NFT Rarity

The foundational model where an NFT's overall rarity score is calculated from the combined scarcity of its individual attributes. Common traits lower the score, while rare traits (e.g., a 'Gold Background' in a collection of 10,000 where only 50 have it) significantly increase it. Rarity is often expressed as a percentile rank (e.g., 'Top 1%').

Different mathematical models aggregate trait data to produce a single rarity score.

• Trait Rarity Ranking: Simple sum of the inverse rarity of each trait (1/%)
• Statistical Rarity: Multiplies trait probabilities, favoring NFTs with multiple rare traits.
• Information Content (IC): Uses -log2(probability), weighting rarer traits more heavily. Platforms like Rarity Tools and Rarity Sniper apply these models, sometimes yielding different rankings for the same NFT.

Rarity is anchored in an NFT's on-chain metadata (stored on the blockchain) or off-chain metadata (referenced via a URI, often on IPFS). The immutability of this data guarantees provable scarcity. Key components include the tokenURI, which points to a JSON file containing the trait definitions, and the provenance hash, which cryptographically seals the collection's metadata to prevent post-mint manipulation.

Not all rarity is algorithmic. Subjective rarity is driven by cultural value, artist reputation, historical significance (e.g., first mint in a collection), or membership in a coveted set (e.g., 'Founder' NFTs). Utility-based rarity grants exclusive access to events, games, or governance rights, creating demand independent of visual traits. This layer often drives significant price divergence from pure trait-based scores.

A collection's rarity distribution—the curve from common to ultra-rare NFTs—directly impacts market dynamics. A long-tail distribution with a few extremely rare items creates a high floor price for common items, supported by the lottery-ticket potential of minting a rare one. Analysis often involves studying the rarity vs. price correlation to identify undervalued assets.

This is the most fundamental method. It calculates a rarity score for each NFT by summing the inverse frequency of its individual traits.

• Formula: Score = Σ (1 / Trait Frequency) for all traits.
• A trait owned by 1% of the collection contributes 100 to the score.
• Example: If an NFT has a 'Gold Background' (1%) and 'Laser Eyes' (2%), its base score is (1/0.01) + (1/0.02) = 100 + 50 = 150. It's simple but can be skewed by common traits and doesn't account for trait combinations.

This method evaluates rarity based on the overall statistical similarity between NFTs. It uses Jaccard Distance to measure how different one NFT is from all others in the collection.

• Compares the set of traits between two NFTs.
• An NFT's rarity is its average distance from every other NFT.
• Key Insight: An NFT with common traits arranged in a unique combination can rank highly. It is more computationally intensive but captures the nuance of overall uniqueness beyond simple trait sums.

This method, popularized by platforms like Rarity Tools, refines the basic score by using the trait rarity percentage directly in the sum.

• Formula: Score = Σ (1 / (Trait Count with Trait / Total NFTs)).
• It's mathematically identical to Trait Rarity Ranking but expresses the trait's rarity as a clear percentage (e.g., 1.23%).
• The final score is an abstract number where a higher value indicates greater rarity. It became an early standard for collections like CryptoPunks and Bored Ape Yacht Club, establishing a common benchmark.

This approach aims to normalize scores by calculating the average rarity of an NFT's traits, rather than the sum.

• Formula: Score = (Σ Trait Rarity) / Number of Traits.
• Purpose: Prevents NFTs with many common traits from achieving artificially high scores simply by having more traits.
• It favors NFTs with consistently rare traits across the board. This method can significantly reorder rankings compared to summation-based models, often elevating items with fewer but exceptionally rare attributes.

Because raw rarity scores can vary wildly in scale between collections, normalization is used to create a standardized 0-100 scale for comparison.

• Process: The highest raw score in a collection is set to 100. All other scores are scaled proportionally.
• Example: If the top score is 2500, an NFT with a score of 1250 gets a normalized score of 50.
• This allows for intuitive cross-collection comparisons and is used by marketplaces like OpenSea in their ranking filters.

This is a market-driven, non-algorithmic method. Rarity is inferred from the trait floor price—the lowest price for any NFT in the collection possessing a specific trait.

• Mechanism: Scrapes marketplace listings to find the minimum sale price for each trait.
• Insight: Reflects real-time collector demand, which may differ from statistical rarity. A statistically common trait with high utility (e.g., a game item) can have a high floor. It provides a purely economic perspective, showing what the market is willing to pay for specific attributes.

Rarity is calculated by analyzing the trait distribution across a collection. Common methods include:

• Trait Rarity Ranking (TRR): Sums the inverse frequency of each trait.
• Statistical Rarity: Multiplies the probabilities of each trait occurring.
• Jaccard Distance: Measures overall uniqueness relative to other NFTs in the set. Platforms like Rarity Sniper and Rarity Tools implement these algorithms to generate scores.

Major NFT marketplaces like OpenSea, Blur, and Magic Eden display rarity metrics directly on asset pages. Features include:

• Rarity rank (e.g., #45 out of 10,000).
• Trait breakdowns showing the percentage of the collection sharing each attribute.
• Filtering and sorting by rarity score, enabling collectors to discover undervalued assets.

Rarity scores feed into pricing models that estimate an NFT's market value. These models analyze:

• Base price of the collection.
• Premium multipliers for rare trait combinations.
• Historical sales data of NFTs with similar rarity profiles. Tools like Upshot and NFTBank use machine learning to provide price estimates based on these factors.

Rarity is central to generative art and Profile Picture (PFP) collections like Bored Ape Yacht Club or CryptoPunks. Key concepts include:

• Layered assets: NFTs are programmatically generated from layers (background, body, headwear, etc.).
• Trait scarcity: Some traits are intentionally minted at lower frequencies (e.g., 1% have laser eyes).
• Floor vs. Rarity Premium: Common traits set the collection's floor price, while rare traits command significant premiums.

While useful, rarity scoring has notable limitations:

• Subjectivity of Traits: Algorithmic scores may not reflect cultural or aesthetic desirability.
• Trait Dependency: Scores can be gamed if traits are not independent (e.g., a 'hat' trait implying a 'head').
• Market Dynamics: Rarity does not guarantee liquidity; market sentiment and utility often drive final price. Advanced models now incorporate trait weighting and community sentiment to address these issues.