Purity

About

Purity is a concept relating to the Elemental Composition of a material. 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)

Purity Multiplier

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.

Purity Table

Here's a table showing the approximate Purity effects based on the Highest element. The values are assume that the remaining elements are all equal, and thus it represents a MINIMUM value.

Element	Percent	Multiplier
25.00	0%	1.00
30.00	0%	1.04
35.00	1%	1.16
40.00	4%	1.36
45.00	7%	1.64
50.00	11%	2.00
55.00	16%	2.44
60.00	22%	2.96
65.00	28%	3.56
70.00	36%	4.24
75.00	44%	5.00
80.00	54%	5.84
85.00	64%	6.76
90.00	75%	7.76
95.00	87%	8.84
100.00	100%	10.00

888888888888888888888888888 multiplies the base stats of items, increasing their stats.

Inspirational example:

Smooth Stone	Stats
Purity Multiplier		Arts & Crafts	Frontier & Wilderness	Hunting & Gathering	Mines & Mountains	Natural Philosophy
	base	340	440	290	375	220
	1.0	340	440	290	375	220
	1.5	510	660	435	562,5	330
	2.0	680	880	580	750	440
	2.5	850	1100	725	937,5	550
	3.0	1020	1320	870	1125	660

As you can see, this is pretty straight forward for Inspirationals, simply multiplying the amount of proficiency given.

Food Example:

Oakworth	Humours
Elements		Blood	Phlegm	Yellow Bile	Black Bile
	Salt	3.0	0.4	0.4	0.4
	Mercury	0.4	3.0	0.4	0.4
	Sulphur	0.4	0.4	3.0	0.4
	Lead	0.4	0.4	0.4	3.0

But for food it gets more interesting. The amount healed and gluttonied by food is multiplied by the purity multiplier (just like with Inspirationals), but the composition of the elements affects Gluttony. Taking a special 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.

Using this, it's very easy to calculate the base stats (purity multiplier 1.0) for Inspirationals and Food. Simply divide the stats gives by the purity multiplier value (shown in Ender's custom client as 'Purity', or calculated using the elements). Remember that the elements are rounded down in-game to two decimals, and that most values are simple and round, like the smooth stone and oakworth examples.

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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.

Source Information

<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