LA and Point Buy

[Endarire]

Greetings, all!

Since D&D 3.5 was balanced around a 25 point buy (or 4d6 drop lowest assign as desired), were level adjustments (LA) in general assigned due to the 25 point buy assumption?

[Eloel]

Greetings, all!

Since D&D 3.5 was balanced around a 25 point buy (or 4d6 drop lowest assign as desired), were level adjustments (LA) in general assigned due to the 25 point buy assumption?

4d6 drop lowest is vastly different to 25 point buy on average, so assuming LA is balanced against one means it's not balanced against the other.

[OldTrees1]

LA was assigned independent of Point buy. (WotC's LA assignments are almost all really suspect)

Point buy has little to no impact on what a fair LA would be for a race since ability scores are not capped and ability modifiers scale linearly with ability scores. While there is still some impact, it can generally be ignored.

[Chronos]

4d6 drop lowest is vastly different to 25 point buy on average, so assuming LA is balanced against one means it's not balanced against the other.
If by "vastly different" you mean "approximately equal".

[Red Fel]

LA is generally - and I say generally, because as mentioned, some LAs just make you go what the crap, WotC - based, not upon ability scores, but upon actual abilities, such as Flight, Powerful Build, SLAs, size increases, etc. Frankly, the two seem fairly unrelated - whatever metric you use to establish ability scores, Pounce is awesome; if you use point buy or elite array, Flight is awesome; and so forth.

Out of curiosity, why do you ask?

[bekeleven]

If by "vastly different" you mean "approximately equal".

After running 100k simulations one time I determined that 27-28 point buy was closer to rolling. My methodology was to generate 100k arrays of (6x4d6b3), sort them, then determine the average highest, second highest ... lowest. From what I recall it was 16, 14, 13, 12, 10, 9.

Edit: Found my old script and ran a 50k array simulation. Here's the output:


Top scores: 18, 18, 18, 17, 16, 16
Mid scores: 16, 14, 13, 12, 10, 9
Low scores: 9, 8, 6, 5, 3, 3
Ave scores: 15.6654, 14.18142, 12.96238, 11.76534, 10.42214, 8.5123

Top/Mid/Low refer to the highest, median, and lowest values in each position of the array. For instance, at least one array in the 50k had a 16 as its lowest score, and none had a value above 16 as their lowest score.

The median array is 16/14/13/12/10/9, which corresponds to 28 point buy. But if you round numbers down more aggressively, you end up with 15/14/13/12/10/8, which is the (25PB) "elite array."

Edit 2: Oh right, being on topic. E6 has a sliding point-buy scale based on level adjustment. It assigns point buy to each character based on LA using the following:



LA
Points


+0
32


+1
25


+2
18


+3
10


+4
0

[Eloel]

If by "vastly different" you mean "approximately equal".

Sure, if every point you buy costs 1.


Chance of 18 = 16PB = 1.62%
Chance of 17 = 13PB = 4.17%
Chance of 16 = 10PB = 7.25%
Chance of 15 = 8PB = 10.11%
Chance of 14 = 6PB = 12.35%
Chance of 13 = 5PB = 13.27%
Chance of 12 = 4PB = 12.89%
Chance of 11 = 3PB = 11.42%
Chance of 10 = 2PB = 9.41%
Chance of 9 = 1PB = 7.02%
Chance of 8 = 0PB = 4.78%
Chance of 7 = -1PB = 2.93%
Chance of 6 = -2PB = 1.62%
Chance of 5 = -3PB = 0.77%
Chance of 4 = -4PB = 0.31%
Chance of 3 = -5PB = 0.08%

On average = 4.75

There are 6 of those, for a grand total of 28.5 PB. Even if scores below 8 all scaled 2 by 2, instead of mimicking the ones above it, we'd still have 27.9 PB.

That is vastly different enough that 28 PB is called out separately from 25 PB is by the PHB.

[bekeleven]

A calculated 2nd-order polynomal trendline for point-buy values is .124x^2-1.721x+6.443 (r^2=.992). If you plug my calculated fractional average array into this equation, the array costs 27.98 points.

The exponential trendline has an R^2 of .958, but it underestimates the lower values in favor of overestimating the higher ones (as seen here (http://i.imgur.com/ZjdPNLx.png)). Because the point where it begins overestimating comes near the end of the data (around 14), the entire array ends up undercosted, clocking in at 25.985 points. The polynomial was a better fit for more reasons than one.

