Introduction to NFT valuation system based on rarity level mapping

特邀专栏作者

2022-12-09 10:02

This article is about 4678 words, reading the full article takes about 7 minutes

What makes some NFTs sell for millions while others sell for relatively little? In the collectible market, is there an inherent correlation between selling price and rarity?

This article is from:Blockin.ai & nftin.ai，This article is from:

Published by Odaily with permission.

Since the development of the digital asset market, the status symbol and social value it represents have become a new commercial value, and NFT (Non-fungible Token) is a symbol of this commercial value. As a digital encrypted asset, NFT , is a non-homogeneous digital asset certificate created, maintained and executed by smart contracts, which is unique, scarce and non-replicable. The value evaluation of NFT comes from multiple aspects such as scarcity, community recognition, holders, etc. Even if it is the same series, the characteristics and forms of each NFT are different, the degree of attention of different attributes, ownership history, etc. form a unique Therefore, its valuation is of great significance. We hope to form a better valuation system and provide a reliable reference price for the rapid transaction in the market.

With the help of NFT's on-chain transaction history and NFT metadata, first, we calculated the rarity scores of items in different collections; second, we evaluated the correlation between NFT rarity and its price; finally, through its intrinsic correlation, we The valuation price system based on rarity level mapping is studied and retrospectively verified in multiple projects.

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Part 1. NFT rarity calculation

As the name suggests, NFT rarity measures how rare an NFT is relative to other collectibles. By looking at the attributes, one might be able to determine that an NFT has some rare characteristics, but how rare is this NFT relative to other NFTs?nftin.aiTake BAYC as an example, as its

As shown above, BAYC has seven different features: background, clothes, earrings, eyes, fur, hat and mouth.

There are different sub-features under each feature, and we calculate the proportion frequency of its sub-features. It is worth noting that we use the Trait count of its features as a derived feature to calculate its proportion. Because each NFT has multiple features and their sub-features, there must be a way to combine the rarities of all features into a single value in order to rank their rarities.

There have also been several methods of calculating rarity previously: trait rarity ranking (ranking only the rarest traits), average trait rarity (averaging the rarities of all traits together), statistical rarity (combining the rarities of all traits multiplication), but the trait rarity ranking puts too much emphasis on rare traits, and the calculation of average and statistical rarity will dilute rare traits. Therefore, accumulating feature rarity scores as a rarity score can better solve the above problems.

The main idea is to score the rarity of each feature of a single NFT, and then add the rarity scores of all features of the NFT to finally obtain the total rarity score of the NFT. That is, the total rarity score of an NFT is the sum of the rarity scores of all its feature values, and the specific calculation formula is detailed in the appendix.

Examples are as follows:

First, calculate the proportion of sub-features

Then, calculate the sub-feature score and the total score according to the reciprocal of the proportion:

As above, the rarity score of each feature value and the total rarity score of each NFT ID can be obtained, so the rarity score considers that NFT ID 2 is more valuable because it has a higher total score.

It is worth noting that considering the different types of sub-features under different features, there are natural differences in the proportion of feature frequencies. We have improved the V1 version above. The main idea of the V2 version is the same as that of V1, so we won’t go into details here. The difference is that the normalization of the number of sub-features is considered, and the combination of features is added as a new derived feature, which enriches The combination of features can more comprehensively reflect the rarity of NFT. Please refer to the appendix for the description and calculation formula of V2.

In addition, we also calculated the V3 version for some projects. The difference between the V3 version and V2 is that three feature combinations have been added. However, due to the number of sub-features in some projects, there are many combinations of the three features, resulting in the calculation of The proportion value of the characteristics is not very distinguishable, so we only calculated the V3 rarity score of some items.

In addition to the calculation of the rarity of the above three versions, considering that some NFTs have not been traded in history, we want to measure the rarity scores of all NFTs that have been traded. Therefore, a dynamic rarity is defined. It is consistent with the static rarity calculation method, the difference is that the data for calculating the dynamic rarity is only the NFT that has been traded for a period of time in history, so the data is only a part of the full amount of NFT. In addition, as time changes, the calculation data set changes at any time, so we update the dynamic rarity in real time every day. In short, the dynamic rarity not only considers the proportion of objective attributes, but also considers the historical transaction situation, which dynamically reflects the rarity of NFT within the transaction time period.

In addition, we have also explored other calculation methods of rarity, such as jaccard distance, jaccard distance is an indicator to measure the dissimilarity of two sets, and can calculate the similarity between two NFT features, the greater the average similarity between NFT and other NFT The rarer it is, the specific calculation method can refer to the appendix.

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Part 2 Research on the correlation between rarity and price

In many cases, people are willing to pay a premium for rarity, but how exactly does rarity affect price? With the help of historical transaction data on the chain, we took several blue-chip projects as examples to evaluate the intrinsic correlation between NFT price and rarity.

Considering that we already calculated the rarity score for each item, we directly explored the correlation between rarity score and price, calculating the Spearman correlation coefficient between the two.

The specific calculation method is as follows:

where n is the number of samples and d represents the rank difference between data x and y.

