D&D 3E/3.5 [3 or 3.5] The average character stats

[Particle_Man]

I got bored and wondered what the average stats are for a 3rd edition D&D character.

In D&D you roll 4 six sided dice per stat, dropping the lowest. Ok, so far so good. That is 1296 possible combinations, so I know enough about spreadsheets to rig one up that adds the 4 dice, subtracts the minimum number, and then orders the results from the lowest (the single 3) to the highest (the 18s). Then I divide that into seven chunks, and check the number at each point after I add a chunk (1/7 of the 1296 results). So I get the following average score: 9, 11, 12, 13, 14 and 15. That is what an average roller of 4d6 drop the lowest would get if they rolled six times (once for str, con, dex, int, wis and chr.

But there is the case of rerolling characters that are too weak. In 3rd ed., a character is too weak if the highest stat is 13 or less.

There is also the case of modifiers. Each stat has a modifier. A 10 or 11 has a modifier of 0, while every two points the stat is above 10 or 11 give a +1 modifier and every two points the stat is below 10 or 11 gives a -1 modifier. So a stat of 3 has a modifier of -4 and a stat of 18 has a modifier of +4. Why is that important? Because of the total of the modifiers of the stats is 0 or less (such as the extreme example of three stats that are 3 and three stats that are 18), the character is too weak and should be rerolled.

So that is two cases where characters should be rerolled, and with some but not total overlap between them (a character with six 10s would have to be rerolled for both of the above reasons for rerolling a character).

And here I am lost. I simply don't have the mathematical knowledge to factor in (or maybe factor out?) the cases where there should be rerolls, and thus calculate what the average score for a character would be, after rerolls are taken into account. Presumably slightly higher.

Any math geeks know how to do this, and what the average character would be?

 

[milo]

I would say that is probably the average since that is the standard array.
You would probably have to group them into arrays of 6 and use the formula for modifiers((stat-10)/2 = mod) and have the program add the six together with an if then statement of
if x(total modifiers) <= 3 then reroll
haven't done any coding for years so forgive me.

 

[milo]

I generally go with the higher powered rolls of reroll 1s in the 4D6 roll. I would be interested if you could get the result of that also. I will watch this thread and hope for results, because I don't think I am as motivated as you.

 

[risner]

I generally go with the higher powered rolls of reroll 1s in the 4D6 roll. I would be interested if you could get the result of that also. I will watch this thread and hope for results, because I don't think I am as motivated as you.

The average of 4d6 reroll 1's is easy.
Rerolled 1 averages 3.5, so (3.5+2+3+4+5+6)/6 = 3.916_

3.916_ * 4 = 15.6_

Or between an 48 and 64 point buy.

 

[Particle_Man]

If you mean roll 4d6, continually rerolling 1s until there are no 1s, and then dropping the lowest die, and if you do not take into account the phb rerolling rules of rerolling characters either a) with no stat higher than 13 or b) with a total modifier of 0 or less (since I don't know how to do that, as outlined in my OP) then a typical character would have:

11 12 13 14 15 16, or a 36 point buy.

From the unfortunate bastard that rolled all 2s on all dice to get 6 6 6 6 6 6 to the lucky sod that got all 18s.

 

[Eitaro]

A bit of code

I was curious about what the average stat score looks like (I remember seeing it in the PHB that the most common scores are between 12 and 13, but that wasn't good enough).
I googled my question and came up with this forum. I haven't posted on this site before, so forgive me if I do something wrong.
Also, I noticed that this thread is about 4 years old.... Hope somebody can make use of this.

% ˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜
function x = DiceTest(sets)
% ------------------------------------------------------------


Tot = 0;
i = 0;
while i < sets
  for k = 1:6
    Roll = ceil(6*rand(1,4));
    % For the "reroll 1's" rule
    for m = 1:4
      while Roll(m) == 1
        Roll(m) = ceil(6*rand);
      end
    end
    Roll = sort(Roll);
    Roll(1) = 0;
    Res(k) = sum(Roll);
    Mod(k) = floor(Res(k)/2-5);
  end
  % If the stats are good enough...
  if sum(Mod) > 0 && max(Res) > 13
    i = i + 1;
    Tot(i) = sum(Res);
    if i == 1
      Stats = [Res];
    else
      Stats = [Stats;Res];
    end
  end
end
Stats;
% Gives you the average that you're looking for :-)
Avg = sum(Tot)/(sets*6)


% ˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜˜
return

I used Octave (It's a free programming/math program). Running this for 10000 characters gave me the average of 13.475.
Hope that answers your question to your satisfaction!

 

[delericho]

There was a long and detailed thread about this a few years ago. IIRC, using the standard rolling method (that is, 4d6-drop lowest and standard rerolls), an average character worked out to about 30.5 points. Of course, you lose a bit of effectiveness due to not being able to fully optimise (by dumping a stat, assigning only even-numbered stats, or similar).

I have no idea what the average set of stats should be. Indeed, I don't know if such a thing is even particularly meaningful with so many dice being rolled.

 

[Cyclone_Joker]

The elite array is just about average. That's why it exists.

 

[Eitaro]

Cool, thanks guys! I was surprised to see that such an old thread would get a response so soon.

I've only heard of the point system recently, but it sounds pretty useful. My DM said that in our 3rd level campaign, we could assign 67 stat points with a max of 16 for any stat. If I had known more about the point system, I would have talked him into using it.