I've found my previous analysis
of the various stat generation methods to be lacking in the details that
really matter for actual use and decided it was high time to fix this with a deeper look.
First, some notes on what the details below mean. Average Roll is the average roll generated by the method. Average < 10 is the chance of all 6 stats you roll being on average less than 10. I think this is a pretty good measure of an unplayable character. Your mileage may vary.
The "at least two 13's or 15's" are the chances of you getting at least either two scores of 13 or higher or getting two scores of 15 or higher. I think these are good indicators for getting a good, solid character. Two 13's make for a good Basic D&D character and two 15's make for a good AD&D character.
The "Chance of" items detail the odds of getting at least one stat of a given value or higher. So "Chance of 13" means the chance to roll at least one stat of 13 or higher. So if you want to see what your chances of rolling up a Paladin are, you need a high chance of 17.
I derived the stats for these different methods by writing javascript programs that randomly generated 100,000 characters for each and doing the calculations from what was rolled up. Some of the methods required some decision making and so will be a bit different from actual human usage. For example, AD&D 2e Method 6 has the player add dice to base score of 8. The program just tries to get as many 18's as possible out of that (which is probably what a lot of players would actually do anyway). Also, the AD&D 1e Method 5 from Unearthed Arcana is a bit simplified as it also includes a 7th score for Comeliness but I just removed that and did it for the normal 6 stats.
I did all the random methods that I could find from the various AD&D rulebooks. The ones after that are either derivations from those, ones from different games, or ones that I have thought up myself.
3d6
(AD&D 1e Method 0)
| Average Roll: | 10.5 | Chance of 14: | 65% |
| Average < 10: | 32% | Chance of 15: | 44% |
| At least two 13's: | 49% | Chance of 16: | 25% |
| At least two 15's: | 10% | Chance of 17: | 11% |
| Chance of 13: | 83% | Chance of 18: | 3% |
4d6 - drop lowest roll
(AD&D 1e Method 1)
| Average Roll: | 12.2 | Chance of 14: | 93% |
| Average < 10: | 3% | Chance of 15: | 79% |
| At least two 13's: | 88% | Chance of 16: | 57% |
| At least two 15's: | 42% | Chance of 17: | 30% |
| Chance of 13: | 98% | Chance of 18: | 9% |
3d6 - roll 12 times, take 6 best rolls
(AD&D 1e Method 2)
| Average Roll: | 12.7 | Chance of 14: | 88% |
| Average < 10: | 0% | Chance of 15: | 69% |
| At least two 13's: | 86% | Chance of 16: | 43% |
| At least two 15's: | 31% | Chance of 17: | 20% |
| Chance of 13: | 97% | Chance of 18: | 5% |
3d6, roll six times for each stat and keep best roll
(AD&D 1e Method 3)
| Average Roll: | 14.2 | Chance of 14: | 100% |
| Average < 10: | 0% | Chance of 15: | 97% |
| At least two 13's: | 100% | Chance of 16: | 82% |
| At least two 15's: | 83% | Chance of 17: | 49% |
| Chance of 13: | 100% | Chance of 18: | 15% |
3d6, roll 12 characters and keep the best one
(AD&D 1e Method 4)
| Average Roll: | 12.5 | Chance of 14: | 98% |
| Average < 10: | 0% | Chance of 15: | 87% |
| At least two 13's: | 96% | Chance of 16: | 62% |
| At least two 15's: | 45% | Chance of 17: | 33% |
| Chance of 13: | 100% | Chance of 18: | 10% |
9d6, 8d6, 7d6, 6d6, 5d6, 4d6 - keep best 3 rolls for each stat
(AD&D 1e UA Method 5)
| Average Roll: | 14.3 | Chance of 14: | 100% |
| Average < 10: | 0% | Chance of 15: | 99% |
| At least two 13's: | 100% | Chance of 16: | 96% |
| At least two 15's: | 94% | Chance of 17: | 79% |
| Chance of 13: | 100% | Chance of 18: | 43% |
3d6, roll twice for each stat and keep best roll
(AD&D 2e Method 2)
| Average Roll: | 12.2 | Chance of 14: | 88% |
| Average < 10: | 1% | Chance of 15: | 69% |
| At least two 13's: | 84% | Chance of 16: | 43% |
| At least two 15's: | 29% | Chance of 17: | 20% |
| Chance of 13: | 97% | Chance of 18: | 5% |
Start with 8 in each stat and roll 7 d6's, add to each stat as desired
(AD&D 2e Method 6)
| Average Roll: | 12.1 | Chance of 14: | 100% |
| Average < 10: | 0% | Chance of 15: | 100% |
| At least two 13's: | 99% | Chance of 16: | 100% |
| At least two 15's: | 78% | Chance of 17: | 96% |
| Chance of 13: | 100% | Chance of 18: | 69% |
6d6, 5d6, 4d6, 3d6, 3d6, 3d6 - keep best 3 rolls for each stat
(AD&D 2e SKills & Powers Method 8)
