When I first started playing D&D it was roll 3d6 six times and there you go (that was BECMI D&D).

In 3.5 D&D we did the 4d6 dl (drop lowest) six times and assign as desired.

But I've found that 5E's bounded accuracy design, and the several ability score increases that will happen, causes the 4d6 dl to result in powerful PCs from the start. I believe it is this rolling method that is mostly responsible for the "hard to challenge the PCs" type of comments I've read. Using point buy actually makes the system work better in my experience. That's why I give standard array or the 27-point buy as options.

For those that really want to roll, I offer a slight variation of the 4d6 dl method - one of those 4d6 dice is an automatic 3, essentially making it a 3d6 dl + 3. This means that an ability score will not exceed 15 (prior to adjustments), just like those that pick point buy. The average roll with this is 11.46, compared to 3d6's 10.5, standard array's 12, and 4d6 dl's 12.25. The point buy of 15-15-15-8-8-8 has an average of 11.5.

I offer this option to those that want to gamble a bit to see if they can get better than the standard array, knowing they aren't going to be so far above other players that bad feelings arise. However, I would allow a mulligan if the roll total was less than 65. When running a game, my desire is to allow the players to run the types of characters they want to, but at least keep them within a reasonable range of each other, and within the ranges that the game's design assumes.

Interesting.  You [Sheldon_Morris] reduced the rolling to better match the standard array, whereas I boosted the standard array to better match 4d6 D.L.

Quote from gtolsen >>

Interesting.  You [Sheldon_Morris] reduced the rolling to better match the standard array, whereas I boosted the standard array to better match 4d6 D.L.

 Exactly. I find that 5E's design is such that every additional +1 bonus is magnified. Having PCs start with 18s for +4 bonuses, than at level 4 (still a low level) get 20s for +5, makes them considerably better than the opponents they are facing.

Consider this, a 1st level PC with an 18 in STR for a +4 bonus is rolling to hit at +6. The monster stat guide in the DMG suggests that a +6 attack bonus is suitable for a CR 5 monster - that's a creature that is supposed to match up well for a party of 4 level-5 PCs! Not to mention AC and other factors.

That's why I advocate for more moderate PC ability scores (compared to what you are likely to get with 4d6 dl) because I believe the system was really created for these, and why you can only get at most a 15 (pre-adjustments) using point buy. It's my opinion that using 4d6 dl, or any method that generates higher scores, is what is mainly responsible for comments that claim PCs in 5E are "superheroes" - if the scores are toned down a bit at the start, the PCs will be "heroes" instead. Neither approach is right or wrong of course, but it helps to know so that you can match it to the group's play style.

Quote from Sheldon_Morris >>

For those that really want to roll, I offer a slight variation of the 4d6 dl method - one of those 4d6 dice is an automatic 3, essentially making it a 3d6 dl + 3. This means that an ability score will not exceed 15 (prior to adjustments), just like those that pick point buy. The average roll with this is 11.46, compared to 3d6's 10.5, standard array's 12, and 4d6 dl's 12.25. The point buy of 15-15-15-8-8-8 has an average of 11.5.

I offer this option to those that want to gamble a bit to see if they can get better than the standard array, knowing they aren't going to be so far above other players that bad feelings arise. However, I would allow a mulligan if the roll total was less than 65. When running a game, my desire is to allow the players to run the types of characters they want to, but at least keep them within a reasonable range of each other, and within the ranges that the game's design assumes.

 I really like your method of rolling 3d6. drop lowest and add 3.  I am going to try that in our next campaign.  And, given the types of campaigns I tend to run, this would work really well. Great idea, especially with the minimum total of 65.

I like the tic tac toe method too.

Roll 4d6 (keeping the highest 3, dropping the lowest) 9 times and put them in a 3x3 grid in the order you rolled. Then you choose a row and a column.

This way you always have two good stats, where the column and row intersect.

I run 4d6 drop lowest, but with the caveat that you can reroll once if you want to (for the whole array) and you have to keep the second one. I basically added the reroll when one player got 5 stats below 10, and I could see that wasn't going to make things fun.

I really like the idea of 3d6, drop lowest, add 3. I will probably steal that for future campaigns!

I roll 4d6, reroll any 1s (even if you reroll a 1, still reroll it ), and drop the lowest.

Just a pondry, wondering if rolling 4d6 drop lowest could be swapped out for rolling 6d4 and dropping the 2 lowest... maximum stat is 16 then, minimum stat is 4, but it's less likely to happen (needing 6 1's on d4's).

I might try throwing the numbers around and seeing what it can come up with some time...

Quote from ThorukDuckSlayer >>

Just a pondry, wondering if rolling 4d6 drop lowest could be swapped out for rolling 6d4 and dropping the 2 lowest... maximum stat is 16 then, minimum stat is 4, but it's less likely to happen (needing 6 1's on d4's).

I might try throwing the numbers around and seeing what it can come up with some time...

 I've played around with using d4s in the past as well. I think the only thing that prevents me from using it is that I found that players that choose to roll (instead of using point buy) have a bit of an attachment to rolling d6s. Probably just a nostalgia thing.

Quote from RichardHailstone >>

I like the tic tac toe method too.

Roll 4d6 (keeping the highest 3, dropping the lowest) 9 times and put them in a 3x3 grid in the order you rolled. Then you choose a row and a column.

This way you always have two good stats, where the column and row intersect.

