Reference
How to Roll Stats: 3d6, 4d6 Drop Lowest, Point Buy and the Standard Array
Every common method for generating ability scores, measured against each other with exact probabilities rather than gut feel. Which is most generous, which is most consistent, and how often rolling actually beats the array.
The comparison
"Beats 72" is the chance a rolled set totals more than the standard array. "Any 18" and "Any 5 or less" are across all six scores.
| Method | Avg score | Avg total | Beats 72 | Any 18 | Any 5 or less |
|---|---|---|---|---|---|
| 3d6 straight | 10.50 | 63.0 | 9.56% | 2.75% | 24.8% |
| 4d6 drop lowest | 12.24 | 73.5 | 56.2% | 9.34% | 6.75% |
| Standard array | 12.00 | 72 | never | never | never |
| Point buy (27) | up to 12.50 | up to 75 | by choice | never | never |
One score: 3d6 against 4d6 drop lowest
Same range, different shape. Dropping a die pushes the whole curve to the right.
- Lowest
- 3
- Highest
- 18
- Average
- 10.50
- Most likely
- 10
- Chance of 18
- 0.463%
3d6 straight.Peak at 10. Average 10.50.
- Lowest
- 3
- Highest
- 18
- Average
- 12.24
- Most likely
- 13
- Chance of 18
- 1.62%
4d6 drop lowest.Peak at 13. Average 12.24.
3d6 is symmetric: 10 and 11 tie for the most common score at 12.5% each, and 3 is exactly as rare as 18. 4d6 drop lowest is not symmetric. Discarding the worst die cannot raise the ceiling, so 18 is still the top, but it lifts everything below it, and the result is a curve that peaks at 13 and falls away steeply to the left. The average moves from 10.50 to 12.24.
Six scores: the whole character
Add six independent scores and the curves narrow. This is the distribution of the total, which is the fairest single number for comparing a rolled character against a built one.
- Lowest
- 18
- Highest
- 108
- Average
- 63.00
- Most likely
- 63
- Beats 72
- 9.56%
3d6, six scores.Average 63.0.
- Lowest
- 18
- Highest
- 108
- Average
- 73.47
- Most likely
- 74
- Beats 72
- 56.2%
4d6 drop lowest, six scores.Average 73.5.
A 3d6 character beats the standard array 9.56% of the time. A 4d6 drop lowest character does it 56.2% of the time. That single figure is why the two methods produce such different tables: one is a lottery most players lose, the other is a lottery most players win, and the array is the price of not playing.
Which to use
Standard array when you want six characters at the same table to be comparable, or when a new player would rather not gamble on a character they will play for a year. Point buy when you want that fairness plus some control over the shape of the character. 4d6 drop lowest when the table enjoys the gamble and can live with the occasional 5. 3d6 straight, usually in order, when the point is to discover the character rather than design one, which is why old school tables prefer it.
If you roll, the stat roller tells you exactly where your array landed on the curve above.
Common questions
What is the difference between 3d6 and 4d6 drop lowest?
4d6 drop lowest averages 12.24 per score against 10.50 for 3d6, a gain of 1.74 per score or about 10 points across six. Both produce scores from 3 to 18, but 4d6 drop lowest skews high: an 18 comes up 1.62% of the time instead of 0.463%.
What is the average of 4d6 drop lowest?
The average of 4d6 drop lowest is 12.24 per ability score, and 73.5 for a full set of six. The most common single score is 13.
Is 4d6 drop lowest better than point buy?
On average, 4d6 drop lowest gives more: 73.5 total against a point buy ceiling of 75 and a standard array of 72. A rolled set beats the standard array 56.2% of the time. But 6.75% of rolled characters carry a score of 5 or lower, which point buy never produces. Rolling is higher on average and far higher in variance.
What is the standard array in 5e?
The standard array is 15, 14, 13, 12, 10 and 8, totalling 72 with a combined modifier of +5. It sits below the 4d6 drop lowest average of 73.5 but above the 3d6 average of 63.0, and it never produces a dump stat below 8.