Gaming · D&D 5e
Ability score method comparator.
Tick the rolling methods you are weighing. See how each compares per score and as a full set of six against the standard array.
Methods
Result
Enter your numbers and press Calculate.
What this calculator does
The Basic Rules offer three ways to get six ability scores: the standard array, point buy and rolling four d6 and keeping the highest three. Tables argue about which is fairer, and the honest answer is a set of numbers. Rolling beats the array on average, loses to it fairly often, and has a long tail at both ends that the fixed methods do not.
This page puts the numbers side by side. For one score it gives the average, the average modifier, the chance of 15 or more and the chance of 8 or less. For a full set of six it gives the average total and the chance the rolled set matches or beats the standard array, by total points and by sum of modifiers. A single-roll calculator for any N and K is on this site; this page is for comparing methods.
Worked example
Rolling 4d6 and dropping the lowest averages 12.24 per score, against 10.5 for 3d6. The standard array (15, 14, 13, 12, 10, 8) totals 72, an average of 12 per score and a modifier sum of +5. A set of six 4d6-drop-lowest scores averages 73.47 in total. The chance it reaches at least 72 is 62%, so about 38% of the time the roller does worse than someone using the array. A 27-point buy cannot go above scores of 15 and tops out at a total of 75.
How it is calculated
Each method's distribution of one score is computed by exact enumeration of every dice outcome (for 4d6 drop lowest, all 1,296 outcomes). Averages are the weighted sums; the modifier is the floor of (score - 10) / 2. A set of six independent scores is built by repeated convolution of the single-score distribution, once for raw totals and once for modifiers, and the chance of beating the array is the tail of that distribution at the array's total (72) or modifier sum (+5). Expected best and worst scores in a set of six come from the order-statistic formulas for the maximum and minimum of six draws. Standard array and point-buy costs are from the Basic Rules.
The standard array, the four-d6 method and the point cost table are in the Basic Rules' "Creating a Character" section. These methods are not in SRD 5.1. The odds are computed here. Last checked 2026-10-26.
What this does not cover
- Racial or background bonuses are not applied; the numbers are for the raw scores.
- The comparison treats each score as independent and does not model arranging rolled scores to taste. Assigning them to abilities is a choice, not a roll.
- Optional rules such as rerolling a whole set below a total are not modelled.
- The 2d6+6 and reroll-ones methods are common house rules and not in the Basic Rules.
Common mix-ups
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Often assumedRolling four d6 means adding all four dice.
What the source saysThe Basic Rules say to roll four d6 and record the total of the highest three dice, then repeat five more times. [1]
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Often assumedWith point buy you can raise a score to 16 or 18 if you spend enough points.
What the source saysThe Basic Rules give you 27 points and a cost table that lists scores from 8 to 15 only, so point buy cannot start a score above 15. [1]
Checked against these sources on .
Frequently asked questions
What is the average of 4d6 drop lowest?
12.24 per score, with a modifier averaging 0.87. Scores range from 3 to 18.
Is 4d6 drop lowest better than the standard array?
On average a set of six gives 73.47 points against the array's 72, but there is about a 38% chance the rolled total comes in below the array.
How does point buy work?
You have 27 points. A score of 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, according to the Basic Rules. You cannot buy a score above 15.
What is the standard array?
The six scores 15, 14, 13, 12, 10 and 8, assigned to abilities as you choose. The total is 72, and it costs exactly 27 points in point-buy terms.
Why compare modifiers and not just totals?
Modifiers are what the game uses, and they come in steps of 2 points. Two sets with the same total can have different modifier sums, so the page reports both.
Sources
Checked
The standard array, the four-d6 method and the point cost table are in the Basic Rules' "Creating a Character" section. These methods are not in SRD 5.1. The odds are computed here. Runs entirely in your browser. Nothing you type is sent or stored.
Disclaimer
TNAADO is not affiliated with Wizards of the Coast. This tool is compatible with fifth edition and uses game names only to describe what it is for. Odds and totals are arithmetic from the cited rules, and your table's house rules may differ.