 This is a really interesting method! You just have to have players that are fine with the potential for vastly different power levels of characters.

I tried it a few times just for the fun of it and had a character with three 17s, before any adjustments! Then another one with two 13s as their highest stat and a low of 9.

Edit: I did a run of 50 samples and the average ability score total was 83.14, or 13.86 in each stat!

I have my players roll 2d6 + 6, and if they don't end up with at least two stats of 15 or higher they reroll their character. Under this system, the absolute lowest anyone can roll is 15,15,8,8,8,8 which is a perfectly viable character. Most of the time this method results in no characters having a negative modifier which is fine by me, these are heroes after all, but there's also still a chance for some negative modifiers to add some spice to the game.

Quote from DanielMorton >>

I have my players roll 2d6 + 6, and if they don't end up with at least two stats of 15 or higher they reroll their character. Under this system, the absolute lowest anyone can roll is 15,15,8,8,8,8 which is a perfectly viable character. Most of the time this method results in no characters having a negative modifier which is fine by me, these are heroes after all, but there's also still a chance for some negative modifiers to add some spice to the game.

 I wouldn't want to play your minimum character, and I doubt anyone else would in a party that used your method of character stat generation.  But the chances are almost infinitesimally small to get that character, so it is not worth discussing.  The median stat would be 13, if you only allowed them to roll once per stat.  The standard deviation is 2.45 for a 2d6 roll.  I believe this means 63% of all stats will fall into the range of 10.55 - 15.45.  63% of 6 stats is 4 stats.  So there is a high probability of getting a stat above 15.45 AND a stat below 10.55.  So a very common set of stats from this would look like 10, 11, 12, 14, 15, 16 or 10, 11, 13, 13, 15, 16, but could easily be 9, 13, 13, 13, 13, 15.   In the last case, your double 15 rule would cause a reroll.

Roll 2d6 to generate a base number. First, add 6 to the base number to get your first ability score. Second, subtract the base number from 19 to get your second ability score. Repeat this process two more times, until you have 6 ability scores. This will create a balanced, but random result.

 Example: Rolling the base numbers of 2, 6, and 10, would produce ability scores of 8, 17, 12, 13, 16, and 9.

The way I personally run my games is roll 6 d20 and 6 d4. subtract the d4's from the d20 rolls. the player chooses what gets changed. 

My group does 4d6 drop the lowest, re-rolling 1s. We also don't do session zero's.

AS DM I let the first player roll 4d6, and the next player rolls 4d6, and the next player rolls 4d6 and we keep going around until I like the six numbers we have (I throw out anything I don't like, and just have someone reroll it).  Then, with a set of six attributes, I let the players use the same set but each arranges their own.

Quote from BigLizard >>

It depends on the system, I assume you are referring to 5e D&D.

I do 2d6+6 down the line and I allow one stat swap.

 That's a pretty interesting one... rolling for stats, as long as I get at least one 6 in any stat I'm generally happy with what I end up with at the end. Someone would need to have some insanely terrible luck to not get a viable playable character with that simple caveat.

Well, because I am a math geek ... I did the statistical analysis on this and compared it to 4d6 drop low

4d6 drop lowest:  Avg 12.25  Stdev 2.84  (note - assumes a 'normal distribution')

Liz Method (2d6+6):  Avg 13  Stdev 2.45  (note - assumes a 'normal distribution')

4d6 drop lowest:  (uses probabilities from the actual distribution)

chance of getting at least one 18 is 9.34% but the chance of getting exactly one 18 is 8.96%

chance of getting at least one 17 or 18 is 30.07% but the chance of getting exactly one 17 or 18 is 25.77%

chance of getting at least one 16, 17 or 18 is 56.67% but the chance of getting exactly one 16, 17 or 18 is 38.91%

chance of not getting anything below 10 is 31.49%

chance of getting at least one <10 is 68.51% but the chance of getting exactly one <10 is 40.13%

Liz Method (2d6+6):   (uses probabilities from the actual distribution)

chance of getting at least one 18 is 15.55% but the chance of getting exactly one 18 is 14.48%

chance of getting at least one 17 or 18 is 40.67% but the chance of getting exactly one 17 or 18 is 32.36%

chance of getting at least one 16, 17 or 18 is 66.51% but the chance of getting exactly one 16, 17 or 18 is 40.19%

chance of not getting anything below 10 is 59.33%

chance of getting at least one <10 is 40.67% but the chance of getting exactly one <10 is % 32.36%

So the Liz method generates higher attributes (which everyone knows easily) but is surprisingly close and much simpler than 4d6 drop the lowest.  I wish I understood how to import the graph.

Yeah, the simplicity of the Liz method is the big appeal to me. I've had to DM for younger kids and some people who just kind of panic at math and easily confuse themselves. Like... with my own group of adult players of D&D, we have one player who gets anxiety when doing too much math on the spot... something about having other people around watching her makes even simple math difficult. Something that takes no explanation would help a lot.

Point Buy.

All my players are remote and some of them are ... devious and like to try to bend rules or take advantage of a situation.    We originally tried the 4d6 and drop the lowest while they created their characters and lets just say, two characters would have been a blend of Confucius, Einstein, an Olympic gymnast, Conan the Barbarian and the most beautiful man/woman in the universe.   Yeah, we quickly moved away from that.

The point buy ensures everyone is playing by the same rules.