Probability vs. Point Buy

[Saeviomagy]

Some groups use non-standard point-buy where getting high ability scores does not scale in cost like standard point buy, making maxed favored scores and pathetically low dump stats extremely attractive. I would not hesitate to lower rewards for such PCs to compensate the lower challenge they are facing compared to standard characters.

Why? So that they're not doing better when compared with hypothetical PC's in a campaign which doesn't use this method?? In optimization competitions, this method of stat generation is always superior, however in a real game, it tends not to be. I mean sure the PC's will go better in combat and the like, but (for instance) the wizard with a str of 6 is making some serious choices when it comes to carrying gear: choices that heavily impact aspects of the game which don't necessarily reap XP.

I think that's why 28 pt buy has a minimum of 8: below that people are making a conscious choice to cripple their characters - and if they want to do that, they can voluntarily lower a stat from 8. It's not something you want to do accidentally.

 

[xazil]

As a point that may be of interest my current campaign lets people generate on the 32 point buy or "4d6 drop lowest, total bonuses have to be at least +1". I went for the point buy with everyone else going the roll and my character is about the middle of the range in stats. Albeit of a sample range of only five.

 

[Tatsukun]

Why? So that they're not doing better when compared with hypothetical PC's in a campaign which doesn't use this method?? In optimization competitions, this method of stat generation is always superior, however in a real game, it tends not to be. I mean sure the PC's will go better in combat and the like, but (for instance) the wizard with a str of 6 is making some serious choices when it comes to carrying gear: choices that heavily impact aspects of the game which don't necessarily reap XP.

I think that's why 28 pt buy has a minimum of 8: below that people are making a conscious choice to cripple their characters - and if they want to do that, they can voluntarily lower a stat from 8. It's not something you want to do accidentally.

No, because they are more powerful than the monsters. If you gave the monsters in a game huge stats, you would up their CR, right? Well, in this case, you are giving the PC's huge stats, so the CR's in the book are a little high. Exactly how much I have no idea, but I think the MM gives some directions on how to advance CR due to better stats.

For example, a pretty common build for cleric is Str 10, Wis 16. So in the system you describe, a player could make that Str 8, Wis 18? You can't in point buy, because the difference between a Wis of 16 and 18 is huge compared to the difference between Str 8 and 10.

That's my two yen

-Tatsu

 

[haiiro]

Some groups use non-standard point-buy where getting high ability scores does not scale in cost like standard point buy, making maxed favored scores and pathetically low dump stats extremely attractive.

I've been doing this in my games for a long time, and it works out just fine. In my current campaign, we use this method: start with a base of 6 in each ability score, and distribute 38 points as you see fit on a 1:1 basis (so 14, 18, 10, 8, 14, 10 would be one possible set of stats). Apply racial modifiers normally.

Sure, it won't work with every group -- some will just abuse it -- but it gives you a lot more wiggle room and fine control than weighted point buy, which is what I like about it.

One thing that's key is making every attribute matter, even to those classes that don't "need" a high X. If this is clear before the game begins, I find players tend to think very carefully about dump stats.

Nice avatar, BTW.

 

[stephenh]

I'm not going to get into which method of stat generation is best, but here is a break down of some of the Stat rolling methods I have seen discussed on there boards.

First some quick notes on the method.

1) All scores are calculated after applying the minimum viable character cut. This is defined (as per PHB or DMG - not sure which off the top of my head) as: a) must have at least 1 stat above 13 and b) total stat modifiers must add up to +1 or more.

2) Randomly rolled stats of 8 or less are assigned 0 points.

3) For all methods I generate a million random characters (actually a million and 1) and generate the statistics below based on this sample. This does not represent a complete sample for any of the methods below (i.e. covering every possible combination), but a sample of this size will have very small and well behaved errors, which I have also given where appropriate. The advantage of this method is that it is very simple to do and it is trivial to add in different (and arbitrarily complex) stat generation methods.

4) For each method I calculate:
a) The mean (this is the average normally used) points obtained by that method (and error on the value I give).
b) The median. For those who don't know this is another sort of average, and in my opinion is a fairer representation of the average in this case. It is the value in which exactly half the values are larger than or equal to and half are less than or equal to. This will always be an exact integer in these tests. (I believe it is fairer because the points distributions are non linear).
c) I also give the 25th and 75th percentile of each method. Roughly speaking 1 in four randomly rolled characters will have a points value less than or equal to the 25th percentile and 1 in for will have a points value greater than or equal to the 75th percentile. i.e. in the "average" group of 4 characters, 1 will have a points value <= 25th percentile, 2 will have characters with points values between the 25th and 75th percentile, and one will have a character with a points value >=the 75th percentile.
d) Finally I give the average (mean) set of stats rolled using each of the given methods, in order from large to small.

I can add other methods if anyone wants them.

