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I mean, realistically, it sounds like you're just asking for the older version of D&D stat rolling - roll 3d6. It results in a lower array, more centered around 12, but still has the chance for both low and high stats at much more rare odds.
3d6 probability:
vs standard 4d6dl:
It does indeed seem pretty simple and convenient. The graphs look good, more accurate than those by dice.run. Are they from another generator?
Those graphs are from anydice. I'm not familiar with dice.run, but anydice has been around a long time (15+ years at this point) and is what most people i'm aware of use for comparing dice stats. It can be a little confusing to use, but its pretty good.
...you can accomplish your goal by calculating running totals based on 4d6 drop low as you roll, then re-assigning the final score(s) in your array deterministically to hit the 27-point limit per the optional point-buy rule, but you'll have to extrapolate point costs for high and low rolls not included in the point-buy table to make that work...
3 (-14)
4 (-10)
5 (-7)
6 (-4)
7 (-2)
8 (0)
9 (1)
10 (2)
11 (3)
12 (4)
13 (5)
14 (7)
15 (9)
16 (12)
17 (15)
18 (19)
(personally, i hate point-buy and the algorithmic gameplay it fosters: the base rule - choice of 4d6 drop low or standard array - provides an ideal distribution if players commit to their choice before rolling)
Well, one way to easily replicate point buy's range per stat (if not its distribution limit over all stats) would be 7 + 1d8. You could also do: Start every stat from 12, and if you want to increase one, you can do so by rolling a d4 as a bonus (rerolling on a 4). However, to do that you'll have to decrease a different one by another / the same d4. So you'll still have the same range, but like with point buy there's an element of control and choice to it.
Regarding bigger ranges, one way could be using that same method, only with bigger dice (and possibly other starting points). E.g. you could start from 11 and roll a d8, rerolling an 8 if you're adding it as a bonus. That example would give you values anywhere from 3 to 18, and it's much more swingy than 4d6dl. Of course, if the high variance is an issue, you can experiment with dropping highest or lowest on 2d8.
For example, if you're dropping lowest on bonus rolls and penalty rolls, you'll get characters with high highs and low lows, or if you're doing it the other way around, you'll get characters where each stat is fairly equal, without much variance to speak of.
There isn't much more I can say without knowing how much variance and player choice you want to include.
Do you happen to know of a source that depicts the different probabilities for stats in point buy? I couldn't find one, but I'd love to see which of your suggestions comes closest to that. They're all still comfortably simple, I like that. I assume that it would become quite complicated to take the higher costs of point buy's high end stats into account.
Point buy is completely deterministic, so I'm not sure what you mean by probabilities... Are you referring to statistics, like which stat is a certain value most of the time?
Exactly! (Not a native speaker, blame it on that.)
Hmm, you'd probably have to have access to something like DndBeyond's data to compile such a chart (or use one they compiled). Problem is, there doesn't seem to be anything like that. The only published data visualisations are about races, classes and names.
So I don't think you can just search for it, the only other option I see is gathering that data (if from a smaller sample) yourself, by creating a poll asking for their ability spreads if they used point buy. You could try and advertise it in appropriate communities, and once you feel like your sample size is big enough, you can calculate the percentages.
I wish there was an easier way (and maybe there is and I just didn't look far enough), but from my chair, that's the only option.
Independently from common choices for point distribution, I was thinking more of how often certain stats end up with certain numbers out of all possible combinations how points could be spent.
I don't think I understand what you mean, might be because we're both ESL.
Are you saying you want a histogram or something about how points can be spent, instead of how players do spend them?
That sounds right