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D&D 5E Different Methods for Rolling Ability Scores (8-15 range)

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Mine is a bit different than your requirements, but I really like it:

* 2d6+4 6 times. You can either take them in order and gain a minor perk, or you can reorder them. If you do not like the result, you can point buy.

Range is 6 to 16. You get one 6 and one 16 in every 6 characters (on average). Average scores are 11, but you usually get one score of 14 or above. However, you also tend to get one score of 9 or below.

PCs created under it often take the point buy option, but those that don't often have a bad stat and a couple good ones.


The High Aldwin
Nice analysis, thanks!
Can we get it with rolling dice?
@Jacob Lewis above has the only easy solution I think.
Yep, that was my linear Method #1 and the most obvious, but it is very swingy.

We might want 2 or 3 dice for a bell curve rather than a flat distribution, but the problem is the range: 8-15.
8 is even and 15 odd, which rules out any pair of dice, which will always have an even max and min.
An odd number of dice will have odd min and even max (for dice of even number of sides).
15-8 = 7, which is our range of numbers.
3 dice: Will have a difference between max and min equal to 3(N-1) where N is the number of sides. So for D4 this is 9:
You could do 3d4+3 for a range of 6 to 15. For 3d3 this is 6: So you could do 3d3+6 for a range of 9-15.

I guess you could try 2d3+1d4+5 for 8-15 but it seems... awkward.
Yes, I've already rejected the awkward combinations, which is why I am not thrilled with the idea of d6 and d8, use best, +7...

FWIW, I also thought of 1d4 + 1d5* + 6, but the average is only 11.5. (* d10, in 2 point increments)

Or you could dry 7+3d8, drop highest AND lowest. This will strongly favour the midpoints, and make 8s or 15s very hard to get.
This will get you some very middle of the road stats, lots of 11s and 12s.
Which was the problem with this. When I was using an expanded range I had an option for 3d10, take middle roll, (i.e. drop high/low) for a range of 8-17. I knew I could transfer that to using a d8, but as you noted the middle stats get clustered and the average of 11.5 is also below the average of the other methods...

I think rolling 7+1d8 might be the best! But I worry because it's not a lot of dice. Therefore there is a much bigger chance of having a skew of good or bad luck, and ending up with awesome, or terrible, stats.
Yep, back to Method #1 rejection.

One option to spice things up a bit, I recently came across "Tic tac toe" rolling...
In our case it doesn't really add enough dice to eliminate fantastic/terrible rolls, but it's something...

You make a 3x3 grid. You label the rows Int, Wis, Cha. You label the columns Str, Dex, Con. Then you fill them by rolling your preferred dice (7+1d8 in our case) 9 times IN ORDER. Then you pick your Str, say, from any of the 3 results in the first column. BUT! once it's picked, it's gone. So if you pick the high number in row 2, say, that's gone and cannot be used to select your Wis in this case.
That is an interesting idea and I'll play around with it. Thanks! :)

And again, great analysis of the dilemma, which is I was wanted to explore the idea on the forum in case anyone thinks of something I haven't.
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The High Aldwin
Can we get it with rolling dice?
Ok, like some other options, a bit convoluted, but...

2d4 (take best roll) + 1d5 + 6 (avg. 12.13)


2d5 (take best roll) + 1d4 + 6 (avg. 12.30)

Ranges are correct, average are good, non-linear, uses rolling, no chart.... but hardly "as simple as possible".

Yeah, I know the distributions are off a bit, particularly at the ends as you noted. The derivation isn't enough to really bother me much, and I can always tweak the values on the table to get them closer.

My greater concern is requiring the player to reference a table to find their score from the roll.

9-15 and 6-15 isn't 8-15, though, so I can't use them as they are. :(

We are trying to avoid 17's and 18's as rolls, though. If we wanted them, it could work.
2d4 and d2 + 5! Final deal!


Ok, like some other options, a bit convoluted, but...

2d4 (take best roll) + 1d5 + 6 (avg. 12.13)


2d5 (take best roll) + 1d4 + 6 (avg. 12.30)

Ranges are correct, average are good, non-linear, uses rolling, no chart.... but hardly "as simple as possible".
Go to:
And enter:
output [highest 1 of 2d4] + 1d5 + 6
And hit Calculate.
Also try:
output [highest 1 of 2d5] + 1d4 + 6

This will give an idea of distributions.
So take first option, there is a :
1.25% chance of an 8
5% chance of a 9
11.25% chance of a 10
20% chance of 11 or 12
18.75% chance of a 13
15% chance of a 14
8.75% chance of a 15.

The tool also lets us roll a given number of such rolls. Lets roll 6:
11, 12, 11, 12, 13, 13
12, 14, 12, 14, 12, 15
12, 9, 11, 15, 14, 11
13, 10, 11, 15, 10, 12
13, 13, 9, 14, 12, 14
13, 11, 11, 13, 10, 13

I wouldn't want to have rolled the 1st set... that 2nd set tho...


To satisfy what I am striving for*, probably not... 🤷‍♂️

* 8 - 15 range, average 12-12.5, non-linear, as simple as possible, rolling, no chart.
  • Start with a 12 as your number in each attribute.
  • For each attribute, Roll a d6 and 3d12.
  • Discard all 1s and 2s and 3s.
  • For 4 to 6, Subtract 1 from your number.
  • For 7 to 12, above, add 1 to your number.
The d6 has a 50% chance to be nothing, and a 50% chance to reduce (net reduction: 66%). For each d12, there is a 25% chance of nothing, a 25% chance of reduction, and 50% chance of increase.

Chance of a 15? ~6%
Chance of a 14? ~16%
Chance of a 13? ~23%
Chance of a 12? ~24% (12 or greater? ~69%)
Chance of an 11? ~17%
Chance of a 10? ~10%
Chance of a 9? ~3%
Chance of an 8? ~1%.

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