Goals

We have all been there everyone is rolling and you roll bad and someone just has God stats, get when you look at point buy the arrays you end up using become very samy after a while.

I wanted to create a point buy method that captured the cost of the relative rarity of 4d6 drop lowest, allowed ever character the range granted by 4d6 drop lowest and allowed for a greater diversity of starting stats and more interesting build option.

Point buy Budget of 100

Attribute	Cost
3	-12
4	-11
5	-10
6	-8
7	-5
8	0
9	5
10	11
11	16
12	19
13	20
14	22
15	28
16	34
17	42
18	48

Example Stats

• 15 14 13 12 10 8
• 18 13 13 9 8 8
• 17 14 13 12 8 7
• 18 17 14 8 7 6
• 15 15 14 10 10 8
• 16 16 16 9 7 7
• 18 18 16 6 4 4

Observations

Because there are two Inflection points around 13 and 6 this method lends itseof to 3 types of arrays:

• Balanced arrays with 2 decent, 2 average and 2 meh stats
• Sad stats with 1 really good and 0-1 decent 2-4 average and 1-2 horrible stats
• Absolute min maxed 2 God stats, 2 terrible stats and 2 meh stats.

You can make some really lopsided arrays but you will have some pretty big character flaws lilly at a -3 to -4, if you choose to go that path.

DMs may still want to limit how many stats above or below 15 or 8 are allowed, but even with a few little tweaks like that you can get some very interesting and balanced arrays (assuming everyone is using this method) in a range normally not accessible only by rolling.

Methodology

Step 1

4d6 drop lowest is a right skewed data set. In order to apply linear factors I need to transform it using e^n, where n is the probability of a roll occurring (from 3-18). This produces a normal centred around the mode (most common number) which occurred at n_13. You can use any base as long as you use the same base later on.

Step 2

I wanted to invert this curve so that the cost increases as rarity increases. So assigning 1 at the mode I can multiply each number by a factor of the percentage increase/decrease between each number moving away from the mean in each direction.

Step 3

Reintroduce the skew by doing a log transform using the same base as you used earlier.

Step 4

Scale until there is at least 1 integer difference between each step away from the mode (For me this was 2.4). Multiply all of the interferes before the mode by -1.

Step 5

Add or subtract whatever value you want to be zero and round to the nearest whole number.

Step 5

Define a point buy budget. By testing some arrays you consider reasonable in this case I used the standard array.