All Ability Score Arrays

[Llamas Notsheep]

Nice analysis Practically speaking, though, I think things will be a bit different for pretty much any character.

Is there any character out there that's actually going to make use of all attirbutes? In practice, having a -1 somewhere isn't going to hurt just about any character. What does it look like if you disregard the -1 for having an 8 or 9 in the array?

 

[77IM]

Personally, I hate having a penalty. Not for any mechanical reasons, but just for role-playing. My favorite array is 16/14/14/11/10/10, although I like all of the 16/14/14 and 16/16 arrays, for the reasons Scott_S describes.

OTOH, I think the 18 arrays and the 14/14/14 arrays can both be viable for some characters. A warlord, for example, could do OK with 14/14/14 and the right racial mods, and someone like a rogue can really benefit from an 18.

BTW, here are all the arrays without any 8s or 9s in them. There are 52. Many are near the "bottom" of the Big List (i.e. starting with a 15 or 14).

18,13,11,10,10,10
18,12,12,10,10,10
18,12,11,11,10,10
18,11,11,11,11,10
17,15,11,10,10,10
17,14,13,10,10,10
17,14,12,11,10,10
17,14,11,11,11,10
17,13,13,12,10,10
17,13,13,11,11,10
17,13,12,12,11,10
17,13,12,11,11,11
17,12,12,12,12,10
17,12,12,12,11,11
16,16,12,10,10,10
16,16,11,11,10,10
16,15,13,11,10,10
16,15,12,12,10,10
16,15,12,11,11,10
16,15,11,11,11,11
16,14,14,11,10,10
16,14,13,13,10,10
16,14,13,12,11,10
16,14,13,11,11,11
16,14,12,12,12,10
16,14,12,12,11,11
16,13,13,13,12,10
16,13,13,13,11,11
16,13,13,12,12,11
16,13,12,12,12,12
15,15,14,11,10,10
15,15,13,13,10,10
15,15,13,12,11,10
15,15,13,11,11,11
15,15,12,12,12,10
15,15,12,12,11,11
15,14,14,13,10,10
15,14,14,12,11,10
15,14,14,11,11,11
15,14,13,13,12,10
15,14,13,13,11,11
15,14,13,12,12,11
15,14,12,12,12,12
15,13,13,13,13,11
15,13,13,13,12,12
14,14,14,14,10,10
14,14,14,13,12,10
14,14,14,13,11,11
14,14,14,12,12,11
14,14,13,13,13,11
14,14,13,13,12,12
14,13,13,13,13,13
​

-- 77IM

 

[Garthanos]

Personally, I hate having a penalty. Not for any mechanical reasons, but just for role-playing. -- 77IM

heh, I computed my own stats in many game systems back in the day.. til the back injury I had a few years ago.. nothing was below average (Back problems really screw with your stamina - bye bye 12 con hello 8 ).

No clue how to compute them in 4e but hey ;-)

Why would I want a hero who was gimped? inorder to be super at one thing... monomaniacs are not interesting in real life ;-) however that one thing in D&D comes down to be close to everything.

Makes me inclined to house rule things to make "off" stats more useful.

 

[Scott_S]

I often like to have one weaker-than-average stat... for roleplaying reasons. Most heroes have a flaw of some sort, and a wide variety of them are possible to model with a "low" attribute.

Low INT is the only one I try to avoid. It annoys me a little that in 4e, it's often the easiest stat to "dump"... but I'm a GM who enforces roleplaying the mental stats, and my players know it, so I don't have to worry about it too much.

 

[77IM]

Hah, we are opposites, because Int is the one stat that I would set low for role-playing reasons. I love playing stupid characters. I'm told I'm quite good at it; I'm not sure whether that is a compliment or not...

