The 5e Standard Array: 15, 14, 13, 12, 10, 8

The standard array in D&D 5e is the fixed set 15, 14, 13, 12, 10, 8. You assign those six numbers to the six abilities in whatever order you like, and that is the whole method: no dice, no budget arithmetic, no chance of a character who cannot function. It exists so a player can build a competent character in about thirty seconds and get on with the game.

It costs exactly the full point-buy budget

People often assume the array is a weaker, simplified alternative to point buy. It is not. Price each of its six scores using the published point-buy cost table and the total lands precisely on the 27 points a point-buy character gets to spend.

That tells you something useful about what point buy can and cannot do for you. Spending the same 27 points differently does not buy more total power; it redistributes it. You can flatten the array towards 13s and 12s, or you can push for a second 15, but the budget does not grow.

How it compares with rolling

This is the comparison that actually matters at a table deciding which method to use, and it is usually argued with hunches. The exact distribution of 4d6-drop-lowest arrays settles it. Enumerating every possible outcome rather than sampling them, here is where the standard array sits.

So the standard array is slightly below the average roll, and close enough that the difference is not what people are really arguing about. Roughly 56% of rolled arrays beat it on raw total, and roughly 48% beat it on modifiers, which is the measure the rules actually use. What rolling changes is not the expected outcome but the spread: about one rolled array in ten comes out below 65, and about one in eight reaches 82 or more. Choosing the array is choosing to give up both tails.

Where to put the six numbers

The placement rule is simple and rarely stated plainly: the 15 goes on the ability your class uses for its attacks or spellcasting, the 14 usually goes on Constitution or on a secondary ability the class leans on, and the 8 goes somewhere the class genuinely never rolls. Beyond that, the useful distinction is between classes that need one high score and classes that need three.

Classes that need one high score

A full caster whose spells all key off a single ability is the easiest case. Put the 15 there, the 14 in Constitution so concentration checks hold up, the 13 and 12 wherever the saving throws you expect to make live, and dump the 8 into the physical ability you will never use. These characters lose very little by taking the array instead of rolling, because they were only ever going to use one high number.

Classes that need three

A character that wants a strong attack ability, solid Constitution and a third ability for its class features is where the array pinches. There is exactly one 15 and one 14 to go round, and the 8 has to go somewhere. These are the builds that benefit most from a good roll and suffer most from a bad one, which is worth knowing before your table picks a method.

Then add the bonus, and mind which rule set you are on

The array is applied before any bonus. Where that bonus comes from changed between editions: under the 2014 rules it comes from your species, and under the 2024 rules it comes from your background. Both hand out three points, spread either as +2 and +1 across two abilities or as +1, +1 and +1 across three. The arithmetic is identical; only the source and the list of eligible abilities differ, so check the entry you are actually using.

One practical consequence. If your bonus is +2 and +1 and you put the +2 on your 15, you start at 17, one point short of the modifier breakpoint at 18. Putting the +1 on an odd score such as the 13 does nothing at all until something else raises it, because modifiers only move on even numbers. That is worth a moment of thought, and it is the same consideration the point buy calculator flags when it tells you whether the next point changes your modifier.

The other 64 ways to spend the same 27 points

If the standard array is one way of spending the 27-point budget, the obvious next question is how many other ways there are, and whether any of them are simply better. We enumerated every combination of six scores between 8 and 15 and priced each one against the point-buy table. Exactly 65 distinct arrays spend all 27 points. The standard array is one of them.

Sorting those 65 by the sum of their six modifiers, which is the number that actually shows up on the character sheet, gives a picture most players have never seen.

The standard array sits in the largest group, at +5. It is a typical way to spend the budget, not an optimal one. Ten arrays reach +6, and a single array reaches +7: 14, 12, 12, 12, 12, 12. That array has no 15 at all, which tells you most of what you need to know about why it is rarely taken. Most classes want one ability as high as possible on day one, and a spread that maximises the total modifier does it by refusing to buy any odd numbers.

Two lessons fall out of that table. First, the raw total and the modifier sum disagree about which array is strongest. The flat 13-and-12 spread has the highest total of any legal array at 75, but its modifier sum is only +6, the same as 14, 14, 14, 12, 10, 8. Second, the standard array is not the array that wastes the fewest points. Its 15 and 13 are both odd, and an odd score at character creation is paying for a point that does not change the modifier until something raises it again.

Where to put a +2 and a +1

Once the bonus is added, the array stops being a fixed set and becomes a small optimisation problem. If your rules let you choose which abilities receive a +2 and a +1, there are really only four placements worth considering, and they do not all give the same result.

