seasong
First Post
On a 3d6 distribution, what is the top 10% of the population, and how can I ensure that the PCs are in it?
(This assumes you want your PCs in the top 10%; the 4d6/drop lowest actually ensures that some of them will be)
This question was driving me batty. The reason is simple: 3d6, over six ability scores, has slightly over 100 trillion possibilities. Even if you boil it down to 3-18, there are over 16 million possibilities. Spreadsheets aren't meant for that kind of abuse, and I'm not enough of a mathematician to sit down and start calculating the probabilities of each die result. So I abused a spreadsheet. I've attached it, in case anyone cares enough, but it's really just a notepad.
I also had to define what I meant by "Top 10%". I went with two possible definitions:
1) Add up your ability scores. The top 10% of that total.
2) Add up the point buy COST of your ability scores. The top 10% of that cost.
On point 2, I went with this extrapolated cost chart:
3: -14
4: -10
5: -7
6: -4
7: -2
8: 0
9: 1
10: 2
11: 3
12: 4
13: 5
14: 6
15: 8
16: 10
17: 13
18: 16
In both cases, I ended up rounding a bit to the top 11%, in order to have a clear markoff.
SUM: If the sum is 80 or more, you are in the top 11%.
COST: If the cost is 36 points or more, you are in the top 11%.
So that leaves a few methods for calculating PC ability scores, if you want your characters to be in the top 11% on a 3d6 distribution:
a) Roll 1d6+12 for all ability scores.
b) Give 80 to 108 points to divide among the scores at a 1:1 ratio. Note that 98 points or more is "1 in 25 million" territory, and 94 points is around "1 in a million" territory.
c) Use the DMG point buy, with 36 to 96 points. Note that 70 points or more is "1 in 100 million" territory, and that even 60 points is "1 in a million" territory.
I like the 90 points (1:1 ratio), as it goes to about 1 in 50,000 territory (or roughly the top 0.002%), but still allows one or two reasonably low scores.
Well, anyway, that's my waste of mental space for the week
.
(This assumes you want your PCs in the top 10%; the 4d6/drop lowest actually ensures that some of them will be)
This question was driving me batty. The reason is simple: 3d6, over six ability scores, has slightly over 100 trillion possibilities. Even if you boil it down to 3-18, there are over 16 million possibilities. Spreadsheets aren't meant for that kind of abuse, and I'm not enough of a mathematician to sit down and start calculating the probabilities of each die result. So I abused a spreadsheet. I've attached it, in case anyone cares enough, but it's really just a notepad.
I also had to define what I meant by "Top 10%". I went with two possible definitions:
1) Add up your ability scores. The top 10% of that total.
2) Add up the point buy COST of your ability scores. The top 10% of that cost.
On point 2, I went with this extrapolated cost chart:
3: -14
4: -10
5: -7
6: -4
7: -2
8: 0
9: 1
10: 2
11: 3
12: 4
13: 5
14: 6
15: 8
16: 10
17: 13
18: 16
In both cases, I ended up rounding a bit to the top 11%, in order to have a clear markoff.
SUM: If the sum is 80 or more, you are in the top 11%.
COST: If the cost is 36 points or more, you are in the top 11%.
So that leaves a few methods for calculating PC ability scores, if you want your characters to be in the top 11% on a 3d6 distribution:
a) Roll 1d6+12 for all ability scores.
b) Give 80 to 108 points to divide among the scores at a 1:1 ratio. Note that 98 points or more is "1 in 25 million" territory, and 94 points is around "1 in a million" territory.
c) Use the DMG point buy, with 36 to 96 points. Note that 70 points or more is "1 in 100 million" territory, and that even 60 points is "1 in a million" territory.
I like the 90 points (1:1 ratio), as it goes to about 1 in 50,000 territory (or roughly the top 0.002%), but still allows one or two reasonably low scores.
Well, anyway, that's my waste of mental space for the week
.
.
