Avastars are groundbreaking in the ‘art-on-chain’ movement.
RANDOMLY GENERATED GOODNESS
Avastars are released in series of 5,000. For each series, people can scroll through a randomly generated gallery of Avastars composed of 12 different traits, ranging from common traits which appear 60% of the time to legendary traits which appear 0.25% of the time.
ON RARITY AND SELF-SELECTION
When you see a selection of Avastars in a gallery, it’s natural to wonder how rare is a given one? And maybe how valuable is it compared to others?
That becomes a difficult question to answer when you look at how the population of minted Avastars came into being.
First, you have the probability of certain traits appearing. So the probability of getting at least 1 legendary trait is about 3% or 1 in 34. But the odds of getting 4 legendary traits is roughly 0.000002% or 1 in 53 million (I’m not going deep on the math in this post.)
As a rough measure, you’d expect the population of Avastar traits to mirror the likelihood of finding them, and they do– but the results are also biased by the x-factor of how collectors are choosing to mint them.
For the most part, collectors are scanning for traits that appeal to them in some way. So if a legendary skin tone, such as Zombie is popular — it will over-index on how many you’ll find in the final minted population.
In fact, just browsing on OpenSea you will find that Zombie is the 5th most popular skin tone. If the Avastars were being randomly minted as generated you’d expect to see many more with the skin tone Mellow Apricot or Brown Sugar, which are Uncommon traits and should appear 90x more often than Legendary traits.
So– the rarity of Avastars is dynamic and changes according to the self-selection of the collectors.
TOWARDS A ‘UNIQUE BY’ RANKING
I wanted to develop an algorithm and system for ranking Avastars that matched how it seems like people are collecting and valuing them.
Anecdotally you would hear people say things like “This is the only Avastar with Zombie skin and Bright Pink eyes.”
And it seemed like it’s more rare a collectible when there are only a few of them, or if it’s unique.
All Avastars are unique if you look at all 12 traits but it seemed like if you could establish the minimum number of traits to establish the uniqueness of an Avastar, that could be useful.
INTRODUCING — ‘UNIQUE BY’
The concept is, an Avastar can be unique by 1, 2, 3,4 or however many traits it takes to distinguish it from all the others. So in the above example, that would be scored UB2 — meaning is it Unique By 2 Traits: Eye Color and Skin Tone.
To further differentiate how unique a UB2 is compared to other UB2’s — I looked at two factors. First, what are the odds that someone else could find this exact UB2?
In the example above, since this Avastar is unique by 2 traits, both Legendary, it should hold its UB2 status longer than a UB2 comprised of a Rare and Uncommon trait. Meaning there’s (very roughly) a 1 in 640,000 chance that someone else will find a Zombie with Bright Pink eyes in a future series.
But compare the above UB2 with this UB2…
This is only unique by 2 Rare traits. So it’s closer to a 1 in 256 chance that someone else could find this combo. Chances are it only exists as a UB2 because no one else wanted to mint that specific combo yet. It will probably settle as a UB3 or a UB4 when all 25,200 Avastars have been minted after series 5 ends.
UNTIL THE DUST SETTLES
I think this is a useful way of looking at the traits, but it will be impossible to settle on a final ranking until the end of series 5 because the population of traits will shift and change.
BUT EVERYONE LOVES LEAGUE TABLES
I couldn’t help ranking the Avastars, so I created a value based on the odds of finding similar traits and the number of traits in the current population that determine the unique by ranking.
And according to that, the Most Unique Avastar distinction goes to this one:
No surprise that Avastar #0 is the most unique. Hopefully this validates the approach though.
The Top 10 is biased towards Founders & Exclusives because those may draw from unavailable traits from future series, and will also contain more legendaries than prime Avastars.
… the Least Unique Avastar is:
And the Bottom 10…
Feel free to comb through the results in this spreadsheet:
Consider this an Open Source metric — I’m open to suggestions to improve it. Find me on the Discord channel.