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Reltzik
2007-03-27, 04:41 PM
A little bit ago I put up my analysis of the pseudo-percentile odds of rolling any given stat-array, which suggested a method of ranking stats. (I'll fix that bug next week and get proper data, I swear.) It was an odds-based system; that is, I was ranking each possible outcome by the odds of getting it.

At the same time, I came up with a different, value-based system... that is, one based on how useful a given set of stats is. Don't worry, this is a lot less of a headache than the last one.

I'm using a couple of basic premises here.

First off, the value of a stat comes, largely, from its modifier. The increase from 12 to 13 is far less valuable than the increase from 11 to 12, or from 13 to 14. However, the increase from 12 to 13 does have SOME value. It helps fulfill prerequesites, provides a bit of buffer against ability damage (if you lose 1 strength from 13, you don't take a modifier hit), and gets you closer to raising your modifier on a level bonus. One of the things that bugs me about WotC point buy is that you start paying the steeper rates when you go up to the odd value, when it's the even value that's worth the most.

Second, I'm going to account for the fact that your highest stat is more significant than your lowest stat. All 11s is worse than 4 11s, one 18, and one 3. The former, you can barely do anything with. The latter would actually make a decent wizard. Just stick that 18 into int and that 3 into charisma. A single high stat more than offsets the single low stat, because you can stick the stat where you want or, even if you're stuck back in the stone ages of the 90s and are assigning as rolled for some reason, you can adapt your character around it. (Unless it's Con. A -4 to your hit die sucks.) WotC attempts to deal with this by making increasing stats increasingly expensive; I'll deal with this by weighting your highest stat more heavilly than your lowest.

So, the system.

To find out how many points a given stat array is worth, perform the following opperations. (Examples given for the Elite and NPC Arrays.)

1: Arrange the stats in ascending order, with the lowest in the first column and the highest in the sixth column.
(Elite Array: 8, 10, 12, 13, 14, 15)
(NPC Array: 8, 9, 10, 11, 12, 13)

2: Convert each stat to its modifier. If the stat is odd, add 0.2 to the modifier.
(Elite Array: -1, 0, 1, 1.2, 2, 2.2)
(NPC Array: -1, -0.8, 0, 0.2, 1, 1.2)

3: Multiply each adjusted modifier by its column number.
(Elite Array: -1, 0, 3, 4.8, 10, 13.2)
(NPC Array: -1, -1.6, 0, 0.8, 5, 7.2)

4: Add up the modifiers. That's the point value of your stat array.
(Elite Array: 32 points)
(NPC Array: 10.4 points)

If you don't like the decimal points, you can multiply the modifier by 5 and then add 1 instead of 0.2 for odd stats. Then the Elite Array is worth 160 and the NPC array is worth 52.

Okay, now someone figure out for me how this is broken.

Erom
2007-03-28, 12:22 PM
I'd add this to the GUI I wrote in the other thread, but it'll have to wait till next week because I'm on the Pacific coast, and the source code is on a hard drive in New England.

I knew I forgot something!

Clementx
2007-03-28, 12:30 PM
"3: Multiply each adjusted modifier by its column number."

While a high stat is worth more than a low, I don't think it is six times what your lowest is. Also, stats of 3 work for video games where your barbarian doesn't need more than 1 skill point and never has to speak. There need to be limits- 8 before racial modifiers is popular and suitable.

Reltzik
2007-03-29, 12:41 AM
Well, one of the features of this system is that it reduces the effect of dump stats. That barbarian's 3 frees up a grand total of -3.8 points, which isn't enough to even raise your highest stat one point if it also increases your modifier. If he has TWO threes (say, INT and CHA), it frees 11.4. That will raise your highest stat ALMOST by 4; say, from 13 to 16. Sure, you can take some 3s. But it doesn't get you much, unless you're DM gave you 60 points or so, in which case you should just expect cheese.

silvadel
2007-03-29, 02:05 AM
Not very good -- I mean the silly 8 10 12 13 14 15 elite array is the same value as 11 11 11 11 13 18. No reason for someone to have a stat lower than 11 and 18 is fairly easy to get... Makes for characters with no weaknesses.

Personally I like to have a low stat to roleplay with anyway and under this system there is no reason to have low stats.

If you are going to go with a system like this... Having it be 2 3 2 2 4 7 might work out better.

Inyssius Tor
2007-03-29, 03:15 AM
I'm not sure what you mean by the last part of your message, but I for one don't see how either of those sets of numbers is inherently better than the other one. I would pick the second one if I were a wizard, sure; with wizards, Int rules all. For a bard, though, I think having a diverse set of abilities would actually be better than a +4, a +1, and four +0's.

Reltzik
2007-03-29, 10:08 AM
Personally I like to have a low stat to roleplay with anyway and under this system there is no reason to have low stats.

You just made the counter-argument for me. Wanting a low stat to roleplay IS a reason to have low stats.

ClericofPhwarrr
2007-03-30, 02:01 AM
One thing that scales on odd levels that you didn't mention is strength; carrying capacity is based off the total strength score, not the modifier. If I have a single spare stat point left over (ie, wouldn't change any modifiers no matter where it was added) when building a physically weak character, it goes to strength; that extra bit of carrying capacity can be quite helpful.

