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

DND_Reborn

Legend
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.
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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!
 

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billd91

Hobbit on Quest (he/him)
You might want to calculate out the distributions for Methods 2 vs 3. They're not the same. There are points where things match up and then places where they don't. For example, 8 is a result only 1% of the time with the 2d10 roll, but 5% of the time with the 1d20. Meanwhile, the 15 comes up 6% of the time with 2d10, but 15% of the time with 1d20. Obviously, you're going to have a hard time making an exact match, but right now the comparison is a bit weird.
 




DND_Reborn

Legend
You might want to calculate out the distributions for Methods 2 vs 3. They're not the same. There are points where things match up and then places where they don't. For example, 8 is a result only 1% of the time with the 2d10 roll, but 5% of the time with the 1d20. Meanwhile, the 15 comes up 6% of the time with 2d10, but 15% of the time with 1d20. Obviously, you're going to have a hard time making an exact match, but right now the comparison is a bit weird.
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.

2d4+7 or 3d4+3 are simple but usually unsatisfying solution.
9-15 and 6-15 isn't 8-15, though, so I can't use them as they are. :(

2d6+6 has a range of 8-18 with an average of 13. A little higher than what you’re aiming for, but a pretty decent method.
We are trying to avoid 17's and 18's as rolls, though. If we wanted them, it could work.
 


DND_Reborn

Legend
2d4+7? That cuts 8 off the bottom end, but 9-15 is pretty close, and it has the 12 average.
I said it was 9-15, so yes it IS pretty close, but to generate scores without cutting off the 8, it doesn't help really. If I wanted 9-15, I would have just done that and not bothered posting the thread.

The complete range I need is 8-15, because that is the range for the other two methods (standard array and point-buy) that we use.
 

Charlaquin

Goblin Queen (She/Her/Hers)
I said it was 9-15, so yes it IS pretty close, but to generate scores without cutting off the 8, it doesn't help really. If I wanted 9-15, I would have just done that and not bothered posting the thread.

The complete range I need is 8-15, because that is the range for the other two methods (standard array and point-buy) that we use.
🤷‍♀️ Good luck then, I guess.
 

tolcreator

Explorer
Can we get it with rolling dice?
@Jacob Lewis above has the only easy solution I think.
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.

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.

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.

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.
 


jgsugden

Legend
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.
 

DND_Reborn

Legend
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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DND_Reborn

Legend
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)

OR

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!
 

tolcreator

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

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

OR

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...
 

jgsugden

Legend
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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