25 or 32...what's the REAL "standard" point buy?

[dvvega]

To answer your question directly: 25 point buy is the STANDARD point buy in the DMG

pg 169 3.5 DMG
1. Standard Point Buy
All ability scores start at 8. Take 25 points ...

Now onto my little commentary of the day. Please note that this is my opinion entirely and I would prefer no abuse from people disagreeing with me, and would welcome discussion.

Being a veteran of (A)D&D from the little booklets onwards, I have used many character generation systems.

From the original 3d6, through the Unearth Arcana (1st ed version) special human generation, through to 3.X point buy. Throw in some home-grown systems, other systems from magazines etc and you have a big bag of stuff.

The biggest problem with ANY of the systems is actually not the method, but the attitude of the players. Many posts in this thread indicate that 32+ is best because they become heroes. But what is a hero? A bunch of numbers, or the deeds accomplished?

Now my opinion on methods:

Rolling is random indeed and I used the random system for my first 3.X campaign because I was used to random generation from previous editions. I had one player roll 2 18s, 3 16s and a 14 right in front of me and the next player using the same dice got nothing above 14. These players started out on completely different levels of ability.

So if a character died and the player decided on a new character I introduced 32 point buy. The only reason I did this was to keep the power levels equal amongst the party attribute-wise. I have found that 32 point buy is over-powered. Most written products use the standard matrix for their encounters. I've not found one that isn't standard (but I don't use FR or LG so maybe it's just my experience).

Statistically speaking:

I generated 12,000 characters using 4d6 drop lowest (using a statistics package, not by hand). This number was simply to ensure that the distribution was accurate as opposed to rolling 10 characters and getting a skewed result. The dead average ability was 12.3333 (12) thus giving an average stat bonus total of +6.

Using the point buy methods, you must make every stat at least 10 to gain the biggest possible stat bonuses. In 32 point buy if you take 2 18's (+4 each) then you have 4 8s (-1) each for a total of +4. The biggest bonus is generally obtained by dividing the points evenly amongst the stats. So 32 point buy would be 4 points to each stat making them 12 and an extra 2 points for 4 stats making them 14 for a +10 stat bonus total.

So you will generally obtain the following:

25 point buy - +6 total (12 each, 1x 15)
28 point buy - +8 total (12 each, 2x 14)
32 point buy - +10 total (12 each, 4x 14)

The 25 point buy method represents the standard 4d6 drop the lowest, however it removes the randomness aspect and thus ensures that everyone is equal at the start.

28 point buy produces slightly stronger characters but not overly so, compared to the standard, they are a little above average.

32 point buy has a huge deviation from the mean. And extra +4 stat bonus over 28 point buy (+6 over 25). This makes a large difference in encounters.

Although none of the abilities gave more than +2, the fact that 32 point buy gives you had 4 abilities granting that +2 makes a world of difference. The Wizard has more HP, better AC, +2 DC to his spells, and a +2 modifier on touch attacks from Strength. The fighter has better will saves, AC, hit points, and some skill points (dubious advantage), and a monk is just even better with every saving throw getting an additional +2.

Of course people will argue that no-one takes that 4x 14s and 2x 12s. They want an 18 in their primary stat! Well that's plain silly. If you're playing a numbers game (which it seems a lot of people are), taking the 14s and 12s gives you a much better chance at survival early on. With the plethora of ability boosts available, it's a moot point that you start with a 14. You will have a 16 soon enough with a +2 item.

So 25 point buy is the average (and standard) system. If you use 25 point buy I would suggest allowing them to roll instead. Why? Because it gives them a chance at breaking the average mould.

28 point buy is a good balance between average and over-powered. With 28 a wizard can get +2 AC, or +2 on his touch attacks in addition to his +2 DC to spells but not everything like a 32 point Wizard would.

32 point buy is just asking for trouble both in using purchased products, and encounters against the average traps and monsters in the DMG and MM.

 

[Perun]

IMC, players use a 35 point-buy method. I decided to switch from standard rolling method (4d6, drop the lowest) after having a character with the equivalent of 41 points and the one with 25 points. Although the 25-point player didn't complain, I as the DM didn't like it.

The other DM in the party also uses the 35 point-buy, but he also allows the option of a standard roll. The player who usually rolls real well (the 41 point guy above) opted to roll, and rolled really low for his tastes. However, in his defence, he created the character with numbers he got. Unfortunately, he's a 3.5 ranger focusing on archery feats, and he's the only warrior in the group

I would prefer the party to use 32, or even 28 points, as 35 seems a bit over the top, but the party doesn't want to even hear about such a possibility. I originally went for such a high number because the party is not known for being balanced (i.e. they always manage to have at least one of the traditional roles missing), and they are playing the RttToEE campaign.

 

[stephenh]

I generated 12,000 characters using 4d6 drop lowest (using a statistics package, not by hand). This number was simply to ensure that the distribution was accurate as opposed to rolling 10 characters and getting a skewed result. The dead average ability was 12.3333 (12) thus giving an average stat bonus total of +6.

Using the point buy methods, you must make every stat at least 10 to gain the biggest possible stat bonuses. In 32 point buy if you take 2 18's (+4 each) then you have 4 8s (-1) each for a total of +4. The biggest bonus is generally obtained by dividing the points evenly amongst the stats. So 32 point buy would be 4 points to each stat making them 12 and an extra 2 points for 4 stats making them 14 for a +10 stat bonus total.