3d6
roll 3d6 and take the result.
mean   = 24.685 +/- 0.005
median = 24
25th percentile 21
75th percentile 28
mean "stat array"
 15.482 (+/- 0.001)
 13.668 (+/- 0.001)
 12.292 (+/- 0.001)
 11.007 (+/- 0.001)
  9.589 (+/- 0.001)
  7.668 (+/- 0.002)

4d6 drop low
roll 4d6 and drop the lowest
mean   = 30.927 +/- 0.008
median = 30
25th percentile 25
75th percentile 36
mean "stat array"
 15.949 (+/- 0.001)
 14.455 (+/- 0.001)
 13.228 (+/- 0.001)
 12.022 (+/- 0.001)
 10.659 (+/- 0.002)
  8.720 (+/- 0.002)

4d6 drop low -- best of 7 rolls
roll 4d6 and drop the lowest -- do 7 times and keep the best 6
mean   = 34.020 +/- 0.008
median = 33
25th percentile 28
75th percentile 39
mean "stat array"
 16.020 (+/- 0.001)
 14.624 (+/- 0.001)
 13.516 (+/- 0.001)
 12.480 (+/- 0.001)
 11.403 (+/- 0.001)
 10.140 (+/- 0.002)

4d6 drop low -- reroll all 1s
roll 4d6 and drop the lowest, but also reroll all 1s rolled
mean   = 37.724 +/- 0.008
median = 37
25th percentile 32
75th percentile 43
mean "stat array"
 16.310 (+/- 0.001)
 15.077 (+/- 0.001)
 14.061 (+/- 0.001)
 13.064 (+/- 0.001)
 11.937 (+/- 0.001)
 10.341 (+/- 0.002)

5d6 drop 2 lowest
roll 5d6 and drop the 2 lowest
mean   = 38.543 +/- 0.009
median = 38
25th percentile 32
75th percentile 44
mean "stat array"
 16.486 (+/- 0.001)
 15.251 (+/- 0.001)
 14.185 (+/- 0.001)
 13.102 (+/- 0.001)
 11.836 (+/- 0.002)
  9.963 (+/- 0.002)

 

[stephenh]

Has anyone worked out the probabilities for the following sort of system?

Everyone starts with all six stats of, say, 13. Then the player manipulates the scores this way: for every one point added to one score, two points are subtracted from another score. The player gets to add and subtract scores in this way, to his heart's content, with the standard limits of nothing greater than 18 and nothing lower than 3. Like usual, racial modifiers go last.

I'm curious because, on the official point-buy systems, it's not possible to get a score lower than 8 (without racial modifiers). Also, I'm curious because I'd like to know what the starting scores should be to be equivalent to 25-point-buy or 32-point-buy, or whatever.

Dave

You can't really work out the probabilities of this method because there is not a random element to it -- what you end up with is totally at the whim of the person creating the character.

What you can say about it is that you will end up with a character worth about 29-31 points in general. This is because you start with a character worth 30 points (all 13s). For every stat you put up to 14 you loose 1 point overall. Moving stats from 14->15 and 15->16 results in no overall points change. moving a stat from 16->17 gains a point overall which just cancels out the one you lost going from 13->14. Finally moving a stat from 17->18 results in a net gain of a point overall.

The above assumes that you gain negative points whan moving stats below 8.

 

[Quasqueton]

Should PC's generated through a higher point-buy count earn less experience toward standard monsters?

An interesting note about previous editions of D&D: it used to be that characters with high stats (in their prime requisite) got a bonus to their earned experience---up to 15% more xp for having a high stat. Ain't that funny?

Quasqueton

 

[Iuz]

An interesting note about previous editions of D&D: it used to be that characters with high stats (in their prime requisite) got a bonus to their earned experience---up to 15% more xp for having a high stat. Ain't that funny?

Quasqueton

One of the rules I was glad to see gone from the RAR in 3E. (not that I ever used it)

 

[Elder-Basilisk]

Stephenh, that's very interesting. When I first started running 3e, I came from a group that allowed players to roll 4d6-lowest three times and take the set of rolls they liked the most. It was a method I was fairly familiar with from 2e. In an effort to make point buy come up with similar characters, I chose 36 point buy. That's the value you come up with for the 75th percentile of 4d6-L. Apparently I was about right....

 

[Gizzard]

OK, I decided to run the figures myself for 4d6-L. It looks like you get a nice curve of some sort; it's pretty widely spread with the peak at 30. This is good, it matches stephenh's numbers. Here is the sweet spot of the probability curve:

points probability
20 1.7%
21 1.9%
22 2.2%
23 2.5%
24 2.7%
25 2.9%
26 3.1%
27 3.2%
28 3.3%
29 3.3%
30 3.3%
31 3.3%
32 3.2%
33 3.0%
34 2.8%
35 2.7%
36 2.5%
37 2.3%
38 2.1%
39 1.8%

This sweet spot covers about 54% of the possible results, which puts it again in line with the existing 25/75 percentile numbers. The sweet spot and the non-point buy results cover 84% of the spectrum; the remaining 16% is pretty spread out. The lowest point buy I saw in 1,000,000 character generations was 1 (pity da foo) and the highest was 83 (wow).

One interesting thing which hasn't yet been mentioned is that almost 30% of the overall results don't map to a valid point buy as they contain a stat below 8. So keep this in mind; if you run a six player campaign, you'll likely see two players with a pretty bad stat.