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How can the Rarity (Rarity) of NFT be evaluated more properly?

2021-12-07 17:19

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Title: How to Evaluate the Rarity (Rarity) of NFT more properly?

Original source: NFTGO

What is the rarity of NFT?

Generally speaking, the rarity of NFT consists of two concepts: feature rarity and asset rarity.

Feature rarity: Measures the frequency of occurrence of each feature, i.e. the percentage of the set that has that feature. For example, the feature "Background_Blue "has a rarity score of 10.44% because there are 522 "Background_Blue" bears out of a total of 5,000 Short Bear Clubs.

Figure 1: Short Bear Club feature rarity

Asset rarity: Represents the total rarity score of the asset and can be used for horizontal comparison and ranking. The value of an individual NFT is often heavily influenced by its rarity. For NFT collectors, when they are considering which NFT to buy, they want the maximum return for the same amount of ETH, so rarity becomes one of the most important reference indicators.

Existing rarity scoring model

10. Rarity Rating by a. Tools

A. Tools is the most widely used Rarity scoring tool by the vacancy. At its core, it is calculated by adding the total inverse of the percentage frequency of each feature.

Figure 2: Rarity model of A. tools (source Medium)

10.Tools, however, recently adjusted its computational model and has not publicly disclosed the details. A. Tools is an NFT Rarity data analysis tool available prior to the OUTBREAK of NFT Summer, and its advantage lies in the simplicity of its calculation model. Users can intuitively see which feature contributes more to the overall rarity score. However, the disadvantage of simple summing is that it may overestimate or underestimate the true rarity of an asset. For example, if the score of a feature or number of features is too high, the NFT ranking will be increased to a certain extent, but users may not pay much attention to the feature.

NFTEXP rarity score

The calculation of the rarity in NFTEXP is more complex and has not yet been disclosed. We can only get a rough idea of the NFTEXP model from the NETEXP website. In the case of the "Chubbies" project, the frequencies of two features are as follows:

Face: From the cardboard share store, 1,053 (10.5%).

Hairstyles: Afro, 1110 (11.1 percent).

Figure 3: Overview of the Chubbies project (source: nftgo.io)

The rarity of the two features is almost identical in percentage terms. But: "Blushed" has a feature rarity rating of 8, while Afro has a feature rarity rating of 17. That's because there are only four hairstyles and 13 facial features. So one "Blushed" has less authentic rarer than "average face" (13 facial features at 7.7 per cent compared with 10.5 per cent) while one "Afro" has more authentic rarer than average (4 hair features =25 per cent compared with 11 per cent for Afro).

The feature rarity of NFTEXP takes into account the influence of the number of categories in the feature. The frequency of each feature is compared with the average frequency and the feature score is adjusted accordingly. However, NFTEXP has the same disadvantage as A. Tools, which will be discussed in more detail in the next section, "Exception Comparison."

A more reasonable rarity scoring model

Generally speaking, synonyms for rare include special and unique. Whether an item is rare or not depends mainly on how different it is from other items in the group. The more different it is, the more special and rare it is. So, if you can quantify the overall difference between this thing and other things in the group, you can reflect its rarity in the group. Based on this principle, NFTGO developed a more scientific method to evaluate the rarity of NFT -- the rarity scoring method based on Jaccard distance (hereinafter referred to as NFTGO rarity scoring).

What is the Jaccard distance?

Jaccard distance is a statistical method used to test for dissimilarity between sample sets, ranging from 0 to 1. Its mathematical formula is:

Jaccard distance is a common data science measurement method used to calculate differences between objects. The logic looks like a Venn diagram, measuring the size of the intersection between sample sets.

How to calculate the NFTGO rarity score?

NFTGO purely calculates the similarity of NFT features based on Jaccard distance. Let's take the BAYC#1154 rarity score as an example:

Calculate the Jaccard distance between #1154 and 9999 other NFT in the same series

Calculate the average of the Jaccard distance, which is the initial data for the rarity score

The range method is used to process the data from the previous step. The mathematical formula of range method is:

Multiply the z-score from the previous step by 100 and you get the final rarity score for BAYC#1154. Then rank the NFT by score in a collection (the rarity score ranges from 0 to 100) to get the final rarity ranking for that NFT.

