Can someone who understands Statistics help me?

[KarinsDad]

Hmm... KarinsDad, you have a point. We should use the 'Average point-buy value' instead of 'The point-buy value of a character with all average scores'.

...

6.3397 x 6 = 38.0382 ...so a 38 pt point-buy might be a better representation of 5d6 drop two lowest.

BTW, I'm rather curious on how you came to the 39.6 pt number. Would you mind sharing your calculation method?

Thanks for replying!
Yanei Wu

I might have errors in mine. I double checked, but did not quadruple check.

But, you appear to have rounding errors in yours. For example, there is only one three possible. You need to roll 5 1s to get it. So, the odds are 1/7776 or 0.0001286. You have it listed as 0.01% (or 0.0001).

I did a spreadsheet of all possible combinations (yes, that took me over 50 cut and pastes to create 7776 rows and took 15 minutes). Not the brightest idea, but I do not have C++ on this computer and am an Excel novice.

I then did a =SUM(B2:F2)-SMALL(B2:F2,1)-SMALL(B2:F2,2) type equation for each row, summing it all up and dropping the smallest two.

I then did a =COUNTIF(H2:H7777,3), =COUNTIF(H2:H7777,4), etc. to figure out how many of each I had. I then multiplied this by the individual point count for each one, summed them up, and divided by 7776.


And actually, my average is 13.43017, slightly off yours as well. So, I could well have errors.

I figure we are in the ballpark though.

 

[wuyanei]

Hmm.... my average is 13.429 which is close enough to 13.43017. I know that I have a rounding error of 0.01%, so the two are close enough that the difference does not matter. I'm just wondering where the (39.6-38.0382)/38.0382 ~ 4.106% difference comes from. I'll check my numbers again.

Not that it really matters. I do agree that 38~39 pt point buy would be the best value to represent 5d6 drop-two-lowest, so I think we can claim to have answered gabrion's original question. Thanks for the discussion, KatrinsDad! Good day, and happy gaming!

Yanei Wu

 

[gabrion]

Thanks a lot everyone!

As a couple of you noticed, the real reason for the question (though it probably wasn't very clear in the first post) was, wuyanei put it, to find...

the 'Average point-buy value' instead of 'The point-buy value of a character with all average scores'

I was having problems with this because higher scores raise the average more than lower ones drop it. It would seem that you've given an answer though, and since I don't know how excel, or statistic in general, work, I'll take what you've given and run with it! Thanks again.

 

[dcollins]

Just simulated the point-buy calculation in C++ (excluding hopeless characters). The average result I come up with is 38.4. Code attached below.

 

[frisbeet]

Here's an exact answer to your 1st question, which wuyanei beat me to.

<5d6> = 13.430

Comes from determining the distributions for each method. It's a little painstaking, but a whiff of combinatorics helps. Here I show my work (scroll right):

"oc" = outcome, the result of your 5d6 drop 2 lowest roll.

	# ways of rolling				prob(oc)				oc x prob		
oc	3d6	4d6	5d6		3d6		4d6		5d6			3d6		4d6		5d6
18	1	21	276		4.63E-03	1.62E-02	3.55E-02		8.33E-02	2.92E-01	6.39E-01
17	3	54	610		1.39E-02	4.17E-02	7.84E-02		2.36E-01	7.08E-01	1.33E+00
16	6	94	935		2.78E-02	7.25E-02	1.20E-01		4.44E-01	1.16E+00	1.92E+00
15	10	131	1111		4.63E-02	1.01E-01	1.43E-01		6.94E-01	1.52E+00	2.14E+00
14	15	160	1155		6.94E-02	1.23E-01	1.49E-01		9.72E-01	1.73E+00	2.08E+00
13	21	172	1055		9.72E-02	1.33E-01	1.36E-01		1.26E+00	1.73E+00	1.76E+00
12	25	167	881		1.16E-01	1.29E-01	1.13E-01		1.39E+00	1.55E+00	1.36E+00
11	27	148	665		1.25E-01	1.14E-01	8.55E-02		1.38E+00	1.26E+00	9.41E-01
10	27	122	470		1.25E-01	9.41E-02	6.04E-02		1.25E+00	9.41E-01	6.04E-01
9	25	91	296		1.16E-01	7.02E-02	3.81E-02		1.04E+00	6.32E-01	3.43E-01
8	21	62	170		9.72E-02	4.78E-02	2.19E-02		7.78E-01	3.83E-01	1.75E-01
7	15	38	90		6.94E-02	2.93E-02	1.16E-02		4.86E-01	2.05E-01	8.10E-02
6	10	21	41		4.63E-02	1.62E-02	5.27E-03		2.78E-01	9.72E-02	3.16E-02
5	6	10	15		2.78E-02	7.72E-03	1.93E-03		1.39E-01	3.86E-02	9.65E-03
4	3	4	5		1.39E-02	3.09E-03	6.43E-04		5.56E-02	1.23E-02	2.57E-03
3	1	1	1		4.63E-03	7.72E-04	1.29E-04		1.39E-02	2.31E-03	3.86E-04

total
# ways	216	1296	7776								average	10.500		12.245		13.430

 

[KarinsDad]

Here's an exact answer to your 1st question, which wuyanei beat me to.

Your 5D6 numbers are identical to mine. This suggests to me that I do not have an error in that portion of my spreadsheet.

So, I double checked my point buy equation and found a minor bug in it.

The real point buy should be 38.04167 which is only 9/1000 of 1% off of wuyanei's answer of 38.0382 (which could be explained by his minor round off).

 

[wuyanei]

HER!