19
What is the rarity score of NFT?
In general, there are 2 types of NFT rarity scores: Trait Rarity(TR) & Asset Rarity(AR)
Trait Rarity measures the percentage of occurrence frequency of each property. For example, the rarity score of trait "Background_Blue" is 10.44% for there are 522 "Background_Blue" bears in a collection of 5,000 uniquely generated NFTs.
Figure 1 Trait Rarity of Short Bear Club
Asset Rarity represents the total rarity score of the asset and can be used for horizontal comparison and ranking. The value of a single NFT is often influenced by rarity. For NFT collectors, when they're thinking about which NFT to buy, they want to spend the same amount of ETH to get the most return out of it, so rarity is one of the most important reference metrics.
Solutions provided by the current market
Rarity score of Rarity.Tools
Rarity.Tools has the widest users for the time being. Its methodology is to add the reciprocal total value of the percentage of each feature's frequency of occurrence.
Figure 2 Image via Rarity.Tools Medium
However, Rarity.Tools adjusted its formula recently and the statistical approach has not been disclosed yet.
Rarity.Tools is an NFT Rare Data Analysis tool that existed before the outbreak of NFT Summer. The calculation model facilitates the users to figure out which feature contributes most to the overall rarity score. But the disadvantage of its simple summary is that it can lead to overestimating or underestimating an asset's true rarity. For example, if the score of a feature or the number of features seems too high, the NFT's ranking may be raised to some extent without concern about the feature.
Rarity score of NFTEXP
The calculation of Rarity score is more complicated in NFTEXP, which has not been disclosed yet. The score takes the population of traits into account. Here is a more practical example illustrated on NFTEXP's website:
For the collection ‘Chubbies’, there are two traits with similar probability:
- Face: Blushed, with 1053 Assets (10.5%)
- Hairstyle: Afro, with 1110 Assets (11.1%)
Figure 3 Image of Chubbies via NFTGO
The two traits look pretty similar at first glance. has a TR of 8, while has a TR of 17. That is because there are only 4 hairstyles, but 13 faces. So, a Blushed Face’s real rarity lies even below the average Face (13 Faces = 7.7% each, has 10.5%), while an has an above-average real rarity (4 Hairstyles = 25% each, has 11%).
The feature rarity of NFTEXP takes into account the effect of the number of categories in the feature, as in the example above. The frequency with which each feature appears is compared to the average frequency, and the feature score is adjusted accordingly. However, NFTEXP has the same drawbacks in asset rarity as Rarity.Tools as detailed in the comparison of anomalies below.
A Better Rarity Score Model
In general, synonyms of rarity are special and unique. Essentially, the rarity of an object depends largely on its differences from other objects: the greater the difference is, the more special and rarer this object will be. Quantifying the combined difference between an object and other things within the group reflects the object's rarity. According to this principle, has developed a more scientific way to assess the rarity of an NFT -- a rarity scoring method based on Jaccard Distance
What is Jaccard Distance?
Jaccard Distance is a statistical method that's been used in testing the dissimilarities between sample sets, with a range from 0 to 1. The mathematical representation is written as:
Jaccard Distance is a common data science approach used to measure the diversity between objects. The logic looks similar to Venn diagrams that measure the size of the intersection among the samples.
How to calculate NFTGO rarity score?
NFTGO calculates the similarity of NFT features purely based on Jaccard distance. Below are the steps how NFTGO calculates the rarity scores of BAYC#1154
- Counting the Jaccard Distance of BAYC#1154 with the other 9999 NFTs in the collection
- Counting the average value of the Jaccard Distance, which is the initial data of rarity scores.
- Normalizing the results from Step#2. The mathematical representation of the normalization formula is written as:
- Multipling the z-score by 100, through which we get the final NFTGO's rarity score of BAYC#1154. Then ranking all scores in its collection. (The rarity score ranges from 0 to 100
Validity of NFTGO's Rarity Score Model
We calculate the NFT rarity score for BAYC and Meebits based on three different rarity models: NFTGO, Rarity.Tools, and NFTEXP respectively to validate our assumptions by collecting the highest offer (max offer price) on OpenSea.
Table 1 The relationship of BAYC rarity ranking percentage provided and its max offer price (Data: 2 October 2021)
Figure 4 The positive correlation relationship between BAYC rarity provided and max offer price (Data: 2 October 2021)
Table 2 The relationship of Meebits rarity ranking percentage provided and its max offer price (Data:2 November 2021)
Figure 5 The positive correlation relationship between Meebits rarity provided and max offer price (Data:2 November 2021)
According to tables and graphs above, the relationship between three rarity score models and the max offer is basically similar. It shows there is a positive correlation with the highest quote. This shows that NFTGO rarity scores reflect NFT rarity objectively and accurately as same as other mainstream rarity score models.
