Actually, I see the reward for rolling is a bigger SPREAD of stats. Sure you can roll an 18, but you can also roll a 3 or 4 or 5 or 6 or 7. You don't get that with a standard array.

Do you see it as something different than randomness? If so, you could use point buy where you allow for negative-cost scores, like here

So how do you get less than 8 in your link ?

I like rolling dice because

1) it's traditional and its 100x more exciting than spreading out your standard array scores, especially if others besides your DM are watching and cheering you on. Your rolls should always be overseen by at least your DM.
2) there is a better spread of scores meaning more variety in your characters.
3) besides the chance of a low (below 8) score, there is also a chance for a good score.

I am an advocate of only rolling your dice once, then taking that roll, or, if you don't like the roll, you have the option to revert to the standard array.

1) I like the 4d6 six times and add +2 to one score (final score cannot be over 17) and subtract -2 from another score (cannot go below 3).

2) I also like another system (detailed elsewhere), with you rolling 3d6 to begin, and every time you roll less than 16 you add a dice for the next roll. You keep doing this until you roll a 16 or more, then you go back to rolling 3d6 next go. Of course if you are rolling four, five, six, or however many dice, only the highest three dice count. In an extreme circumstance and with very poor dice rolls, you could be rolling as many as 8d6 on the final roll.

The two options above can give scores with a pretty wide spread.

Quote from Chillearth >>

So how do you get less than 8 in your link ?

 On the sidebar there's a 'Custom Rules' option where you can change the lowest and highest buyable scores, the total number of points, and the point price of each score.

I like rolling dice too. I wasn't trying to advocate against it, but rather trying to understand what is it that you like about it. For me, the excitement is a natural result of the randomness. 

I use 2 sets of six rolls 5d6kh3 (keep highest 3) which averages to 14, keep the set of the 2 you like better. Players could also choose a point buy system where any value from 3 to 18 can has an available point cost and anyone can afford six 14s for their attributes. Players also start at level five, so you can see I don't care for lower powered play.

Rolling shenanigans have been around for decades and unless you're a mathematician looking to get some sort of precision through statistical analysis, the best you can go with is your gut or a consensus which has been 4d6 drop lowest since I was about 13 (currently 47).

Generally speaking however the impact of ability scores on the balance of the game is actually quite minimal as a whole and in modern gaming and modern communities, control is preferred over randomness.  The thing about rolling dice is that it comes from an era of gaming (old school D&D) where players didn't "create" characters they "generated" characters, so in my view it's kind of out of place in a gaming environment that is so heavily focused on creation.  It feels like an unnecessary complication for players to contend with that want to have control over how their character is designed.

I found with modern gamers, I don't even bother with a "system" for creating ability scores, their narrative senses are so sharp, that I just let players choose their scores according to their characters depiction and the result is scores that are almost always lower than any point buy,  rolling or fixed system I or the book have come up with for them.  Players these days are very good at self-governance, so I just let them pick whatever they want.  Works fine.

I've had a DM that's let me use 8d20 drop the lowest two.

Quote from DatPenguin77 >>

I've had a DM that's let me use 8d20 drop the lowest two.

 That must have been an interesting stat distribution.  Not planning to do the math but I would guess average of 12-13.

Usually, I let my players roll 4d6 for the first 2, 4d6 drop the lowest for the next 2, and 3d6 for the last 2.

(this will not work on dnd beyond)

Why the difference in number of d6 rolled?

Quote from HeroZero >>

Quote from DatPenguin77 >>

I've had a DM that's let me use 8d20 drop the lowest two.

 That must have been an interesting stat distribution.  Not planning to do the math but I would guess average of 12-13.

 It was interesting, we had some other homebrew modifications to stats as well. But that was because my DM had us fighting monsters/enemies typically deemed too high for our current levels. For example, we were fighting greater demons around level 3.

Quote from OSR4Ever >>

Rolling shenanigans have been around for decades and unless you're a mathematician looking to get some sort of precision through statistical analysis, the best you can go with is your gut or a consensus which has been 4d6 drop lowest since I was about 13 (currently 47).

