Fair Random Stat Generation

[Camelot]

Yeah, that's the kind of math I wasn't capable of! Thanks! I rolled up two characters with 2d6+6, and they are both rather overpowered. The highest stat I got was only 16 (though racial made it 18), but the lowest was only 12, for both of them!

So, I guess the probability amounts to the same, but I still want a way that guarantees 8 - 18 range without having to start over! Maybe 4d6, drop lowest, but reroll all 1s will work. This will give you at least a 6, and it probably won't get that low anyway. I shall find out...

 

[Garthanos]

So, the weight average of your curve is 26.27 point-value, compared to the 22 points in the "official" point-buy. That's considerably better.

adjusting the weighting of the point buy method and centering it properly sounds like something worth fixing (though I do love my Character Builder app) .. after all if its supposed to only be used for heros why is it zero for a 10? instead of the 13?

 

[Paul Strack]

So, I guess the probability amounts to the same, but I still want a way that guarantees 8 - 18 range without having to start over! Maybe 4d6, drop lowest, but reroll all 1s will work. This will give you at least a 6, and it probably won't get that low anyway. I shall find out...

4d6 (re-roll 1s, drop the lowest) is even more generous than 2d6+6. It works out to an average of 30.85 point-buy-value, and an average score of 13.43.

If you want to (a) retain the spread of the point-buy system and (b) keep the range to 8-18, I would recommend:

1) Use 4d6 drop the lowest.

2) Raise any score below 8 to 8.

3) If the highest score is below 16, raise it to 16 (so the character can have decent primary score).

That will be ensure you will get playable characters, and the "average" character will only be a bit better than the point-buy character. It has the advantage of being very close to the "official" rules as well.

 

[Camelot]

I did try out the 4d6 reroll 1s drop lowest, and it did come out way to good for all the times I tried it.

Your way sounds reasonable, keeping it fair yet still random. Thanks!

 

[willows]

Here's a relatively easy way to do this without probability gymnastics.

Make several stat arrays using the same point-buy total. It doesn't matter how many.

Make a list of the ability scores in whatever order you want. It doesn't matter what order they're in.

Finally get two sets of d6 and d4, in two colors you can tell apart easily. Designate one color 'high' and one 'low'.

To create a character, first roll a d-whatever (depending on how many arrays you have) to select a stat array.

Then roll 2d6. Assign the highest value in the array to the stat indicated by the high die, and the second-highest according to the low die. If you roll doubles, use the indicated stat for the high value and the player gets to choose the second value.

Cross those ability scores off your list.

Use the same procedure, with the matching d4s, for the third and fourth-highest stats.

Just flip a coin for the last two.

 

[Elric]

77IM posted a method of randomly generating stats that would come out to the same total modifiers across characters. See http://www.enworld.org/forum/4e-fan-creations-house-rules/253570-balanced-ability-rolling.html.

From a balance standpoint, two problems I see are that many characters don't need, say, Cha/Wis so a character who gets high scores in both misses out on some benefits, and the fact that an 18 ability score pre-racial is worth a lot; characters with only a 16 may be somewhat left out.

Random rolling would make it difficult to play many the Strength-based classes unless they can swap around the rolls they got (e.g., swap a 16 Con with a 12 Strength). Wisdom has a lot of classes using it as a primary stat as well. So if you don't let characters assign their ability scores to the various stats, they'll need higher raw scores in general to have similarly effective characters.

 

[Camelot]

When you roll stats, you roll six scores and then assign them to whichever stats you prefer. So, say your scores are 13, 15, 9, 12, 13, and 16. You assign the 16 to the score you want to be the highest while the 9 and 12 are assigned to scores you don't plan to use. I don't think it's fair to have predetermined scores, because then you're railroaded into a certain set of classes, and the idea you had for a character could be ruined.

For real games that I DM, I'm going to have my players stick to point buy. But sometimes, I just like a bit of random craziness. =)

 

[BartD]

Random without crazyness

I once calculated all the possible 22-point combinations (it's really not that many when a computer does it for you) and listed them in order from lowest to highest spread (so from 14-13-13-13-13-13 to 18-14-11-10-10-8). You then just generate a random number between 1 and X and look up the stat array.

However, most of those arrays will be suboptimal compared to actual pointbuy so I don't know if they can be called balanced?

 

[eamon]

However, most of those arrays will be suboptimal compared to actual pointbuy so I don't know if they can be called balanced?

This is significant. In order to have a balanced die-rolling system, you'll need to have well above 22 point-buy points on average. Firstly, the flexibility of being able to distribute points just how you need them is clearly quite valuable, and secondly, simply counting point-buy points commonly overstates the value of a distribution.

To see this, simply consider a character with a certain number of 18's. The first 18 is very valuable, being your primary stat. The 2nd 18 is much less valuable - it's nice, but it's worth much, much less. The 3rd 18 is generally almost worthless - it raises one non-AC defense and for some classes increases your options when it comes to power selection (but even this is only partially true since you can't raise that 18 throughout your career, and you'll run into weapon/implement selection issues). The forth 18 is worth even less - good for a few skills, and if Dex wasn't one of your primary 3 stats, it might raise your init. The 5th 18 might help your hitpoints somewhat. The 6th 18... well, you know those skills you dumped? Well, I guess you don't entirely suck at them, not that it really matters.

Despite the great variety in value, if you're generating stats independently, those characters that have many high stats will significantly raise the average point-buy level, while hardly being overpowered.

 

[77IM]

I once calculated all the possible 22-point combinations (it's really not that many when a computer does it for you) and listed them in order from lowest to highest spread (so from 14-13-13-13-13-13 to 18-14-11-10-10-8). You then just generate a random number between 1 and X and look up the stat array.

Hahaha -- I just did the same thing! I went to post it on the forums and noticed this very relevant thread here...

Anyway you can see the Big List here: http://www.enworld.org/forum/4e-fan-creations-house-rules/259634-all-ability-score-arrays.html

-- 77IM