-- 77IM

 

[Jurph]

Alright, I'm back. Had to think long and hard about Scott_S's assertion that many small bonuses lack the utility of a large bonus. I went back to the arrays and calculated the sum of the squares of the bonuses. These arrays give the top value (21):

18 14 11 10 10 8
18 14 10 10 10 9
16 16 12 12 10 8

and these give a value of 20:

18 12 12 12 10 8
16 16 13 11 10 8
16 16 13 10 10 9
16 16 12 11 11 8
16 16 12 11 10 9

The population of sum-of-squares scores runs from 21 down to 8 and the "champion" (+8) arrays range from 18 down to 12.

You could also conceivably set the exponents in the simple sum-of-squares formula to be somewhere between 0 and 2 according to your class needs. That way a score of 8 in your lowest attribute wouldn't matter (the lowest score would be raised to the zeroth power and always contribute 1 to the total) and a high score in your highest would get the full benefit of being squared. MAD classes would need a preference equation that was (approximately) 2,2,1.5,1,1,0 but a class like a wizard could choose 2,1.75,1.5,1.25,1,0 and get a more skewed array.

 

[BartD]

Great thread

Jurph, those arrays look like the ones people actually choose. What happens if you don't count (-1)^2=+1 from an 8 or 9 as a good thing?

Also, an odd score is a litle better than the next lower even score since i can be raised or become even in heroic tier. So maybe increase the value of bonuses from odd scores by 1/2 or 1/3 sor omethng like that?

By the way, seeing that...
18 costs 16 points and gives +4 which you count as (+4)^2 = 16,
16 costs 9 points and gives +3 which you count as (+3)^2 = 9,
14 costs 5 points and gives +2 which you count as (+2)^2 = 4,
12 costs 2 points and gives +1 which you count as (+1)^2 = 1 and
10 costs 0 points and gives +0 which you count as (+0)^2 = 0,
it seems that cubed scoring very closely follows the point-buy costs except odd scores are worth less.

 

[Jurph]

BartD, I hadn't noticed that - I've never actually done the point-buys by hand because I've always had a computer doing the substitutions for me. It makes sense though!

Good catch on that squared negative! If you want to ignore the lowest score, you can reduce (or eliminate) its contribution to your overall value formula. For example, my dwarven paladin - who has a serious case of MAD, and so values his second and third stats pretty highly - settled on

FoM = A² + B^1.5 + C^1.5 + D¹ + E¹ + 0

Where A through F are the values of the bonuses given by my highest through lowest ability scores, respectively, and the Figure of Merit is rounded (up or down) by truncating decimals. I've already prioritized my attributes and added my racial bonuses, so I'm seeing values as high as 22 and as low as 10.

I'm also using a "defense" stat to measure the total points of additional defense I get (values range from 4 to 7) and a "hp" stat so I can see how many hit points I'll have. Summing all three values -- the merit equation, the defense value added, and my hit points -- gives a range of values from 96 to 79. Subtract 78 from all of them, and I end up with a merit scale that runs from 1 to 18*... with only one array getting an 18. The winner (for my case) is:

18 12 12 12 10 8

and the best runners up are:

14 14 14 14 12 8
16 14 14 13 10 8
18 13 12 11 10 8
18 12 12 11 11 8
18 12 12 11 10 9

That first runner-up looks like a stinker but gets two 16s after racials and ends up being mediocre at combat but much more difficult to land a hit on than your average lvl1 -- that's what I get for valuing additional defense and hit points, I guess. The other arrays also look like they could be useful, depending on your play style.

I think this figure-of-merit calculation would turn out very differently for a fighter, or a mage, or even a character with a different race. For example, a dragonborn paladin will probably value high all-around defense, but because she has +CHA and +STR, she will probably adjust things accordingly. A mage might want to spend points for INT, CON, and WIS and either let racials beef up the primary or soak low scores in other areas, so would choose to square the value of the top three bonuses and let the rest drift in the breeze.

* What are the odds that this figure of merit would happen to end up being the range of character traits in D&D? Kind of a cool coincidence, but ultimately meaningless.