What are the Best 4e Ability Score Arrays?

I’ve been following an interesting thread about 4e ability score arrays at ENWorld.  Poster 77IM calculated all of the possible arrays on a 22-point buy, and posted the list.  Turns out there are 121 unique arrays, in case you were wondering.

Then the analysis began.

Poster Jurph isolated the arrays that give the best overall bonuses — what he called “champion” arrays, with ability modifiers that total +8:

16 14 12 12 12 10
16 13 12 12 12 12
15 14 12 12 12 12
14 14 14 14 12 8
14 14 14 14 10 10
14 14 14 13 12 10
14 14 14 12 12 11
14 14 13 13 12 12

They are, unsurprisingly, the arrays that forego spending lots of points on a single high attribute, and instead spread the bonuses around.  So, are the arrays with the biggest bonuses the best?

I think not.  I wrote most of the following in reply:

I'm guessing he pumped Strength and dumped Wisdom.

Of these 8 arrays, I’d consider only the first one competitive, because in 4e, having a high bonus in your primary stat is of great importance. With less than a +3 bonus, you’re decidedly weakening yourself. A +3 bonus is about par, and requires either a 16 or a 14 plus racial bonus.

However, to be really competent, you’ll generally want an 18 in that primary stat, which means a 16 in your starting array plus a favorable race. Only the first two options offer that, and the 16/14 array (offering a secondary +2, three +1s, and a +0) is clearly better than the 16/13 array (offering five +1s), because no reasonable build requires bonuses in all six stats.

(I suppose a bard who really pushed the jack-of-all-trades thing might go for the 16/13 array, but he’d be pretty incompetent with any attack that relied on a +1 stat.)

Now, of the 7-point arrays, we could have:

16 16 12 12 10 8

This is one of my favorite arrays. It provides an 18 primary after racial, a 16 or 18 secondary, and two +1s. A single -1 is not a problem for most builds. The 12s will meet many prerequisites by paragon level, and can be bumped a point to meet a 15 prerequisite by epic if necessary (or two points to meet it by paragon). The tertiary stat will be a little weak without bumping, but many builds don’t really have a firm tertiary stat. In addition, there are enough bonuses to spread around to ensure at least a small boost to all defenses.

16 14 14 13 10 8

This is a solid array when a tertiary stat is necessary. You still get the 18 primary, a 14 or 16 secondary and tertiary, and an additional +1, which ensures decent defenses all around. The 13 also qualifies for many feats, and will be a 15 by epic without boosting. The single -1 is again not an issue for most builds.

16 14 14 12 11 8

A slight variation of the above. This one pushes off the “feat qualifier” 13 in exchange for reaching a 12 in the fifth stat faster. I prefer the one above, but this one is stronger if for some reason you need to place your four top stats into two of the “linked pairs”, leaving you with one low defense. It’s also a little better if you need two 13s in otherwise unimportant ability scores in order to qualify for feats.

16 14 14 11 10 10

Another variation on 16/14/14, this is generally weaker than the above two, but it’s a prime option if you really want to avoid taking a negative. You get an 18 primary after racial, a 14 or 16 secondary and tertiary, no negatives, and the 11 lets you qualify for feats and (if necessary) get a small defense bonus, with some bumping.

The 18 arrays are also worth considering in some cases:

18,14,11,10,10,8
18,13,13,10,10,8
18,13,12,11,10,8

These have very small bonuses overall because of the opportunity cost of getting that 18. However, they’re the only way to start out with a +5 bonus (after modifier). For builds that rely mainly on a single stat (like many wizard builds), it might be worth the sacrifice. 18/14/11 gives a decent secondary, 18/13/13 and 18/13/12 offer some easier feat qualifications and, possibly, bonuses to each defense.

I don’t see any of the champion arrays beating these out in actual play. 16/14/12 might be on-par, but I don’t see it as superior.

Focusing for a couple of strong bonuses is usually the better option in 4e than spreading lots of little ones around.

Following this post, Jurph added an additional reply:

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.

These look like the arrays people (including me) actually use frequently.  I hadn’t thought of a sum-of-squares approach myself, but I was happy to see that my intuition was fairly good.  I’m still not sure this covers the whole story — my gut tells me that both of the 16/14/14 arrays are solid options — but I find the whole analysis intriguing.

Related posts:

1. Developing Roles
2. My Elves are… Odd
3. Defining Roles
4. Narration in Combat
5. Deep Psi