About a year to two ago, I ran a sample size of 4d6 drop lowest compared to array. This was the result. Funny enough, the average was exactly the same as the array. It's almost like they knew what they were doing...
I've seen pretty much the same results. I was bored one day an wrote a program to generate a million characters.
My observation, taking into account that point buy doesn't allow numbers outside of 8-15 if you translate the resulting numbers into point buy cost:
- Take the numbers as rolled, no restrictions, no reroll. Average 21 points
- Only allow numbers between 8 and 15. Average: 27 points
- Throw out numbers below 8, allow 18. Average: 34 points.
- Throw out numbers below 8, roll until you get at least 1 18. Average 40 points.
So if you really follow 4d6, drop lowest you are worse off (on average). Many groups of course use the Creative Hero Enhanced Attribute Templates (C.H.E.A.T.) system (frequently with the permission of their DM) when rolling stats for characters. If you roll enough characters you will eventually have a good one, something I took advantage of in the old D&D video games like Baldur's Gate.
But the biggest problem I have with rolling dice for stats (unless you C.H.E.A.T.) is the wide disparity of results. In my test I grouped the results of 6 to represent a typical gaming group and compared the difference in point buy cost for each character. What I found was that in the majority of "tables" there was a significant difference in ability scores. Using point buy as a yard stick, most tables had a difference of 30 points or more. That's a huge variation, if not in outright combat ability, in options for what people can play and how much they can contribute to out of combat skills.
For my example, Player 1 rolled 8, 6, 12, 16, 17, 13, which would have cost 35 points with a point buy.
Player 2 on the other hand rolled 6, 8, 9, 16, 10, 9, which would have cost 14 points with a point buy.
I look at those numbers and can say that while the method to generate the numbers may have been technically fair, the result is not fair.
Player 1 can write up a character with any class and cut a shining heroic figure. Player 2 ... not so much. Can you come up with a character that would "work"? Sure. If they do any of the martial classes their strength or dex is decent, but their hit points are going to be significantly lower than Player 1's.
Story Time: the last time I did straight by-the-book roll 4d6 drop lowest, I rolled a decent character, my wife rolled incredibly poorly (a single 14, a 10 and everything else below) while another gal (Sue) at the table rolled a couple of 18s and a low roll of 14.
Neither my wife nor Sue were happy with the characters. Sue felt guilty, my wife had a significantly gimped character with stats that could not represent the heroic character she had envisioned when we were discussing what we wanted in the campaign.
When my wife asked if she could reroll or use the point buy system from the living campaign, the DM just laughed, and said something along the lines of "that's too bad you rolled bad but it's fair because everybody rolled".
Sue eventually committed suicide-by-goblin because she felt guilty. Since you can't be forced to testify against your spouse, I can neither confirm nor deny that she secretly adjusted her numbers to something reasonable.