I thought it would be nice to have a dice mechanic for 5e’s character creation with an output more similar to the point buy system, since the default dice mechanic leads to overall higher stats. This could be a system with the same output range as point buy as well as one that still offers the possibility of rolling very high numbers (16-18) but with a higher probability to roll very low than 4d6 drop lowest.
Do you already know of such a dice mechanic? Or could you maybe provide a source for the probabilities of a stat having a certain number in the point buy system, so as to make it comparable to 4d6 drop lowest? The latter would give a starting point to play around with dice.run in order to create a system as desired.
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.
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...
(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?