A rarity score is a single numerical metric assigned to an individual NFT token that quantifies how statistically uncommon that token is within its collection by aggregating the inverse probabilities of each of its individual traits — calculated by dividing 1 by the frequency of each trait value and summing those values across all trait categories — producing a score where higher numbers indicate greater rarity (because rarer traits contribute larger values to the sum), enabling direct comparison of any two tokens within the same collection and generating a ranked rarity leaderboard that secondary market participants use to identify potentially underpriced rare tokens and justify price premiums. Rarity scores are relative, not absolute: a score of 200 in one collection does not equal a score of 200 in another; the scores only have meaning when compared within the same collection.
Rarity Score Calculation
Standard Formula (Rarity Score Method)
The most common rarity score formula:
$$text{Rarity Score(token)} = sum_{i=1}^{n} frac{1}{P(text{trait}_i)}$$
Where:
- $n$ = number of trait categories
- $P(text{trait}_i)$ = probability/frequency of that specific trait value = (count of tokens with this trait) / (total tokens)
Example Calculation
Collection size: 10,000 tokens
Token #4521 traits:
| Trait Category | Trait Value | Count in Collection | Frequency | Contribution (1/freq) |
|---|---|---|---|---|
| Background | Gold | 150 | 1.5% | 66.7 |
| Fur | Alien | 50 | 0.5% | 200 |
| Eyes | Laser Eyes | 120 | 1.2% | 83.3 |
| Mouth | Grin | 1,500 | 15% | 6.7 |
| Hat | None | 6,000 | 60% | 1.7 |
| Clothes | Tuxedo | 300 | 3% | 33.3 |
| Total | 391.7 |
Token #4521 rarity score: 391.7
A common token with all high-frequency traits might score 15–30; an ultra-rare might score 1,000+.
Alternative Rarity Calculation Methods
Statistical Rarity (Multiplicative)
$$text{Statistical Rarity} = prod_{i=1}^{n} P(text{trait}_i)$$
Lower number = rarer. More extreme: a single ultra-rare trait dominates the product.
Problem: One rare trait can overwhelm all others; doesn’t balance trait rarity well.
Average Trait Rarity
$$text{Avg Rarity} = frac{1}{n}sum_{i=1}^{n} P(text{trait}_i)$$
Simpler; less sensitive to single ultra-rare traits.
Normalized Rarity
“`
Min score in collection: 12.4 → maps to 0
Max score in collection: 1,847 → maps to 1
“`
Rarity Score Providers
| Platform | Method | Notes |
|---|---|---|
| Rarity.Tools | Sum of 1/trait probability | Original; widely referenced |
| Rarity Sniper | Similar to Rarity.Tools | Launched 2021; live updates post-reveal |
| Trait Sniper | Custom scoring | Real-time reveal sniping |
| OpenRarity | Open standard (2022) | Attempts to standardize across collections |
| Howrare.is | Solana-focused | Dominant Solana rarity tracker |
OpenRarity (2022)
- Uses information-theoretic approach
- Published as open-source library
- Aim: replace competing proprietary scores with one community standard
Rarity Score in Practice
Revealing a Rare Token
Reveal occurs → Rarity tools calculate scores within minutes →
Token #4521 score: 391 → Rank #47 of 10,000
Immediate Twitter notification from rarity bots
Whale DMs holder with offer
Holder lists at rarity premium: 5 ETH (vs. 0.1 ETH floor)
“`
“Rarity Sniping”
“`
Block reveals → Bot reads new metadata → Calculates score →
If rank < 100 → Submit buy transaction immediately
Execute: buys rare token at floor price before anyone notices
“`
Anti-sniping: some projects reveal in batches, delayed reveals, or randomize reveal order.
Limitations of Rarity Scores
| Limitation | Description |
|---|---|
| Ignores aesthetics | A statistically rare combination may not be visually appealing |
| Trait desirability | Community preferences override stats (some common traits are “cooler”) |
| Cross-collection incomparability | Score of 200 means nothing without context |
| Trait category weighting | All categories weighted equally; real market may weight some much more |
| Missing trait | The absence of a trait (e.g., “no hat”) has a rarity itself; some calculators handle this differently |
| Gaming | Artists can inflate rarity of specific tokens by adding many rare traits; scores can be manipulated |
History
- 2021 Jul: Rarity.Tools launches; first standardized NFT rarity scoring platform
- 2021 Aug: Rarity Sniper launches; rarity sniping becomes a market strategy during BAYC era
- 2021 Q4: Rarity scores become canonical secondary market tool; “what’s the rarity rank?” a standard question
- 2022: Rarity wars: competing platforms use different methods → same token scores differently → confusion
- 2022 Sep: OpenRarity open standard announced; multi-company collaboration to create canonical scoring
- 2023–2024: Rarity scoring remains important for PFP collections; less relevant for open editions and 1/1 art