CapnZapp
Legend
(This post started out as an aside to a reply to the following post but I decided there would be better chances of a discussion in a new thread)

For example, I don't think it is too uncommon for a DM to "reasonably" say "choose either random rolling or the default array; you have to keep what you rolled but if you're super unhappy with the results you can resort to the default array instead."
Are you aware this very likely results in a significantly higher average than if the DM just stated "everybody starts with the default array, full stop."
That is because you simply roll - if you roll great (or at the very least "interesting") you keep that result. Otherwise you plead, whine or bully your DM into allowing you to switch to the default array.
Thus making the default array approximate the mathematical floor of results rather than the average.
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The proper way of giving out this choice would instead be (this is just one example to illustrate my point out of many):
Choose either random rolling or the default array. If you don't like your random rolls, you can instead choose the following array: 15, 13, 12, 10, 8, 6
That is, the "fallback" array is less generous than the array you're initially allowed to choose.
(It's obviously important you tell this to the players before they make a choice. Otherwise they're likely going to try to cajole you into allowing them to keep the default array, or make a re-roll, or whatever)
Also important: This fallback array shouldn't be merely a cosmetic downgrade either, like an array such as 15, 14, 13, 10, 8, 6 where you get to keep the only numbers that matter, the top 2 or arguably top 3. In my example above, I intentionally only retain the top 1 number; everything else is downgraded and your lowest stat is now a mechanically impactful weakness)
Whenever the DM offers you a choice of chargen method, ask yourself - what are my chances of "gaming the DM"I let the players do what they want, but they all chose the array.

For example, I don't think it is too uncommon for a DM to "reasonably" say "choose either random rolling or the default array; you have to keep what you rolled but if you're super unhappy with the results you can resort to the default array instead."
Are you aware this very likely results in a significantly higher average than if the DM just stated "everybody starts with the default array, full stop."
That is because you simply roll - if you roll great (or at the very least "interesting") you keep that result. Otherwise you plead, whine or bully your DM into allowing you to switch to the default array.

Thus making the default array approximate the mathematical floor of results rather than the average.
---
The proper way of giving out this choice would instead be (this is just one example to illustrate my point out of many):
Choose either random rolling or the default array. If you don't like your random rolls, you can instead choose the following array: 15, 13, 12, 10, 8, 6
That is, the "fallback" array is less generous than the array you're initially allowed to choose.
(It's obviously important you tell this to the players before they make a choice. Otherwise they're likely going to try to cajole you into allowing them to keep the default array, or make a re-roll, or whatever)
Also important: This fallback array shouldn't be merely a cosmetic downgrade either, like an array such as 15, 14, 13, 10, 8, 6 where you get to keep the only numbers that matter, the top 2 or arguably top 3. In my example above, I intentionally only retain the top 1 number; everything else is downgraded and your lowest stat is now a mechanically impactful weakness)