The closer the absolute value is to 1, the closer the relationship between the two variables; the closer to 0, the less close the relationship between the two variables. The correlation strength corresponding to the correlation coefficient is as follows:

0.8-1.0 Very strong correlation

0.6-0.8 strong correlation

0.4-0.6 Moderate correlation

0.2-0.4 weak correlation

0.0-0.2 Very weak or no correlation

We take the five blue-chip projects BAYC, MAYC, cryptopunks, moonbirds, and doodles as examples to calculate the correlation between the transaction price and its rarity score (V2) in the past two months. The chart is as follows:

The above chart shows that there is a weak correlation between the rarity score and price of a single item among most items.

x > 10: Legendary

6 < x <= 10: Rare

2 < x <= 6: Classic

x <= 2: Normal

It can be seen from the above figure that whether it is dynamic rarity or static rarity, the higher the level of NFT, the greater the average historical transaction price. Therefore, we conclude that although there may be no obvious correlation between a single NFT and the price, But overall, the selling price of high-grade NFTs is still relatively high, that is, people are willing to pay higher prices for rarer NFTs.

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Part 3 Valuation system for rarity level mapping

It can be seen from the above research that the higher the rarity level, the higher the general transaction price at that level, so we considered designing a valuation system based on rarity level mapping, which relies on historical transaction data and NFT rarity level Estimate the latest NFT market price.

Due to the instability of NFT prices in the market, the horizontal line of historical transactions cannot represent the current transaction horizontal line. The price of NFT traded every day and every month also fluctuates within the range of its horizontal line. Taking the historical transaction price of BAYC as an example, the following figure shows its transaction Fluctuation:

Therefore, for NFT transactions of different projects, we consider looking for a horizontal line value that can measure the daily transaction situation as the anchor point of the transaction distribution. Due to the average value, the minimum and maximum values are easily affected by extreme values, and we use the median value as the daily transaction price. The anchor point and calculate different indicators based on the median, as shown in the figure below, there are upper and lower limits, etc., so as to roughly restore the transaction distribution in different periods, and estimate the latest transaction prices of different NFTs according to the distribution rules of historical transactions.

Note: Upper quartile: Q3 Median: Q2 Lower quartile: Q1 Interquartile range (IQR): Q3 - Q1 Upper limit: Q3 + 1.5*IQR

Lower limit: Q1 - 1.5*IQR Maximum value: max Minimum value: min Average value: mean

1. The method is summarized as follows:Calculation of Historical Ratio

2. : Calculate the ratio_high and ratio_low every 3 days in the past six months, and find the average of all ratio_high and ratio_low, ratio_high_avg, ratio_low_avg.Calculate the latest virtual upper and lower limits based on historical ratios

3. : Calculate the virtual upper and lower limits Virtual_upper and Virtual_lower from the ratio_high_avg/ratio_low_avg obtained above and the latest medianLatest Valuation Cohort Formation

4. : Generate the latest valuation queue based on the virtual upper and lower limits and the distribution of all transactions in the latest period, fill the original transaction data within the upper and lower limits into the interval [lower limit, upper limit], and exclude the data outside it as the final fitting Distribution of the valuation cohort.：

Valuation cohort rank mapping

a. Average the raw transaction prices within the different classes. (If some level values do not exist in the latest trading cycle, the average value of the two levels before and after will be used to fill in order)

b. According to the rarity level of the item (which has been divided into 20 levels according to the normalized rarity score (V2)), the average value of transactions in different levels is mapped to all items in different levels to obtain the valuation.

It is worth mentioning that, in order to ensure the objective accuracy of the valuation, we first cleaned the transaction data before the valuation, as follows:

a. Remove the obvious brushing behavior and the corresponding trading platform.

b. Considering that at the beginning of the project, the transaction market is unstable, so for different projects, the transaction data ranging from the previous few months are excluded.

c. There are individual transactions whose ratio to the transaction median of the day is too small, which cannot objectively reflect the market level and are excluded.

In addition, in the above calculation version, we found that some valuation results did not meet our valuation expectations in the backtracking of historical transaction results. For example, the valuation of some high-rare IDs is too different from the day’s pending order price and the actual real transaction price. Therefore, based on the above version, we have revised the valuation of some IDs with high rarity levels: For IDs that have had high-priced transactions in history, calculate the average ratio_avg of their historical transaction ratios separately, and use the latest cycle transaction digits median*ratio_avg to replace the estimate for the rank map.

Due to the existence of multiple versions of rarity ratings, we experimented with different methods of rarity rating mapping valuation under different projects and conducted retrospective verification. From the perspective of comprehensive results and efficiency, the rarity rating mapping of the V2 version is better, so At present, the valuation using static rarity level V2 mapping is displayed online.

Valuation Accuracy Verification

In order to measure the accuracy of the valuation system, we calculate the mean absolute percentage error (Mean Absolute Percentage Error, MAPE) based on the predicted price on a certain day and the actual transaction price on that day.

Among them, yi represents the actual value, y^i represents the predicted value, and n is the number of NFT.

The verification results of several blue-chip projects are listed below, and the verification date is data after 2022 (2022-01-01 to 2022-11-15):

The following shows the scatter plot of the predicted price and the actual transaction price in several projects going back nearly two months (2022-10-01 to 2022-11-15)

Conclusion and Summary

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appendix

V 1:

V2:

appendix

a. Normalization of feature score calculation

Feature normalization considers the difference in feature rarity scores caused by the number of sub-features under different features. For example, in the BAYC project, Earring has 7 different sub-features and Mouth has 33 different sub-features, then in general, Mouth has a more discriminative rarity score than Earring, so feature normalization is considered.

b. Pairwise combination of features

Based on the permutation and combination of multiple features, the proportion statistics of different feature combinations are enriched, and the rarity can be described in a higher-order way. For example, BAYC has a total of 7 different part features, then the number of different combinations in pairs is: Combine( 7, 2) = 21, and the rarity score is calculated using the combination of pairs as a new feature. The calculation method of the combined feature rarity score is the same as above, and will not be repeated here.