Rolled, arrayed or bought: what each ability-score method gives you

A table about to make characters has to settle one question before anyone picks a class: where do the six ability scores come from? The free rules for the 2024 core rulebook list three methods and leave the choice to the referee (D&D Beyond — Free Rules: Creating a Character). They are not equivalent, and the difference is easy to put numbers on.

This note compares the three. It adds plain 3d6, rolled six times, as a baseline of our own, so that you can see what the “drop the lowest” rule is doing. Everything below is exact: the dice figures come from listing every possible roll, and the fixed methods come from the rule text.

The three methods, as the free rules describe them

• Standard array. Use these six scores: 15, 14, 13, 12, 10 and 8.
• Random generation. Roll four six-sided dice, add up the three highest, and repeat until you have six totals.
• Point cost. You get a budget of 27 points, and each score has a price from a table: 8 costs 0, 9 costs 1, 10 costs 2, 11 costs 3, 12 costs 4, 13 costs 5, 14 costs 7 and 15 costs 9.

(All three descriptions are paraphrased from the page listed in Sources, read on 2026-10-31.)

The numbers for a single score

The average rolled score is 12.24 with four dice and 10.5 with three. The standard deviations are 2.85 and 2.96. Individual scores land outside the 8 to 15 range of the point-cost table more often than you might expect: 18.8% of single drop-lowest scores and 20.8% of plain 3d6 scores. The tails are the interesting part:

What a full set of six looks like

A set is sorted from highest to lowest here, and the table gives the expected value of each position. These are exact averages over every possible set of six rolls.

The point-cost column is a range because that method lets you choose. There are 65 different sets of six scores (ignoring order) that spend exactly 27 points, and their totals run from 69 to 75. Three sets reach the maximum total of 75: 10, 13, 13, 13, 13, 13; 11, 12, 13, 13, 13, 13; and 12, 12, 12, 13, 13, 13. The standard array itself costs exactly 27 points (9 + 7 + 5 + 4 + 2 + 0), so it is one of the options of the point-cost method.

Two things follow from the table. First, a set generated by drop-lowest averages 73.5, slightly above the fixed array’s 72 and just under the point-cost maximum of 75. Second, the fixed methods sit near the rolled average, so a referee who offers the array as an alternative to rolling is offering something very close to an average roll.

How often does a roll beat the array?

Because a rolled set varies, the useful question is how often it comes out above or below the fixed 72.

Under drop-lowest, about 38% of sets total less than the array’s 72, and about 62% match or beat it. A fixed array removes that risk entirely, at the price of removing the chance of a very strong set: no array that costs 27 points totals more than 75, while a rolled set can total much more.

Plain 3d6 behaves quite differently from the rule in the free rules. More than a third of sets total 60 or less, and nearly two in three include a score of 7 or lower. That contrast is the practical case for the keep-the-highest-three rule: it takes a lot of the sting out of a bad roll.

What this means for the table

These are our observations from the numbers, not rules:

• If everyone at the table should start on equal footing, the standard array and point cost give that, because every character spends the same 27 points (the array is one way of spending them).
• If the table likes variation, random generation gives it, and the spread is real: the standard deviation of a six-score total is about 7.0 for drop-lowest.
• If a table is worried about one weak character beside a strong one, a simple compromise is to let each player choose rolled or array, or to set a minimum total for rolled sets. The numbers above show what such a minimum would exclude: a minimum total of 67 would reject about 16% of drop-lowest sets (a total of 66 or less).

Method

• Rolled scores. A script lists all 1,296 ordered rolls of four d6, drops the lowest die of each and counts the totals. Plain 3d6 uses all 216 rolls of three dice. Set-level figures convolve six independent scores, and the position averages use exact order-statistic formulas on the single-score distribution. No sampling or simulation is involved.
• Fixed methods. The array sum (72) and point-cost table come from the free rules page. The script enumerates every multiset of six scores from 8 to 15 and keeps those costing 27 points or less (1,197 sets, of which 65 cost exactly 27).
• Baseline. Plain 3d6 is not one of the three methods in the free rules; it is included so the effect of keeping three of four dice is visible.
• Check it yourself. Every figure for one score can be reproduced by hand from the 1,296 outcomes (the companion note on 4d6 drop the lowest lists them). The sums for fixed methods use only the table above.

Sources

• D&D Beyond — Free Rules: Creating a Character: the standard array, the roll-four-keep-three method and the 27-point cost table (page read 2026-10-31).
• OpenStax — Mean or Expected Value and Standard Deviation: expected value and standard deviation of a discrete distribution.
• System Reference Document 5.2.1: the same three methods and the same point-cost table appear in the SRD, checked on 2026-10-31 against the official PDF (version 5.2.1).

This work includes material from the System Reference Document 5.2.1 (“SRD 5.2.1”) by Wizards of the Coast LLC, available at https://www.dndbeyond.com/srd. The SRD 5.2.1 is licensed under the Creative Commons Attribution 4.0 International License, available at https://creativecommons.org/licenses/by/4.0/legalcode.

Written for: a player or referee choosing how to generate ability scores who wants to know what each method actually produces.