Advantage of NFTGO rarity rating

By comparison, it is found that the Rarity scores of A. tools and NETEXP may overestimate or underestimate the Rarity of an NFT asset, while the NFTGO Rarity score can give reasonable results in these abnormal situations. The following table shows the anomalies in computing the Rarity ranking for the Bored Ape Yacht Club(BAYC) series of NFTGO, A. Tools and NFTEXP Rarity scoring models.

Table 1: Comparison of tool rarity ranking results (Data: October 2, 2021)

Of the 26 outliers, the Rarity rating of the first 22 apes was overestimated by a. Tools and NFTEXP because "apes with four characteristic attributes" accounted for a large proportion of the total score. The Rarity rating of the last four apes was underestimated by a. Tools and NFTEXP because "apes with five characteristic attributes" accounted for a small percentage of the total score.

In the case of BAYC #947, which NFTGO ranks as #9994, it's almost the least rare ape at 406. However, by the vacancy.Tools it is ranked 775 with a Rarity of 168.23. This is because BY the vacancy.Tools it simply adds each feature and the number of features (however it actually has no additional special features). As you can see in the picture below, this monkey has no distinctive features. So why is this ape ranked in the top 10% by A. Tools? It is clear that the feature number is overrepresented in the rarity score, accounting for 136.7 points out of a total score of 168.23. The total number of apes with four characteristic attributes was 254, and the total number of apes with six characteristic attributes was 5,323. According to the Rarity calculation formula provided by A. Tools, an ape with four attributes would be rarer than an ape with six attributes, which is not quite reasonable.

Figure 4: Details of the Rarity rating by A. Tools on BAYC #947 (Data: December 2, 2021)

Figure 5: Details of NFTGO's rarity score for BAYC #947 (data: December 2, 2021)

Looking at BAYC #2832 and BAYC #8742, it is clear that BAYC #2832 should be rated higher because of its diverse features. Also, the highest bid for BAYC #8742 is also higher than that for BAYC #2832, so it is more profitable to purchase BAYC #2832, and A. Tools underestimates its Rarity.

Figure 6: Details of the Rarity rating by A. Tools for BAYC #2832 and BAYC #8742 (Data: December 2, 2021)

Figure 7: Details of NFTGO's rarity score for BAYC #2832 (data: December 2, 2021)

Figure 8: Details of NFTGO's rarity score for BAYC #8742 (data: December 2, 2021)

Figures 7 and 8 show NFTGO's rarity score for BAYC #2832 and BAYC #8742. As you can see from the "Features" view on the right side of the page, BAYC# 2832's feature properties generally vary between 1% and 3% (even rarer than BAYC#1154!). And the lowest value of BAYC #8742 feature attribute is 12.42. Obviously, the Rarity score of NFTGO is more reasonable than that of A. Tools.

In addition, the Rarity scores of CryptoPunks by A. Tools and NFTGO also reflect the difference in their accuracy. By the vacancy.Tools V2, nearly half of the top 20 Punk names are featueless. NFTGO rates this type of Punk lower, due to the lack of diversity of these zero-feature punks, which should lower the rarity rating and ranking.

Figure 9: CryptoPunk ranked top 21 by a. Tools

Figure 10: Top 20 CryptoPunks in NFTGO

Table 2: CryptoPunk rarity Ranking comparison (Data: November 2, 2021)

In conclusion, compared with the Rarity score by THE QUALITY of Jaccard distance, NFTGO Rarity score is reasonable and accurate, and you can use it as a reference for collecting NFT.

conclusion

Rarity scores are an aid when buying or selling NFT. Although the rarity model we used is statistically correct, different NFT project parties give more important announcements about certain attributes. The official statement from Cool Cats, for example, states that ordinary items like beanie hats or hats are worth less than rare items like computer heads or ape man costumes. There are other ways to judge the value of NFT assets, such as artistic appreciation value or liquidity premium. Also, you may prefer a green background to a red one, which is influenced by your subjective aesthetic.

To calculate the collective difference of an NFT asset based on The Jaccard distance, to help users discover the collective comprehensive difference of NFT, actually quantifies the concept of "rarity" in a more essential way. You can already view the rarity rankings and rarity scores of all NFTS on NFTGO. Hopefully, the NFTGO rarity score will help you make a better decision when buying or selling NFT.

If you have any comments or suggestions on the NFTGO rarity model, please email team@nftgo.io.