Thinking a bit on potion weight, I started from a lightly modified version of your formula:
potion weight = [ (ingredients weight)^(1/2) +
x ] / (
y +
z * alembic quality)
and tried to calculate the values of x, y and z to met certain conditions that we can set as we like more. Note that I'm doing the square root of ingredients weight to reduce the huge difference between the maximum ingredient weight (40) and the minimum one (0.2). Using the square root heavy ingredients will be much more usable, while still giving heavy potions. Very light ingredients, on the contrary, will produce potions weighting more than them, but this is right since the bottle has a weight too, so excessively light potions are unrealistic.
I considered the following datas:
- minimum ingredients weight: 0.2 (2 x 0.1)
- maximum ingredients weight: 40 (4 x 10)
- minimum alembic quality: 0 (no alembic)
- maximum alembic quality: 1.5 (grandmaster)
Now, we have 3 variables, so we can choose 3 conditions to met. I chose the following conditions.
1) Minimum potion weight: 0.25
It's the weight of quality potions, the lightest ones sold by vendors. This should be obtained with minimum ingredients weight (0.2) and maximum alembic quality (1.5).
2) Maximum potion weight: 4
This is heavier than potions sold by vendors (the bargain ones weight only 1.5), but we should keep in mind that it comes out of 4 very heavy ingredients and with no alembic, so this isn't something you'll really see in an alchemist's shop.
3) alembic influence: 40%
This means that a potion weighting 1 without alembics, will weight 0.6 with the best alembic (1.5).
Well, considering those 3 conditions we have the following values, rounded to the second decimal:
x = 0.24
y = 1.64
z = 0.73
And so our formula becomes:
potion weight = [ (ingredients weight)^(1/2) +
0.24 ] / (
1.64 +
0.73 * alembic quality)
Keep in mind that all the numbers I used in this post, the weights and the 3 conditions can be freely changed if you find them unbalanced or unrealistic. I've built an excel spreadsheet that can give x, y and z for any combination of weights and conditions we want to try. That is, hoping I didn't screw up something.
Here's a table with potion weights using the values I gave above for x, y and z:
alembic qualityingr 0 0,5 1 1,2 1,5 20,2 0,42 0,34 0,29 0,27 0,25 0,220,4 0,53 0,43 0,37 0,35 0,32 0,280,6 0,62 0,50 0,43 0,40 0,37 0,330,8 0,69 0,56 0,48 0,45 0,41 0,361 0,75 0,62 0,52 0,49 0,45 0,401,2 0,81 0,66 0,56 0,53 0,49 0,431,4 0,87 0,71 0,60 0,56 0,52 0,461,6 0,92 0,75 0,63 0,60 0,55 0,481,8 0,96 0,79 0,67 0,63 0,58 0,512 1,01 0,82 0,70 0,66 0,60 0,533 1,20 0,98 0,83 0,78 0,72 0,644 1,36 1,12 0,94 0,89 0,82 0,726 1,64 1,34 1,13 1,07 0,98 0,878 1,87 1,53 1,29 1,22 1,12 0,9910 2,07 1,70 1,43 1,35 1,24 1,1012 2,26 1,85 1,56 1,47 1,35 1,1915 2,51 2,05 1,73 1,63 1,50 1,3320 2,87 2,35 1,99 1,87 1,72 1,5230 3,48 2,85 2,41 2,27 2,09 1,8440 4,00 3,27 2,77 2,61 2,40 2,12
Hope this can be of help.