So you will generally obtain the following:

25 point buy - +6 total (12 each, 1x 15)
28 point buy - +8 total (12 each, 2x 14)
32 point buy - +10 total (12 each, 4x 14)

The 25 point buy method represents the standard 4d6 drop the lowest, however it removes the randomness aspect and thus ensures that everyone is equal at the start.

Unfortunately the 25 point buy, does *not* represent the standard 4d6 drop lowest -- it is actually a bit below average -- see my earlier post. The real 4d6 drop lowest average is equivalent to 29 points ( actually 29.1). This then increases if you exclude very low scores (for example, 6 stats of 3), to something nearer 34.

 

[stephenh]

The real set of averages you obtain using 4d6 drop lowest are: 15.67, 14.18, 12.96, 11.76, 10.41 and 8.51. The 'standard' array which is normally given (i.e. 15, 14, 13, 12, 10, 8 and which adds up to 25 points) comes from rounding off the real averages in an arbitary manner -- as can be seen there is much more rounding down then rounding up. For example the average highest stat is more likely to be 16 then 15. This is why the real points average of 4d6 drop lowest is 29 points rather than 25 points.

Also remember that these averages include the effects of sets of really bad rolls (such as 6 eights, which most people would re-roll), and excluding these will push the averages up higher.

 

[d4]

32 point buy is just asking for trouble both in using purchased products, and encounters against the average traps and monsters in the DMG and MM.

i hear a lot of people saying this, and i have to say it just hasn't been my experience. i've used 32-point buy in every d20 campaign (whether it be D&D or Star Wars d20) that i've run since 3.0 came out. in those four years, i've never run into any balance problems with the PCs.

 

[mmu1]

32 point buy is just asking for trouble both in using purchased products, and encounters against the average traps and monsters in the DMG and MM.

Not true... If it were, every game using 4d6 drop lowest would be an unbalanced nightmare of uber-powerful chaarcters. The actual standard character generation method (p. 7,8 of the PHB) is 4d6 drop lowest, re-roll the set if the sum of the modifiers is 0 or less, or if the highest score rolled is 13 or less - and as it was pointed out a couple of times, this method of generating scores results in an average far higher than 25 - in fact, usually higher even than 32.

 

[pdkoning]

this is correct as far as i've read and calculated.

however, the only true non-munchkin method for ability generation is 3d6 rolled by the referee six times in order of stat

In order of stats is something I really dislike. What if you want to play a bard and have 8 cha? or a wizard with 10 int?

I like both 28 points balanced point boy method and 4d6 -L. Even 3d6 can be fun for non-power players.

In our campaign we use 4d6-L and we assign those numbers as we wish.

 

[dvvega]

StephenH ...

I totally forgot about the reroll your stats if the modifiers sum to 0 or less, or if no ability is above 13.

So I went and added the proviso that the modifiers must sum to 1 or more and that at least one ability must be > 13.

The stat average across 12000 characters (6 abilities each) was 12.5 and the modifier average over 12000 characters was 6.05.

I'm not sure where you are getting your distribution values from on 4d6, I simply generated 12000 characters.

Now according to the central limit theorem the 4 dice throw away the lowest will create a normal distribution with the highest concentration around the 12.25 mark. Take this as 12 or 13 it doesn't matter much for the sake of discussion. As and aside, 3d6 heads towards the 10.5 area.

Just to make sure nothing was going weird, I also generated 50000 characters. The averages came out at 12.5 for abilities and 6.05 for modifiers.

Thus, I am confused as to how you can state that 4d6 results in 29 points. I am using the standard 4d6 method given in the PHB, not discarding any particular rolls, and tossing the whole set of 6 abilitiers if the conditions are not met.

 

[stephenh]

StephenH ...

Thus, I am confused as to how you can state that 4d6 results in 29 points. I am using the standard 4d6 method given in the PHB, not discarding any particular rolls, and tossing the whole set of 6 abilitiers if the conditions are not met.

If you look at my average values of each of the stats from high to low you can see that the average result you get from the four of them is indeed about 12.3 (add them up and divide by 6). What I did was generate 1 million characters randomly using 4d6 drop low. For each of these characters I then worked out what points value they had. Then I took the average (mean) of each of these 1 million points values. This comes to 29.1 points.

It is wrong to simply base calculations on the average roll 4d6-L roll of about 12.3 because in the points system the points are not distributed evenly -- slightly higher values are worth many more points than slightly lower values. You need to actually generate X sets of 6 stats and calculate the points value of each of those X stats, and take the average of that.

 

[dvvega]

StephenH,

now I understand what you did. Interesting method.

The only problem that I can see with your method is that you are not working from a 100% even distribution.

You should average each discrete variable (in this case each ability score) before calculating the points to build - not average the points total. This is because the points total is dependent on the abilities whereas the abilities are each discretely generated from 4d6 discard the lowest.

Taking your 1,000,000 characters, you should average each seperate ability and then calculate the point score total to achieve that average.

Your current method is skewing the results because you do not have a uniform distribution. Since the only way we can obtain a uniform distribution is to generate an infinite number of characters, we must use mathematics to calculate our averages. Doing this produces an average of 25 points for 4d6 discard the lowest AFAIK.

Of course I could be wrong and if anyone can show me the error of my statiscal calculations I'll be most glad to listen.