FWIW, my group was missing half the players tonight, so we decided to make a "secondary" game for the players who routinely
are showing up... and here were their ability scores rolling 4d6k3:
18, 15, 13, 12, 12, 9; avg. 13.17, total 79
18, 12, 11, 11, 11, 11; avg. 12.33, total 74
14, 14, 13, 13, 11, 9; avg. 12.33, total 74 (my rolls)
16, 14, 14, 11, 10, 7; avg. 12, total 72
So, only one had the same average as the standard array, the other three were all higher.
Now, just so people know: 65 points or less is about 13% chance, why 85 points or higher is a bit over 5%. 65 points could be 14, 12, 10, 10, 10, 9. Which adding in racial bumps could be easily decent enough to play.
As for "agreement" with
@Hussar. While I don't consider tossing out a bad set of rolls if that option is agreed upon beforehand as "cheating", I do support (both mathematically and anecdotally) that most players who roll will have better scores. For an entire group (4-5 or more players) to roll scores and have them all be below 72 points is very small; statistically significant small, even.
Anyway, it is "always higher to roll"? No, of course not.
Is it "pretending to be fair"? As long as all the rules are established for how the table wants to do it, yes, it is fair.
Unfortunately, I know and have known MANY players in the past who will cheat/fudge rolls to get better scores. I just ignore it. If it that important to them, I let them have it. It was more common in AD&D where you really needed higher numbers for ANY bonus, but it happened in 3E and even now in 5E.