[ace rooster]

Wait, 3.5 is supposed to be balanced? :smalltongue:

LA was designed (I use the word loosely) with many questionable assumptions, including that the monk is balanced, ergo anything stronger than a monk is overpowered and needs to be nerfed. Most monster HD are better than monk...

[ZamielVanWeber]

LA was designed around the assumption that all classes are of approximate equality in power. Sometimes the game just goes bananas though, with most templates vastly over costed (hello celestial creature, vampire), some nice and solid (phrenic, half-fey, saint, gravetouched ghoul), and then we have a couple of painfully under costed ones (feral, half-minotaur, white dragonspawn).

Generally template aren't worth the cost.

[Chronos]

Like I said, "approximately equal". I never said that it was "exactly equivalent", or anything like that.

[Eloel]

Like I said, "approximately equal". I never said that it was "exactly equivalent", or anything like that.

25 PB is as approximately equal to 28 PB as 28 PB is to 32 PB. And 32 PB to 36 PB.

By transition of approximate equality, 25 PB is approximately equal to 36 PB.

[OldTrees1]

25 PB is as approximately equal to 28 PB as 28 PB is to 32 PB. And 32 PB to 36 PB.

By transition of approximate equality, 25 PB is approximately equal to 36 PB.

Approximately equal does not have the transitive property. That's what makes it different from equal.

[eggynack]

Approximately equal does not have the transitive property. That's what makes it different from equal.
Yeah, induction doesn't really work if you say "n is kinda like n+1". I mean, what if the 4d6b3 were off of 25 point buy by only, say, .0001 points somehow? In that case, would you say the two are approximately equal? Cause I definitely would, and you can apply the same fallacious induction in that case as you can with a three point difference. Besides, 25 isn't as approximately equal to 28 as 28 is to 32. It's only approximately as approximately equal.

[Necroticplague]

No. LA is mostly arbitrary fiat, without much balance concern thrown into it. Quite a few things are given very high LA for no reason other than it seems to make you not want to play them.

[Urpriest]

MAD is a feature of classes, not races. Since only PCs have point buy, it's conceivable that CRs are balanced with a given point buy in mind, and it's conceivable that classes are, but there's no conceivable way LA could be.

[ZamielVanWeber]

No. LA is mostly arbitrary fiat, without much balance concern thrown into it. Quite a few things are given very high LA for no reason other than it seems to make you not want to play them.
Because of the khaasta thread I was reading through my Fiend Folio and noticed that a lot of the LAs seem reasonably fair (Nerra are the big exception)

[danzibr]

If by "vastly different" you mean "approximately equal".
This made me literally lol.

25 PB is as approximately equal to 28 PB as 28 PB is to 32 PB. And 32 PB to 36 PB.

By transition of approximate equality, 25 PB is approximately equal to 36 PB.

Approximately equal does not have the transitive property. That's what makes it different from equal.
Right, not transitive.

And if it were, why stop at 36 pb? 0 pb is approximately over 9000 pb.

[Necroticplague]

Because of the khaasta thread I was reading through my Fiend Folio and noticed that a lot of the LAs seem reasonably fair (Nerra are the big exception)

+42 STR, +26 DEX, +28 CON, +10 INT, +12 WIS, +24 CHA.
Regeneration 50, At will detect thoughts, dimension door, ethereal jaunt, knock, nondetection, plane shift, and suggestion, SR 39, 5 Slam attack, ability to grant itself any 4 (EX) abilities and change it's size, and improved Rend (in addition to normal rend, does 2 CON damage).
LA:-8.
Yep, LA correlates to strength of creature.
Admittedly, it has 44 freaking RHD......

[danzibr]

+42 STR, +26 DEX, +28 CON, +10 INT, +12 WIS, +24 CHA.
Regeneration 50, At will detect thoughts, dimension door, ethereal jaunt, knock, nondetection, plane shift, and suggestion, SR 39, 5 Slam attack, ability to grant itself any 4 (EX) abilities and change it's size, and improved Rend (in addition to normal rend, does 2 CON damage).
LA:-8.
Yep, LA correlates to strength of creature.
Admittedly, it has 44 freaking RHD......
Wait, what is this? I see no Nerra with this stuff.

[ZamielVanWeber]

+42 STR, +26 DEX, +28 CON, +10 INT, +12 WIS, +24 CHA.
Regeneration 50, At will detect thoughts, dimension door, ethereal jaunt, knock, nondetection, plane shift, and suggestion, SR 39, 5 Slam attack, ability to grant itself any 4 (EX) abilities and change it's size, and improved Rend (in addition to normal rend, does 2 CON damage).
LA:-8.
Yep, LA correlates to strength of creature.
Admittedly, it has 44 freaking RHD......