Why Are NFTGO Rarity Metrics Superior?
Because our model makes a comprehensive assessment of an asset’s actual rarity, which will help you to figure out the appropriate price. The mainstream rarity score” on the current market might mislead you to overestimate or underestimate the real rarity of an asset.
The following table shows the abnormal value of rarity scores of BAYC, when we compare three sets of rarity ranking from NFTGO, Rarity.Tools and NFTEXP.
Table 3 BAYC Rarity Ranking and Max offer Price (Data: 2 October 2021)
Among the 26 NFTs with abnormal values the top 22 data sets are overestimated by Rarity.Tools and NFTEXP since "trait count = 4" take a large proportion in the overall score. The last 4 data sets are understatemated by Rarity.Tools and NFTEXP because "trait count = 5" takes a small proportion in the overall score.
In the case of BAYC #947, NFTGO ranked it as the least rare ape, with a rarity of 406. However, Rarity.Tools ranked it 775th with a rarity of 168.23. This is because of Rarity.Tools simply adds each feature and number of features (however, it doesn't actually have any additional special features). As the picture below shows, the monkey has no particular characteristics. So why is this ape in the top 10% of Rarity.Tools and NFTEXP? It is clear that the number of features is too high for the rarity score, with 136.7 out of a total score of 168.23. The total number of apes with four characteristic attributes is 254, and the total number of apes with six characteristic attributes is 5,323. According to the rarity formula provided by Rarity.Tools, it doesn't make sense that apes with four characteristic attributes are relatively scarce compared to apes with six feature properties
Figure 6 Rarity.tools rarity score details for BAYC#947 (Data:2 December 2021)
Figure 7 NFTGO's rarity score details for BAYC#947 (Data:2 December 2021)
BAYC #2832BAYC #8742 as a comparison, and it's quite obvious that BAYC #2832 should be rated higher because of its diversified characteristics. Besides, it should also be noted that the max offer price of BAYC #8742 is higher than BAYC #2832. Therefore, purchasing BAYC#2832 would be profitable since underestimation of its rarity score.
Figure 8 Rarity.Tools rarity score details for BAYC#2832 and BAYC#8742 (Data: 2 December 2021)
Figure 9 NFTGO's rarity score details for BAYC#2832 (Data: 2 December 2021)
Figure 10 NFTGO's rarity score details for BAYC#8742 (Data: 2 December 2021)
As is shown in view pane, percentages of most values of BAYC#2832 are from 3% to 1%, which are even lower than those of BAYC#1154. While the lowest one of BAYC #8742's value is up to 12.42%. It is obvious that the rarity score model of NFTGO shares a larger validity than that of
Rarity.Tools. This conclusion can also be verified by the last price of BAYC#2832 and BAYC #8742 (0.41ETH V.S --).
We have also compared Rarity.Tools and NFTGO's rarity ratings for CryptoPunks. We found that nearly half of the top 21 in Rarity.Tools' ranking for CryptoPunks were Punks with zero characteristic! NFTGO has a lower ranking for this kind of Punk because of the lack of diversity.
Figure 11 Top 21 Punks in Rarity.Tools
Figure 12 Top 20 Punks in NFTGO
The results show that NFTGO's rarity scoring method based on Jaccard Distance performs better in measuring dissimilarity than Rarity.Tools and NFTEXP.
Conclusion
Rarity score is an auxiliary tool for investors to buy or sell an NFT. While our rarity model is statistically correct, sometimes the official website of a NFT project gives more important announcements about certain traits. For example, Cool Cats officially states that common items such as eaves urinals are worth less than rare items such as computer heads or ape-man clothing. Moreover, there are other ways you can gauge the value of an NFT asset such as artistic height or liquidity premium. Beyond that, you would prefer the green background more than the red background, which is a subjective evaluation.
Calculating the group differences of an NFT asset based on Jaccard Distance helps us discover the group comprehensive differences of NFTs, which actually quantifies the concept of "rarity" more essentially. You can view the rarity rankings and rarity scores of all NFTs on NFTGO. We hope that NFTGO rarity score will help you make more reasonable decisions when collecting NFTs.
If you have any suggestions about NFTGO's rarity model, please email [email protected].