| Average Roll: | 11.9 | Chance of 14: | 94% |
| Average < 10: | 4% | Chance of 15: | 82% |
| At least two 13's: | 87% | Chance of 16: | 62% |
| At least two 15's: | 43% | Chance of 17: | 35% |
| Chance of 13: | 98% | Chance of 18: | 12% |
8d6, 7d6, 6d6, 5d6, 4d6, 3d6 - keep best 3 rolls for each stat
| Average Roll: | 13.5 | Chance of 14: | 100% |
| Average < 10: | 0% | Chance of 15: | 98% |
| At least two 13's: | 99% | Chance of 16: | 89% |
| At least two 15's: | 83% | Chance of 17: | 66% |
| Chance of 13: | 100% | Chance of 18: | 30% |
3d6 - reroll if less than 7
| Average Roll: | 11.0 | Chance of 14: | 69% |
| Average < 10: | 14% | Chance of 15: | 48% |
| At least two 13's: | 55% | Chance of 16: | 27% |
| At least two 15's: | 12% | Chance of 17: | 12% |
| Chance of 13: | 87% | Chance of 18: | 3% |
3d6 - reroll if less than 8
| Average Roll: | 11.4 | Chance of 14: | 72% |
| Average < 10: | 6% | Chance of 15: | 51% |
| At least two 13's: | 60% | Chance of 16: | 29% |
| At least two 15's: | 14% | Chance of 17: | 12% |
| Chance of 13: | 89% | Chance of 18: | 3% |
3d6 - roll 7 times, take 6 best rolls
| Average Roll: | 11.2 | Chance of 14: | 71% |
| Average < 10: | 14% | Chance of 15: | 49% |
| At least two 13's: | 58% | Chance of 16: | 28% |
| At least two 15's: | 13% | Chance of 17: | 12% |
| Chance of 13: | 88% | Chance of 18: | 3% |
3d6 - roll 8 times, take 6 best rolls
| Average Roll: | 11.6 | Chance of 14: | 76% |
| Average < 10: | 6% | Chance of 15: | 54% |
| At least two 13's: | 66% | Chance of 16: | 31% |
| At least two 15's: | 16% | Chance of 17: | 14% |
| Chance of 13: | 91% | Chance of 18: | 4% |
3d6 - roll 9 times, take 6 best rolls
| Average Roll: | 12.0 | Chance of 14: | 79% |
| Average < 10: | 3% | Chance of 15: | 58% |
| At least two 13's: | 72% | Chance of 16: | 35% |
| At least two 15's: | 20% | Chance of 17: | 16% |
| Chance of 13: | 93% | Chance of 18: | 4% |
3d6 - reroll ones
| Average Roll: | 12.0 | Chance of 14: | 86% |
| Average < 10: | 2% | Chance of 15: | 65% |
| At least two 13's: | 80% | Chance of 16: | 39% |
| At least two 15's: | 25% | Chance of 17: | 18% |
| Chance of 13: | 96% | Chance of 18: | 5% |
5d6 - drop 2 lowest rolls
| Average Roll: | 13.4 | Chance of 14: | 99% |
| Average < 10: | 0% | Chance of 15: | 94% |
| At least two 13's: | 98% | Chance of 16: | 80% |
| At least two 15's: | 73% | Chance of 17: | 51% |
| Chance of 13: | 100% | Chance of 18: | 19% |
6d6 - drop 3 lowest rolls
| Average Roll: | 14.3 | Chance of 14: | 100% |
| Average < 10: | 0% | Chance of 15: | 99% |
| At least two 13's: | 100% | Chance of 16: | 92% |
| At least two 15's: | 90% | Chance of 17: | 70% |
| Chance of 13: | 100% | Chance of 18: | 32% |
2d6 + 6
| Average Roll: | 13.0 | Chance of 14: | 96% |
| Average < 10: | 0% | Chance of 15: | 86% |
| At least two 13's: | 95% | Chance of 16: | 67% |
| At least two 15's: | 53% | Chance of 17: | 41% |
| Chance of 13: | 99% | Chance of 18: | 15% |
3d6, roll three times for each stat and keep best roll
| Average Roll: | 13.0 | Chance of 14: | 96% |
| Average < 10: | 0% | Chance of 15: | 83% |
| At least two 13's: | 96% | Chance of 16: | 58% |
| At least two 15's: | 47% | Chance of 17: | 29% |
| Chance of 13: | 100% | Chance of 18: | 8% |
3d6, roll four times for each stat and keep best roll
| Average Roll: | 13.6 | Chance of 14: | 99% |
| Average < 10: | 0% | Chance of 15: | 90% |
| At least two 13's: | 99% | Chance of 16: | 68% |
| At least two 15's: | 63% | Chance of 17: | 36% |
| Chance of 13: | 100% | Chance of 18: | 11% |
3d6, roll 3 characters and keep the best one
| Average Roll: | 11.5 | Chance of 14: | 86% |
| Average < 10: | 3% | Chance of 15: | 66% |
| At least two 13's: | 77% | Chance of 16: | 41% |
| At least two 15's: | 22% | Chance of 17: | 19% |
| Chance of 13: | 97% | Chance of 18: | 5% |
3d6, roll 5 characters and keep the best one
(Adventurer Conqueror King Optional Method)
| Average Roll: | 11.9 | Chance of 14: | 92% |
| Average < 10: | 0% | Chance of 15: | 75% |
| At least two 13's: | 87% | Chance of 16: | 49% |
| At least two 15's: | 30% | Chance of 17: | 24% |
| Chance of 13: | 99% | Chance of 18: | 7% |
3d6, roll 6 characters and keep the best one
| Average Roll: | 12.0 | Chance of 14: | 94% |
| Average < 10: | 0% | Chance of 15: | 78% |
| At least two 13's: | 89% | Chance of 16: | 52% |
| At least two 15's: | 33% | Chance of 17: | 26% |
| Chance of 13: | 99% | Chance of 18: | 7% |