Three of the four placements reach the same ceiling: a modifier sum two points higher than you started, which is the most this array can gain from a +2 and a +1. The one that falls short is the instinctive choice, putting the +2 straight onto the 15. That gives a 17, and 17 carries the same +3 as 16, so the second point of the bonus changes nothing today. Of the three that reach the ceiling, putting the +2 on the 14 and the +1 on the 15 is the one most players overlook, and it produces two 16s, which suits a character that leans on two abilities equally. The 17 is not useless, since the next increase takes it to 18, but it is worth knowing you are trading a point of modifier now for that future breakpoint.

With a +1, +1, +1 bonus the ceiling is the same +2. Only the 15 and the 13 are odd, so only two of the three +1s can each lift a modifier. The third +1 lands on an even number and waits for a later increase to do anything. Which spread you are allowed, and which abilities are eligible, is set by your species under the 2014 rules and by your background under the 2024 rules, so the choice is constrained by the entry you picked.

Slot by slot: the array against a sorted roll

The comparison with rolling earlier in this guide looked at the whole array at once. It is more revealing to sort a rolled array from highest to lowest and compare it with the standard array position by position. These figures are exact, computed from the distribution of a single 4d6-drop-lowest roll rather than from simulation.

Read the columns together and the shape of the difference becomes clear. At the top, rolling usually wins: four rolled arrays in five contain at least one score of 15 or better, and the average highest roll is 15.66. In the middle, the array is roughly level with a typical roll, and at the fourth position it is actually slightly better. At the bottom, the rolled array is usually better again, because the array commits to an 8 and seven rolled arrays in ten do not go that low.

So the standard array is not simply a little below average across the board. It is noticeably flatter at the top than a typical roll, about level in the middle, and a little harsher at the bottom. That is exactly the profile you would design if you wanted to make a character reliable rather than exceptional.

What a single roll actually looks like

Most arguments about rolling are really arguments about a handful of memorable outcomes, so it helps to put numbers on them. For one roll of 4d6 dropping the lowest die, the average score is 12.24 and the most common single result is 13, which comes up 13.27% of the time.

An 18 on a single roll comes up 1.62% of the time, so across six rolls a player sees at least one about once in eleven characters. Nearly half of all rolled characters have at least one score of 8 or below, which is the same dump the standard array gives you by design. And about one rolled character in fourteen has nothing above 13, which is the outcome that makes tables adopt the array in the first place.

Why the modifier table rewards even numbers

That single rule explains most of the optimisation above. It is why 14, 12, 12, 12, 12, 12 has the highest modifier sum of any 27-point array, why the second bonus placement beats the first, and why the standard array deliberately includes two odd scores for the bonus to land on. It is also why a point-buy calculator that flags modifier breakpoints saves more time than one that only tracks the budget.

Planning ahead to your first ability score increase

The array decides where you start. The first ability score increase, which most classes gain at 4th level, decides where you are for most of the campaign. Under both rule sets the basic option is +2 to one ability or +1 to two, with a normal maximum of 20. Check your own class table for the exact levels, since a few classes gain extra increases.

The table shows why the 16 and 17 starting points behave differently. A character starting on 16 wants the full +2 to reach 18. A character starting on 17 reaches 18 with just a +1, which frees the other +1 for an odd secondary score such as a 13 or 15. That is the real value of taking the 17 at character creation: not the extra point now, but the flexibility it buys at 4th level.

When the array is the right choice, and when it is not

• New players. Point buy asks someone who has never played to price trade-offs they cannot yet judge. The array gives them a sound character immediately.
• One-shots and convention games. Character creation time is table time, and the array is the fastest method that still produces a competent character.
• Groups that value parity. If the table has had a bad experience with one lucky roller outshining everyone, the array removes the problem entirely.
• Characters who need one ability. A class that keys everything off a single ability loses very little by taking the array, as shown above.
• Not ideal for characters needing three abilities. Point buy can produce 15, 15, 15 or 14, 14, 14, which the array cannot. If your concept needs three strong numbers, point buy fits it better on the same budget.
• Not ideal for tables that enjoy randomness. Some groups want the surprise of a rolled character and accept the spread that comes with it. That is a legitimate preference, not a mistake.

Common mistakes with the standard array

• Forgetting to add the bonus at all. The array is the starting point, not the finished score.
• Putting a +1 on an even score at 1st level without a plan to raise it later. It does nothing to the modifier until something else adds another point.
• Dumping Constitution. It sets hit points for every class and it is what concentration checks roll against, so the 8 almost always belongs somewhere else.
• Mixing methods, such as taking the array and then rolling for one score. Choose one method per character; that is what makes the methods comparable.
• Treating the 13 as a throwaway. Some rule options, such as multiclassing, set a minimum score in particular abilities. If you might use one, check the requirement before you put the 13 anywhere.

Where to go next

The array is one of three ways to get a set of scores. Point buy vs rolling compares the other two head to head with the probability math behind each, and 4d6 drop lowest gives the exact distribution that rolling actually produces, which is the honest way to see how a rolled array stacks up against 15, 14, 13, 12, 10, 8.

Common questions