Generally speaking however the impact of ability scores on the balance of the game is actually quite minimal as a whole and in modern gaming and modern communities, control is preferred over randomness.  The thing about rolling dice is that it comes from an era of gaming (old school D&D) where players didn't "create" characters they "generated" characters, so in my view it's kind of out of place in a gaming environment that is so heavily focused on creation.  It feels like an unnecessary complication for players to contend with that want to have control over how their character is designed.

I found with modern gamers, I don't even bother with a "system" for creating ability scores, their narrative senses are so sharp, that I just let players choose their scores according to their characters depiction and the result is scores that are almost always lower than any point buy,  rolling or fixed system I or the book have come up with for them.  Players these days are very good at self-governance, so I just let them pick whatever they want.  Works fine.

 There were very few games during the 70s-80s that did not have a lot of randomness involved in character creation. Generally speaking nobody complained about it because that was how it was. Champions (HERO System) and GURPS were the notable point buy systems of the time.

I think using random rolls or an array greatly depend on your group. Some lean heavily towards one or the other.

Quote from Wysperra >>

There were very few games during the 70s-80s that did not have a lot of randomness involved in character creation. Generally speaking nobody complained about it because that was how it was. Champions (HERO System) and GURPS were the notable point buy systems of the time.

The earliest point buy system I can identify off hand is Superhero 2044 (from 1977), though it wasn't a particularly good game so it didn't have a lot of impact.

It's worth noting the category of pool-based systems, which used multiple pools (say, attributes, skills, and maybe a few other types) but didn't let you shift points between those pools. Shadowrun (1989) and Vampire (1991) are well known in this category.

It's also worth noting the category of lifepath system (first example: Traveller).

It's technically possible to have fair random systems -- typically this means you gain a fixed number of bonuses in character creation, but it's random what those bonuses are.

I love love love Shadowrun! Although I haven't kept up with it for decades.

Traveller was a standout in the random character generation system. You chose how many years you spent building background skills and rolled on random tables to see what you got. And one of the rolls was DEATH! I don't think any other game gave you death during character generation. Pretty sure Elric came close with summon greater demon at level 1 but at least you got to play your character =) Yes, current Traveller does not do that.

Quote from Xukuri >>

Why the difference in number of d6 rolled?

 I usually want my players PC’s to have pretty drastic ability scores.

My group rolls 4d6 7 times, reroll ones and drop the lowest set, then place them where you like.

Then if someone who had lower rolls really wants an 18 in a stat, they must replace their second highest set with an 8.

My group has always enjoyed rolling, and we all enjoy playing somewhat more optimal characters. We also prefer taking feats to ASIs and this tends to help not make people feel as pressured to skip taking cool feats in order to bump up stats, though we don't discourage anyone if they do wish to take an ASI either. 

Last few campaigns, we’ve each taken ONE shot at 4d6 drop the lowest die 6 times.  If you like the rolls, you use them.  If not, you fall back to standard point buy from the Players Handbook.

I roll 5 d 6 and throw out the lowest an highest rolls, every DM i played with has ok’d me using that method. I think it’s fair, and it’s always been reasonable method achieving the same result.

thats to powerful

I think that sounds less strong than 4d6 toss the lowest.  Let me analyze it and I'll get back to you.

OK, so let's look at 5d6 toss the lowest and the highest ...

Well, this tends to produce the average result, which is 3 x 3.5 = 10.5.  But, it tends to produce that average more than it would produce either extreme result. While 3d6 would simply produce more 10s and 11s than 3s or 18s, you're 5d6 toss the high & low would almost never produce an 18 or a 3. 

To be specific, a 3d6 produces an 18 one time in 216, or a little less than 0.5%; and the same for a 3.

A 4d6 drop the lowest, produces an 18 twenty-four times in 1296 throws, or about 1.85%, while producing a 3 only one time in 1296 or 0.08%.  So you can see how 4d6 toss the lowest skews higher.

The 5d6 option has fewer 18s and fewer 3s so you get a crazy number of 10s and 11s.  I wouldn't want to build a PC with all the attributes between 9-12, or with all the attributes under 13 for that matter.  This might be an interesting way to roll an NPC if rolling an NPC is your thing, but I don't think it would be cool for a PC.