Rolling DnD Character Stats — 4d6 Drop Lowest vs Standard Array vs Point Buy
Every fifth-edition character starts with six numbers, and there are three sanctioned ways to get them. They produce noticeably different characters, and the choice says more about what your table wants from a campaign than most people realise.
Method 1: 4d6, drop the lowest
Roll four d6, discard the lowest die, add the other three. Do that six times and assign the results to the six abilities as you like.
This is the traditional method and it is the only one with any randomness in it. Here is what it actually produces, out of the 1,296 equally likely combinations of four d6:
| Score | Ways | Chance | At least this high |
|---|---|---|---|
| 18 | 21 | 1.6% | 1.6% |
| 17 | 54 | 4.2% | 5.8% |
| 16 | 94 | 7.3% | 13.0% |
| 15 | 131 | 10.1% | 23.1% |
| 14 | 160 | 12.3% | 35.4% |
| 13 | 172 | 13.3% | 48.7% |
| 12 | 167 | 12.9% | 61.6% |
| 11 | 148 | 11.4% | 73.0% |
| 10 | 122 | 9.4% | 82.4% |
| 9 | 91 | 7.0% | 89.4% |
| 8 | 62 | 4.8% | 94.2% |
| 7 | 38 | 2.9% | 97.1% |
| 6 | 21 | 1.6% | 98.8% |
| 5 | 10 | 0.8% | 99.5% |
| 4 | 4 | 0.3% | 99.9% |
| 3 | 1 | 0.08% | 100% |
The average score is 12.24, and the most likely single result is 13. Across six rolls the expected total is about 73.5.
Some consequences worth knowing before you sit down to roll:
- An 18 is genuinely rare. 1.6% per score, which works out to roughly a 9% chance of seeing one anywhere in your six rolls. Most characters never roll one.
- A 16 or better is common enough to expect. 13% per score, giving about a 57% chance of at least one across the six.
- So is a dud. An 8 or lower appears 10.5% of the time per score, so there is roughly a 49% chance of at least one in a set. Half of all rolled characters have a real weakness.
- A 3 is a once-in-a-lifetime event. One in 1,296 per score, about one in 216 characters.
Dropping the lowest die is doing a lot of work here. Straight 3d6 averages 10.5 and produces an 18 once in 216 rolls; the drop lifts the average by nearly two points and makes high scores twenty times more likely.
You can roll a set right now — 4d6kh3 in the notation box rolls four dice and keeps the best three, and it shows every die so you can see what was dropped.
Method 2: the standard array
Take these six numbers and assign them as you like: 15, 14, 13, 12, 10, 8.
That is it. No dice, no negotiation, and every character at the table starts equal. The total is 72, slightly below the 73.5 that rolling averages, and the shape is deliberately unexciting: one strong score, one weak one, nothing extreme in either direction.
The array exists because rolling produces variance between players, not just within a character. One person rolling a 17 and a 16 while another rolls a 9 and a 10 creates a gap that lasts the entire campaign and that no amount of good roleplay evens out. If your group is likely to find that annoying, the array removes the problem entirely.
Method 3: point buy
You get 27 points and spend them raising scores from a base of 8. Costs escalate at the top:
| Score | 8 | 9 | 10 | 11 | 12 | 13 | 14 | 15 |
|---|---|---|---|---|---|---|---|---|
| Cost | 0 | 1 | 2 | 3 | 4 | 5 | 7 | 9 |
You cannot go above 15 before racial bonuses, and you cannot go below 8.
Notice that 13→14 costs two points instead of one, and 14→15 costs two more. That escalation is the whole design: it makes a specialist expensive and a generalist cheap.
Here is a fact worth knowing: the standard array costs exactly 27 points. 15 (9) + 14 (7) + 13 (5) + 12 (4) + 10 (2) + 8 (0) = 27. The array is not an alternative to point buy, it is one particular point-buy spread that the designers picked as a sensible default.
Two common shapes at the extremes:
- 15, 15, 15, 8, 8, 8 — three excellent scores and three bad ones, for 27 exactly. The most specialised build the system allows.
- 13, 13, 13, 12, 12, 12 — 5+5+5+4+4+4 = 27. Competent at everything, exceptional at nothing.
Most players end up somewhere between, usually with a 15 in their main ability and an 8 in whichever one their class ignores.
Which should your table use?
Roll if the campaign is about the story more than the balance. Rolled characters are memorable — the wizard with 8 Constitution and the fighter with an 18 Strength both generate play that a flat array never will. The cost is that one player may simply have a better character than another for twenty sessions.
Use the standard array for a one-shot, or for a group where fairness matters more than flavour. It takes thirty seconds, produces no arguments, and every character is viable.
Use point buy when players care about builds. It gives the same total resources as the array but lets a player decide whether they want to be a specialist or a generalist. It is the default in organised play for exactly this reason.
House rules worth considering
If your group wants to roll but not to suffer:
Roll seven sets, keep six. Costs nothing, removes the worst outlier, and takes a minute.
Reroll the whole set if the total is under 70, or if no score is 14+. A common floor, and it prevents the genuinely unplayable character without flattening the good ones.
Roll one set, everyone uses it. The variance stays — the party might all be strong or all be fragile — but nobody is unluckier than anyone else. This is a surprisingly good compromise and it is underused.
Roll, then let anyone swap to the standard array. Take the dice if you like them, take the array if you don’t. It costs the DM nothing and it removes the one real objection to rolling.
The maths behind the choice
The reason 4d6-drop-lowest and point buy feel so different comes down to the same principle that governs every dice question: more dice means more predictable. Four dice with the worst removed is a fairly tight distribution — 61% of scores land between 12 and 16 — but “fairly tight” across six rolls still leaves plenty of room for one player to end up meaningfully ahead.
Point buy just removes the dice. Whether that is a loss or a relief is genuinely a matter of taste, and it is worth asking the table before session zero rather than after someone rolls a 3.