What is the math of dice rolled, arrays, and point buy?

[gorilla-turtle]

How does one figure out how many or what type of dice (and what rerolls or dropped or added or whatever) constitutes what type of array of stats and what point buy one could get and be of a similar level on average? I'm not sure how 3d6 x 6 gets 15 / 14 / 13 / 12 / 10 / 9, and how that's a... 25 pb, if I remember right?

[Cambrian]

Average on 3d6 is 10.5 so that array is certainly not based off of 3d6.

4d6 drop lowest averages just under 13 so that probably average for that method.

Using the PF point buy system that works out to 16 point buy (7+5+3+2+0-1). Usually though I find games use 20-25 point buy since MAD classes really get screwed in low point buy games, and SAD classes tend to be casters who don't need the help.

[Jeff the Green]

How does one figure out how many or what type of dice (and what rerolls or dropped or added or whatever) constitutes what type of array of stats and what point buy one could get and be of a similar level on average? I'm not sure how 3d6 x 6 gets 15 / 14 / 13 / 12 / 10 / 9, and how that's a... 25 pb, if I remember right?

A one-tailed t-test (http://en.wikipedia.org/wiki/Student's_t-test) will determine how far off you are from the mean, giving a p-value of 0.069. So in other words if you're rolling 3d6 you'll get something with an equal orhigher sum of ability scores as 15/14/13/12/10/9 nearly 7% of the time.

A KS-test (http://en.wikipedia.org/wiki/Kolmogorov%E2%80%93Smirnov_test) might be better at sussing out differences (e.g. there's less variance in the sample than there'd be in a true roll), though that's probably overkill. Someone with more stats knowledge than me might know a better test.

Edit:
Anti-ninjaed:

Average on 3d6 is 10.5 so that array is certainly not based off of 3d6.

Not true. As mentioned, the mean isn't significantly off (P>0.5). I'd bet the combination of mean and variance are, but I can't remember what test you'd use for that other than KS, and that'd involve putting together a 3d6 dataset that I'm not up to right now.

[Cambrian]

Not true. As mentioned, the mean isn't significantly off (P>0.5). I'd bet the combination of mean and variance are, but I can't remember what test you'd use for that other than KS, and that'd involve putting together a 3d6 dataset that I'm not up to right now.
http://catlikecoding.com/blog/post:4d6_drop_lowest
This link shows the array is based off of 4d6 ;)

[Story]

Using the standard 4d6 with rerolling rules suggested in the PHB, the odds of getting a 15, 16 or 17+ are all roughly one third, with 16 being the most likely. The elite array is actually a bit below what you'd get on average from rolling.

[TuggyNE]

Using the standard 4d6 with rerolling rules suggested in the PHB, the odds of getting a 15, 16 or 17+ are all roughly one third, with 16 being the most likely. The elite array is actually a bit below what you'd get on average from rolling.

As is 25-point buy. The correct average is just a touch under 28 point, in fact.

[Jeff the Green]

http://catlikecoding.com/blog/post:4d6_drop_lowest
This link shows the array is based off of 4d6 ;)

I'm aware that the elite array is based off of 4d6b3. It's wrong to conclude that from the average of the elite array and the average of 3d6, however.

[Cambrian]

I'm aware that the elite array is based off of 4d6b3. It's wrong to conclude that from the average of the elite array and the average of 3d6, however.I don't think you understood my post. It was a litmus test to see if the array given could reasonably be based off of 3d6-- no complex math (or nit picking) was required.