SpiderBrigade
2007-03-30, 10:06 AM
I'd add this to the GUI I wrote in the other thread, but it'll have to wait till next week because I'm on the Pacific coast, and the source code is on a hard drive in New England.

I knew I forgot something!Erom, not to be a burden but are you also planning on updating that GUI with a fix for the "thousand-cube" problem mentioned in the other thread? Because getting an accurate result for a stat array's percentile is still very interesting.

Erom
2007-03-31, 10:43 AM
Erom, not to be a burden but are you also planning on updating that GUI with a fix for the "thousand-cube" problem mentioned in the other thread? Because getting an accurate result for a stat array's percentile is still very interesting.

I believe Reltzik is planning on recalculating those array percentiles. If he does, I'll absolutely add the new data to the GUI. It's actually a really easy thing to change on my end- one I have the new data it'll only take 10 minutes to update.

Erom
2007-04-04, 09:03 AM
Jump over to this (http://www.giantitp.com/forums/showthread.php?t=38306&page=2) thread if you want a little java app that can create characters using this method.

Reltzik
2007-04-04, 12:04 PM
Sweet work on the GUI, Erom. Let's play around with a test barbarian at 200, 250, and 300 points. (This is using the multiply-by-5-to-avoid-fractions system.) The barbarian will balance strength and con as its highest stats, with dex next, a little spare thrown into wisdom, and charisma as a dump stat.

16 12 16 10 12 10 is 200 points under this system, and 32 points under standard point buy.
16 14 16 10 10 8 is 200/30 points as well. I'd actually think of this build as equally potent to the one above, but it'd be a near thing, so I won't crticize std. point buy for those two points.

Further dumping of Charisma is doesn't help much. Dropping it all the way to 3 lets me raise strength and con to 17. It doesn't let me bump a modifier up, though.

18 13 18 10 10 10 is 244/43.
18 14 18 10 10 6 is 250/-. Note that, while you CAN get your dump stat below 8, it doesn't help much. This gets ranked as 42 under std point buy, which is what you'd have if the charisma is 8.


18 17 18 10 12 10 is 299/53 points.
18 18 18 10 12 4 is 300/- points. The GUI ranks it as 54 std point buy, which is what you'd have if the charisma was 8.

Okay, so this tells us that 200 points is somewhat high-powered, and beyond that is insane. So let's try 175.


14 12 16 10 12 10 is 175/28. The only stat you're going to bump up by dumping Cha is Int.

So it looks like 150-200 is good power level for a barbarian. Now let's try wizard. Intelligence is, obviously, going to be our main stat; that's going straight to 18 ASAP. Next will be Dex, for the AC and reflex mods, and then just a touch of Con and Wisdom, for hit points, spot checks, and fort/will saves. We'll dump both Cha AND Str, though focus on Cha, since Str helps with carrying capacity.

10 12 11 18 10 10 is 149/29 points.
8 12 12 18 10 8 is 150/26 points. I think we'll agree that it's the better build for a wizard, despite it being ranked 3 points lower under std. point buy.

6 12 12 18 12 6 is 150/- points.
3 14 12 18 12 3 is 148 points.

All right, now at 175....

9 13 12 18 12 9 is worth 173/31
6 14 12 18 12 6 is worth 175/-

And at 200...
9 14 13 18 13 9 is worth 200/34
7 14 14 18 13 6 is worth 200/-
5 14 14 18 14 4 is worth 197/-

This doesn't strike me as spectacularly broken yet. Now let's try a monk, the class who's name is synonymous with Multiple Attribute Disorder. Strength, Dexterity, Wisdom, and Con will all tie for most important stats. Charisma and Int we'll hold back on, but we can't afford to dump them; we need the skill points and the "don't kill me" aspect. Besides, I think we've established by this point that dumping isn't all that useful.

14 12 13 10 14 10 is 149/25 points.
15 13 14 10 14 10 is 174/29 points.
15 15 15 11 15 10 is 200/37 points.
17 15 15 11 16 10 is 250/44 points.
18 16 16 10 16 10 is 300/50 points.

Hmm. Now this is interesting. Trying to fix a MAD character up is HARDER under this system. Note how the same value under this system gets us a lower value under the standard system; meaning that you could have bought MORE under standard. However, in each case it's only off by a couple of points compared to our wizard and barbarian.

So, next question. Where does this system DIFFER from point buy? My guess is that it's when we've got 2 or 3 high stats and everything else is kept low. Let's try a tank fighter. Maxed strength and Con, dumped Cha and Int, neutral Dex and Wis.

16 10 16 8 10 8 is 150/24
17 10 17 6 10 6 is 146/-
17 11 17 8 10 8 is 165/31
18 10 17 7 10 6 is 172/-
19 10 17 10 10 10 is 200/37
18 10 18 8 10 6 is 200/-

So, yeah. This fighter is REALLY benefitting from the system -- the other 200-pointers were coming in somewhere around 32 points on standard point buy. The problem here is that the jump from 16 to 18 is evaluated just the same as from 12 to 14 if it's the same nth-highest stat. One of the advantages of standard point buy is that the cost of increasing stats is increasingly expensive. I thought I'd done that here, but I guess I didn't.

Stay tuned, I'm playing around with a way of tweaking the algorithm to correct the problem. You should be seeing it sometime tonight.