🌾Rarity Score (Calculation)

Rarity Score is determined by the rarity of the NFT, which dictates border color (Rarity Title). The Rarity Title determines the $REMN farming efficacy & ranges from Obsidian (gray) to Relic (red).

Avatar Rarity Score values range from 1600 and above. Each of the 16 traits has a minimum normalized score of 100, and the total rarity is the summation of all traits.

It determines $REMN farming amount.

Rarity Score	Rarity Title	Farm Power
1600-2150	Obsidian	1000
2150-2400	Emerald	2000
2400-2700	Lapis	3000
2700-3200	Amethyst	4000
3200-4500	Gold	5000
4500-7000	Relic	6000
?	?	?

Rarity Score determines the Rarity Title which determines the farm speed (Farm Power).

Rarity Score may affect multiple mechanics in different ways in the future, but currently will affect idle commission deployments. A constant amount of $REMN is allocated per second, divided by the total Farm Power in the pool.

For example:

-100 $REMN is given out per second (hypothetically)

-User has a 3600 Rarity Score character

-Character will fall under Gold category with a Farm Power of 5000.

-Assuming the total Farm Power in the entire pool is 100,000, then the user has 5%, granting the user 5 of the 100 $REMN per second.

Users may withdraw the $REMN after lock period (to be determined) on Polygon network.

Note: Values are not final.

Rarity Title is shown with a colored border in the example above

These character NFTs are dynamic, allowing you to exchange equipment that you gain through events and tournaments. For example, the Trial events run monthly, with opportunities to earn equipment that may be able to boost your Rarity Score.

Rarity Score is calculated as:

$$FP = 100*\sum_{t=1}^{16} \sqrt[R]{\frac{1}{(p_t/c_t)}} = \sqrt[R]{ \frac{1}{(p_1/c_1)}} + \sqrt[R]{\frac{1}{(p_2/c_2)}} + \sqrt[R]{\frac{1}{(p_3/c_3)}} + ... + \sqrt[R]{\frac{1}{(p_{16}/c_{16})}}$$

Where:

t = trait type index

p = probability of randomized trait type

c = ceiling (most common) probability of trait type

R = root constant, currently 1.92 (lower value increases gap between common-rare, vice versa)

There are 16 traits where each trait has a minimum rarity score of 100.

This formula sums a normalized rarity score from each trait, allowing for traits to be balanced compared to each other. The root function decreases the gap, allowing legendary traits to be valuable enough but not overshadowing the more common traits.

Users can experiment at the Builder.

Example

$$RarityEarScore = 100* \sqrt[R]{\frac{1}{(p/c)}} = 100* \sqrt[1.92]{\frac{1}{(0.025/0.5)}} = 100* \sqrt[1.92]{20} ≈ 476$$

The above is for Remnant Avatar NFTs.

Alter Genesis NFTs' Rarity Score will be calculated with their Frame Rarity & Star Rarity. This formula is to be announced at a later date.