Statistical Ranking

How is rarity calculated?

CryptoPiggos are created from different categories of traits.

Background, clothing tops, clothing bottoms, facial hair, accessories etc

For each trait in a trait category, a percentage weight is assigned. The sum of all weights in a trait category equals 100%

As an example, if we were creating soccer player NFT's, we may have the following trait categories, traits, and their associated weights.

Stadium Background (trait category)

Attribute	Weight
Wembley	50%
The Maracana	50%

Player Shirt (trait category)

Attribute	Weight
Brazil #10	10%
Generic Spanish shirt	45%
Generic Italian Shirt:	45%

The possible combination of images would be:

Brazil #10	Wembley
Generic Spanish shirt	Wembley
Generic Italian Shirt	Wembley
Brazil #10	The Maracana
Generic Spanish shirt	The Maracana
Generic Italian Shirt	The Maracana

So, 6 possible combinations.

If the weights were evenly distributed across the two sets of traits (50% and 33 & 1/3% respectively),

The chance of anyone combination being selected would be 1/2 * 1/3 = 1/6 (the probability of each independent trait selection multiplied together to find the intersection)

In our case, we have assigned a much lower probability for the "Brazil #10" shirt being randomly selected.

So, the probability of a "Brazil #10, The Maracana" soccer player being generated is 1/2 * 1/10 = 1/20 (5% chance)

This is much lower than a "Generic Spanish Shirt, The Maracana" being generated, as the probability for this trait combination is 1/2 * 9/20 = 9/40 (22.5% probability)

Resulting Probabilities:

Attribute Name (Shirt cat)	Weight	Attribute Name (background cat)	Weight	Probability
Brazil #10	10%	Wembley	50%	5%
Generic Spanish shirt	45%	Wembley	50%	22.5%
Generic Italian Shirt	45%	Wembley	50%	22.5%
Brazil #10	10%	The Maracana	50%	5%
Generic Spanish shirt	45%	The Maracana	50%	22.5%
Generic Italian Shirt	45%	The Maracana	50%	22.5%

We do the same for CryptoPiggos, where the selection of each trait from a category is an independent event.

We use a weighted random function (where the trait and its associated weight are passed into the weighted random function) on each trait category to select the individual traits to be combined.

As above, the probability of a Piggo being created with a specific set of traits is a product of each of the selected trait probabilities.

We also have some dependencies across traits for some Piggo types.

For example, if a Soccer background trait is selected, the generated Piggo has to have a Soccer Jersey for its clothing top trait.

The resulting options for subsequent traits are re-evaluated to ensure that the options are appropriate for that type (in this case, a soccer player).

The weights are re-scaled for a trait category where there are traits that are no longer relevant for a Piggo type.

We use the calculated Piggo probability to assign a rarity index value to the Piggo.

To do this we use the following formula and normalize the results to be between 1 and 10:

log (P(T1 and T2 and T3... and Tn) * 10^n))

where n is the number of trait categories.

So, if the probability of creating a Piggo with a particular set of 7 traits was .00005, the formula would result in a value of ~2.7

The formula would result in a value of ~4.7 for a Piggo probability of .005.

The first Piggo would be considered rarer than the second.

For a log(P(T1 and T2 and T3... and Tn) * 10^n) value up to 10, the resulting nonnormalized rarity value would be <= 1, from 11 to 100, rarity < 2, from 101 to 1000, rarity < 3 and so on .

Based on this formula, we use the above example,

Brazil #10 with Wembley background. The probability is 5%, with 2 traits. Hence, (0.05 x (10x10)) = 1

Generic Spanish Shirt with Wembley background. The probability is 22.5, Hence (0.225 x (10x10)) = 4.5 ~5

The results are Brazil #10 has a rarity of 1 and General Spanish Shirt has a rarity of 5.