A request for those with math abilities for point-buy systems

[The Dark Harlequin]

ok, so I have noticed that several people on this board are quite good at doing statistics and probability (as evidenced by the several point-buy threads)
now I have a question/request for you people.
I would like to offer both a point-buy system and a rolling system for my campaign world. I subscribe to the belief that PCs shouild be HEROES and not have especially substandard ability scores unless the player works something out with the DM beforehand.
In other words I would like the averaqge ability to be at 13.5-14
Of the rolling systems I have seen I really like the idea that was mentioned of assigning 3d6 to each stat and then adding a number of d6's to the scores beofre you roll. So a typical character might add 9d6 to their abilities like so
Str 5d6
Dex 4d6
Con 3d6
Int 6d6
Wis 4d6
Cha 5d6
and then keep only the highest 3 rolls for each score (NO re-assigning)
So the first part of my question, what number of other dice (6, 9, 12, 300?) would give an average score of around 13.5-14 in each ability

Now for the second part. I like the idea of a point buy system as well...i see the merits of both types, and as a DM I would like to offer both options to players. SO, I need a point buy system that allows an Ave score of 13.5-14 or so and allows for high scores to be possible as well.

I dont know if anyone can or will do this for me...but I would be very interested to see what you all can turn up...
and I wouldnt mind seeing a few original point buy systems turn up either as I am not that big a fan of the standard WOTC table...
I wouldnt ask this if i could do it myself, but I suck at math...thanks

 

[Dr. Zoom]

13.5 to 14 for average ability scores would require about 5d6 for each ability. The 3d6 for each is 18 dice, so 12 would be your number of extra dice. I am making an educated guess on the numbers, mind you.

Using 32 point buy from the DMG will get you close to that average. You could have 5 scores of 14 (6 points gets you a 14) and a 10, or 4 14's and 2 12's. If you want more, just increase the points. 36 points buys you 6 scores of 14. I suggest not surpassing this number unless you want the DM to work alot harder to balance each encounter.

 

[Alomir]

Here are the average scores for rolling n dice, and keeping the top three:

dice: avg score:
3 --- 10.5
4 --- 12.24
5 --- 13.43
6 --- 14.27
7 --- 14.90
8 --- 15.39
9 --- 15.78

If your players put the same number of dice into each score, they'd need between five and six dice for each. They're not going to do that, of course, so their overall averages are going to be a bit lower than if they did (because the scale is not linear; 4 dice + 8 dice is less than 6 dice + 6 dice). I would say to try somewhere in the low 30s for total dice, maybe 32 or 33 (so 14 or 15 extra dice).

What don't you like about the standard point-buy table?

- A

 

[bret]

For point buy, it is pretty easy to figure how many points you want.

Figure out the average attribute you want and then how high you want a single attribute.

Since you are going for an average of 13, straight 13s would cost:
6 * 5 = 30 points.

If you wanted them to have straight 13s with a single 17, you would give out 5 *5 + 13 = 38 points. You will note this is quite a bit above the normal point buy limits.

The numbers that you really need is what is within 1 standard deviation for the various rolling methods, so that you know how low and high those methods would normally go. With 12d6, drop lowest three, there is a much better chance of rolling an 18 than a 3.

 

[Artoomis]

Mixing point-buy and die-roll methods together generally does not work. No matter how you structure it, somehow the die rollers end up with better stats.

Do they cheat? Perhaps. Maybe they just generate 50 characters and choose the best. Of course, that's really cheating - if you are going to do that, you miught as well just pick nuymbers out of the air.

I do not like ANY of the random methods precisely because there is virtually ALWAYS the suspicion that someone cheated in getting their extraordinary stats.

 

[Xeriar]

Just some observations:

25 point buy - top 10% of population
32 point buy - top 5% of population
38 point buy - top 1% of population

...

52 point buy - top .01% of population

On straight 3d6. Numbers are approximate, of course.

 

[Emongnome]

My observations with 5d6 are very close to Alomir's: 13.49 I believe, with a standard deviation of 1. My numbers are based on around 250 rolls done in Excel. I'm not a statistics genious, but that should still be reasonably close to the actual.

 

[Alomir]

Here are the average scores for rolling n dice, and keeping the top three:

dice: avg score:
3 --- 10.5
4 --- 12.24
5 --- 13.43
6 --- 14.27
7 --- 14.90
8 --- 15.39
9 --- 15.78

Should have 'named my sources': the 3d6 and 4d6 numbers are easy enough to obtain analytically (avg for 3d6 is hopefully pretty clear, avg for 4d6 = 15869/1296). The others I got from making a few runs of 10 million rolls each using MATLAB, as I was too lazy to figure out the mathematics (really, the interest is there, I just didn't have the time).

However, it just dawned on me that it would be more accurate to just zip through all of the possible rolls, and get an exact value (much less than 10 million, except for the 9d6 case, which is just over 10 mil). Here they are again with standard deviations:

dice:__avg:____std:
3 --- 10.500 -- 2.958
4 --- 12.245 -- 2.847
5 --- 13.430 -- 2.603
6 --- 14.274 -- 2.364
7 --- 14.903 -- 2.150
8 --- 15.389 -- 1.965
9 --- 15.775 -- 1.804

As I said before, this system is somewhat weighted towards people who go for lots of reasonable scores, as opposed to a few big scores. For example, if I have 18 extra dice, and put 3 into each score (6d6 each), I'd have an average score of 14.27; if instead I put 6 into three scores (3 3d6 scores, 3 9d6 scores), I'd have an average score of 13.14, more than a point less.