Its ECL 52; once ECL breaks 20 you are in epic and everything starts flying out the window. And since my point was about Fiend Folio, whereabouts is that? I cannot seem to find it.

[Necroticplague]

Wait, what is this? I see no Nerra with this stuff.

Huh? I have no clue what a nerra was. it's just the first thing I could think of when I thought of 'horribly mis-LA'd creatures'. It's also one of my favorites, the Protean.


Its ECL 52; once ECL breaks 20 you are in epic and everything starts flying out the window. And since my point was about Fiend Folio, whereabouts is that? I cannot seem to find it.
Actually, ECL 36 (that negative wasn't a typo).

Sorry, I thought we were talking about LA in general, so a poor LA example from any book would do. It's from ELH, as the ECL probably gives away.

[danzibr]

Huh? I have no clue what a nerra was. it's just the first thing I could think of when I thought of 'horribly mis-LA'd creatures'. It's also one of my favorites, the Protean.


Actually, ECL 36 (that negative wasn't a typo).

Sorry, I thought we were talking about LA in general, so a poor LA example from any book would do. It's from ELH, as the ECL probably gives away.
Ahh, thanks.

And I was indeed wondering about that negative.

[ZamielVanWeber]

Huh? I have no clue what a nerra was. it's just the first thing I could think of when I thought of 'horribly mis-LA'd creatures'. It's also one of my favorites, the Protean.


Actually, ECL 36 (that negative wasn't a typo).

Sorry, I thought we were talking about LA in general, so a poor LA example from any book would do. It's from ELH, as the ECL probably gives away.

1) Okay, no longer confused,
2) Good lord -8? Then again this is the point where casters have been casting epic spells for some time, so its all out the window anyways. Unless you banned epic spells, then this thing is ridiculous.
3) Most things in the Fiend Folio have low level adjustments, the big exceptions being the ethergaunts which all cast as wizards at ECL-3 amongst other goodies such as SU Dominate Monster 3/day or the ability to automatically notice anyone who gets within 40 feet, and the sillit with a whopping +11 for no adequately explained reason. It is barely strong than the kalareem, which has 4 fewer RHD and an LA of +3 and keeps shard weapon proficiency and reflective spell resistance.

[Endarire]

Thanks, all!

I already was familiar with the existence of E6's point buy/LA table. I also knew that LA in general is whacked. I was curious if point buy was to blame/credit.

[atemu1234]

Like I said, "approximately equal". I never said that it was "exactly equivalent", or anything like that.

Statistically, the difference is in the bell curve, not just the average. It's very different.

[sideswipe]

Wait, 3.5 is supposed to be balanced? :smalltongue:



i got to this point in the thread and after all the hard math i read thid and it made me laugh. good job ace rooster.

[Chronos]

Quoth atemu1234:

Statistically, the difference is in the bell curve, not just the average. It's very different.
But point buy doesn't have a curve, so it's meaningless to compare that way. Point buy also can't get you any score under 8, so if a roll does that, you can't compare that to point buy, either. But to the extent that you can compare the two, they're not more than about 10% different.

[Eloel]

But point buy doesn't have a curve, so it's meaningless to compare that way. Point buy also can't get you any score under 8, so if a roll does that, you can't compare that to point buy, either. But to the extent that you can compare the two, they're not more than about 10% different.

Sure (25 vs 28, but sure), but as I argued before, the same can be said for any consecutive advised point-buy. 28-32 and 32-36 are just as close, and noone goes around calling 28 approximately equal to 32.

[eggynack]

Sure (25 vs 28, but sure), but as I argued before, the same can be said for any consecutive advised point-buy. 28-32 and 32-36 are just as close, and noone goes around calling 28 approximately equal to 32.
Aside from the fact that those numbers are further apart, by numerical distance and percentage alike, I see no issue with calling 28 and 32 point buy close enough for most purposes. And, if I were to see such an issue, it certainly wouldn't be on the basis of your strange transitive argument.

[Flickerdart]

Given that higher ability scores cost more and specialization is very important to the system, 25-28 is much closer together than 28-32. The difference between a 17 and an 18 is not inconsiderable, but the difference between an 11 and a 12 is marginal.

[ComaVision]

After running 100k simulations one time I determined that 27-28 point buy was closer to rolling. My methodology was to generate 100k arrays of (6x4d6b3), sort them, then determine the average highest, second highest ... lowest. From what I recall it was 16, 14, 13, 12, 10, 9.

Edit: Found my old script and ran a 50k array simulation. