Proposal: Add Trait Count to OpenRarity

Since launching OpenRarity on September 21st, we’ve gotten a lot of great feedback from the community. One of the most frequent points of feedback has been around the inclusion of Trait Count into the rarity ranking algorithm. As a result, we explored what adding Trait Count would look like and would love to get your feedback.

One of the core tenets of OpenRarity is to adhere to publicly defined metadata. While this remains true, it’s also important to us to stay open-minded and invite the community to participate in designing the best rarity algorithm that we can all trust and get behind.

Let’s dig in 👇

## How does Trait Count work?

In traditional rarity ranking algorithms, Trait Count is a “meta-trait” that gets added as an additional trait before rarity is calculated.

For example:

This treats Trait Count just like any other attribute, and thus can have a significant impact on rarity rank.

## Trait Count and Information Content

As we discussed in our launch post, OpenRarity takes a different approach to calculating rarity by using Information Content (IC). While traditional rarity produces the probability of a token having a Green Hat or a Blue Hat, IC produces the probability of a token having a Green Hat and a Blue Hat, which is more mathematically accurate.

Let’s look at the case of calculating rarity for Doodles. Traditional rarity would evaluate, for example, the probabilities of one NFT having Pink Beard, Green Bowlcut or Yellow Backpack. In contrast, IC produces the probability of this token having Pink Beard, Green Bowlcut and Yellow Backpack. In this case, the IC method accounts for the fact that this NFT has all of these attributes and not that it might have at least one of these attributes. This difference in approach will also apply with Trait Count as an additional trait, and its impact on rank may vary from collection to collection.

## OpenRarity with Trait Count Experiment

We plotted the rank distribution grouped by trait count for each rarity strategy across several high volume collections.

### Key takeaways

• Legacy Rarity tends to consider low trait count tokens much rarer than Information Content does, even when including trait count in Information Content.

• The fewer Trait Count options in the collection, the more rarity ranks will be impacted by Legacy Rarity due to Trait Normalization.

• Including trait count in Information Content tends to produce a distribution signature that is more similar to Legacy Rarity, but is never going to be an exact match.

### Data analysis

In the charts below, the Y axis is the rank, and the X axis is the trait count. Each group will show three columns that show rank distribution for:

1. IC: Information Content as it is today

2. IC+TC: Information Content with Trait Count included

3. Legacy Rarity: Curio’s previous rarity formula that sums the normalized inverse trait probabilities of an asset. Extremely similar, but not always identical to Rarity Tools and Rarity Sniper.

Bored Ape Yacht Club

For BAYC, Legacy Rarity considers tokens with Trait Count 4 exceptionally rare. Around 3% of BAYC tokens have 4 traits, making “Trait Count: 4” the 100th scarcest trait in the collection (out of 175 traits). However, after Trait Normalization, Legacy Rarity considers Trait Count 4 to be the 4th rarest trait in the collection in terms of score—just behind “Mouth: Bored Unshaven Dagger”, which only 28 tokens have and is the 2nd scarcest trait in the collection.

The fewer Trait Count categories in the collection, the more a collection’s rarity ranks will be impacted by Legacy Rarity’s Trait Normalization on Trait Count.

Pudgy Penguins

Another good example is Pudgy Penguins. In Pudgy Penguins, all tokens either have 4 or 5 traits—with 3% of tokens having 4 traits and 97% having 5 traits. From the distribution above, we can see that Legacy rarity considers all tokens with 4 traits to be within the top 200 rarest tokens in the collection. Why?

Pudgy Penguins has 5 native trait categories (Background, Body, Face, Head, Skin). Each category has an average ~34 options to choose from (eg. “Pineapple Suit” is one option from the “Body” category). Trait Count on the other hand only has 2 options to choose from.

Since Trait Normalization attempts to boost trait categories with fewer options and there are only 2 trait category options for Trait Count in Pudgy Penguins, Legacy Rarity considers Pudgy Penguins in trait count 4 to be among the rarest tokens in the collection.

In terms of scarcity, Trait Count 4 is the 119th scarcest trait out of the 175 traits in the collection, but it is the 22nd rarest trait in terms of rarity score in Legacy Rarity. The 21st rarest trait is “Head: Hatched Gold”, which is only present for 0.1% of tokens making it the 20th scarcest trait. The 20th rarest trait is “Skin: Ice”, which is present in 0.2% of tokens making it the 23rd scarcest trait.

This phenomena of Legacy Rarity greatly impacts the ranks in most collections since Trait Count is often the trait category with the fewest options in any given collection.

Azuki

For Azuki, we can see that adding Trait Count to IC bumps Azuki #2152 to rank #1 because it’s the only token with Trait Count: 5. On the flip side, we see that IC+TC finds items with Trait Count 8, 9, or 10 to be rarer than Legacy Rarity does.

World of Women

IC+TC improves the rank distribution for Trait Count 7 and 8 in World of Women, although all Trait Count 11s are ranked higher than Legacy Rarity.

Doodles

Adding Trait Count to Doodles seems to line up more squarely with Legacy Rarity. A near exact match.

Moonbirds Oddities

For Oddities, the distribution on Trait Count 4 and 5 shifts higher, but will likely not satisfy holders as rank divergence can still be as high as 5,000.

## Discussion

As we can see in the data, adding Trait Count to OpenRarity’s Information Content algorithm tends to increase the rank of the rarer Trait Counts. When comparing it to traditional rarity, for example in the case of BAYC, it may not get closer to the results that community may expect. On the other hand, with Doodles, it does match up much more closely.

Given these results, we propose adding Trait Count to OpenRarity as it does push ranks in the right direction. The one caveat being that our underlying methodology, Information Content, will make it so our results will not necessarily match Legacy Rarity perfectly.