Purity affects items in dramatic ways, multiplying their effect on study, eating, and such. This multiplier is very apparent at higher levels of study and gluttony. Purity is predicted to be a strong incentive for both trade and warfare.
Every item is composed of the 4 alchemical elements of Salt, Mercury, Sulfur, and Lead. Depending on the relative amounts of each element, an item will have a certain level of "Purity". The more concentrated one particular element is, the higher its purity and the more potent it becomes.
Purity has two effects in-game:
- Potency multipliers for Food and Inspirationals. (High purity food is more filling, and Inspirationals give more points)
- Changing the probability of certain Gluttony events. (This allows for greater certainty of a particular Humour result)
For determining the bonus multiplier for a Food or Inspirational, you take the Sum of the Squares of each element. Items that are high in one particular element have a higher potency for the same reason that (32+ 12) is more than (22+ 22). Each element is expressed as a fraction of 1, 41.33 salt is 0.4133.
The "Sum of Squares" yields a raw value that is always between 0.25 and 1.00 The formulas for the Purity Percentage and Purity Multiplier thus contain modifying numbers which will make the values span the range from 0-100% or 1-10x.
Purity Percent = ( (Salt2+ Mercury2+ Sulfur2+ Lead2- 0.25) *4/3 )
- Subtracting 0.25 changes makes the range 0.00 to 0.75. Multiplying by 4/3 Makes it 0.00 to 1.00, or 0% to 100%.
Purity Multiplier = ( (Salt2+ Mercury2+ Sulfur2+ Lead2) *12 ) - 2
- Multiplying by 12 makes the range 3.00 to 12.00, and subtracting 2 makes it 1.00 to 10.00.
The purity Percent and Multiplier can be easily inter-converted by this formula: Multiplier = (9 * Percent) + 1
An item with 33% purity has a 4x multiplier.
Here's a table showing the approximate Purity effects based on the Highest element. These values assume that the remaining elements are all equal, and thus it represents a MINIMUM value.
Increasing the value of the highest element by 25 will roughly Double the value of an item.
Purity% forms a steady quadratic progression as the Element increases, and the Multiplier is 1 + Quadratic. This can most easily be seen by subtracting 1 from the Multiplier value.
- 3.56 - 1.00 = 2.56 = 1.602
- 4.24 - 1.00 = 3.24 = 1.802
Taking an example food like Oakworth, the composition of the elements is very important during Gluttony. When it's 25/25/25/25, there is a 25% chance to get any of the Humours to increase by 3.0. But if the area you found it in has a 0/0/50/50 composition, you can only get get 3.0 for Yellow Bile and Black Bile (both have a 50% chance).
So while the values do increase for Gluttony (Oakworth with purity 2.0 will give 6.0 and 3x 0.8), the composition of the elements have a big impact too. So while 100/0/0/0 gives 10 purity, it can only gluttony for 30/4/4/4, while 0/0/50/50 only has 4 purity, it can give either 1.6/1.6/12/1.6 or 1.6/1.6/1.6/12, which can be better if you want Yellow or Black Bile.
<mightyagrippa> so, what's the salem analog to sqrt(quality/10)?
<loftar> It's basically the sum of the square of the individual elements (as represented from 0.0 to 1.0).
<loftar> But linearly normalized to the range 0.0-1.0 rather than 0.25-1.0.
<mightyagrippa> so, after you have the quality number in (0,1), how does it translate to humor/skill gain multiplication?
<loftar> Usually, but not necessarily, by using it to generate a multiplier from 1-10.
To calculate the raw purity, a number between 0 and 1, use [(Salt^2 + Merc^2 + Sulp^2 + Lead^2)-.25]*(4/3).
To calculate the purity multiplier for humors and skills, use (Salt^2 + Merc^2 + Sulp^2 + Lead^2)*12-2.
For example, a waxing mushroom with 20% salt, 50% mercury, 15% sulphur, and 15% lead would have
[(.2^2+.5^2+.15^2+.15^2)-.25]*(4/3) = .1133 raw purity
(.2^2+.5^2+.15^2+.15^2)*12-2 = 2.02 purity multiplier