You can dispense with capping rolls at 15 and allow an occasional 16 or 17. It's a little easier and the average is 12.50 if you do so it's still within your desired overall average.

Sure, it works well, but since the other methods have a compressed range of 8-15, I would just like a way to roll the same range within the criteria I've outlined in the thread.

IMO the only issue with rolling 4d6 drop lowest is when one player gets really lucky and their success due to higher ability scores starts to disrupt other players. It isn't a huge problem IME, but it does seem to surface from time to time.

Personally, I love point-buy as a player and stick with it, another player in my group uses the standard array most of the time, but the other players usually want to roll.

You can dispense with capping rolls at 15 and allow an occasional 16 or 17. It's a little easier and the average is 12.50 if you do so it's still within your desired overall average.

Sure, it works well, but since the other methods have a compressed range of 8-15, I would just like a way to roll the same range within the criteria I've outlined in the thread.

I mean,not really: as noted in the OP, the average is identical, and the difference from abilities on the higher or lower ends of the aprectrum is essentially non-existant.

Sorry, typo, 4d6 like normal, but putting a floor and a ceiling in place. 8 and 15 would become marginally more common, but the average is a wash with the array or point buy.

1d8+7+Pity Method:
Roll 1d8+7 six times and assign your scores. If the total of your rolls is less than 73 or 74 (Depends if you want 12.166 or 12.333 average) you add one point to each attribute from lowest to highest excluding any score already at 15, repeating as necessary until you reach the target number. If your total is higher you subtract from any attribute in any order you want so long as you don't reduce any attribute below 8. Since the average of 1d8+7 is 11.5 it is more likely a player will increase attributes instead of decreasing them. Players who roll above the threshold get the benefit of more control over their attributes. Everyone ends up with the same total number of points so there is little worry about fairness amongst players.

If 73 is the target number then 72.9% of players will be adding to their rolls, 5.5% will hit it exact, and 21.6% will need to subtract. For 74 the numbers are 78.4%, 4.8%, and 16.8%. All numbers rounded to the nearest tenth of a percent.

Roll 2d4 + 7. Which would result in a range of 9-15 so do the following...

In the event a player rolls two ones on the two d4s (normally generating a value of '2'), roll a d20, if the result of the d20 is 1-10, the roll is set to '1', if the result of the d20 is 11-20 the roll is set to '2'.

Examples:

die 1 = 1, die 2 = 3 result of 4
die 1 = 4, die 2 = 4 result of 8
die 1 = 1, die 2 = 1, die 3 = 9 result of 1
die 1 = 1, die 2 = 1, die 3 = 16 result of 2

This will make lower scores of 8 and 9 slightly less likely (I expect your players will be okay with that ) but would eliminate the completely linear result of using a single d8 and get an average value pretty close to your stated goal.

You make six piles You deal 1 face up card to each pile, then numbers are equal to the numbers the ACE can be a 1 or a 10, and the other face cards are 10. The player can choose for you to deal into each pile as many times as they want (until run out of cards) however the ending number is only the 1s digit not the 10s...then you add that number to 8.

so lets say I deal a 2, a 7, and an ace (count as 1) that is 11 so 1+8=9 but if that ace counts as a 10 it is 19, and as such 9+8=17

someone either here or facebook had one that was more like playing solitaire.

Today I was thinking about the standard array (15, 14, 13, 12, 10, 8) and point-buy compared to rolling ability scores using the suggested 4d6, drop lowest because, well, I am a nerd and have free time now.

First, the average for standard array is 12, while the average for point-buy ranges from 11.5 - 12.5, averaging 12.05 roughly if you consider all possible sets. IME, however, point-buy has a slightly higher average overall in use, about 12.2 or so. Finally, rolling 4d6, drop lowest, has an average of 12.24.

I am looking for methods that have an average of roughly 12-12.5, the closer to 12.25 the better, that will randomly generate scores from 8 - 15.

I have some ideas (see spoiler's below) for methods for rolling scores from 8 to 15, inclusive, because our group likes the range offered by the standard array and point-buy, and we find when players do roll 4d6, drop lowest, their scores tend to be too good. But we have some players who love to roll their ability scores, so I am trying to develop a method for them.

Method #1 is a simple d8 + 7, but this produces an average of only 11.5, and given the linear nature is not as appealing.

Method #2 and 3 involve rolling either 2d10 or 1d20, respectively, and consulting the chart. The averages are 12.22 and 12.2, so that is good, but I am not a fan of consulting a chart for such purposes. View attachment 149324

Method 4 involves rolling both 1d6 and 1d8, taking the best roll, and adding 7. This allows for rolling and doesn't require the chart, is non-linear although is skewed, and has a good average of 12.23. But, the idea of rolling dice of two different sizes is somewhat off-putting.

What can you come up with that is (hopefully) simple, generates scores from 8 - 15, and averages about 12.25 or so? Any ideas?

If you look at the spoiler, are any of the methods I have more appealing to you personally?

Finally, if you have a method you've developed for determining ability scores and wish to share it, please do!

for those who love to roll dice:
first we have d6T :
a d6T uses 3,3,3,4,5,6 in lieu of 1,2,3,4,5,6 so it averages 4 and not 3.5

then you roll dice;
standart point buy was 25 points as I recall
so, because average is 4, plus 25 x 4 = 100, target sum of your dice rolled is 100 ( for a 25 point buy )
so roll, roll, roll until you achieve 100 ( min dice rolled if only 6's is 17 ( for a total of 102 ) , while max dice rolled is 34 ( if only 3's ) )

I'm not sure there is anything that can fully meet the requirements. Simplicity means we can't mix in too many different dice types, and you've said you don't want tables if they can be avoided. The narrow range makes it a lot harder to sub out one die for another (e.g. switching to d4 instead of d8), and the need for an average result higher than the arithmetic mean (12.25 rather than 11.5) means you have to be doing some kind of "best X out of Y" to boost the chance of high stats....but those types of tricks really only work when you have a moderately wide range.

The best options I can come up with use fudge dice (that is, d6 with two sides blank, two sides +1, two sides -1), usually labelled "dF" for ease of use. These are either:

11+[highest 4 of 6dF], treating a rolled 7 as 8. (This is very rare, you'd have to roll all six dF as minus, so in practice you'll almost never see it.)
12+[highest 3 of 4dF], and flip a coin; if tails, subtract 1, otherwise keep the score as-is.

Assuming you're willing to use fudge dice, the first is simpler but (very rarely) permits values outside the desired range. It's also slightly stronger than you've asked for, having an average slightly higher than 12.54 (since AnyDice is keeping that very very rare value of 7 and I'm not.)

The second is spot on for your distribution desires (average 12.29, range 8-15), but it requires you to flip a coin in addition to rolling the fudge dice, and that coin is only "negative," never positive, which might not be popular with players.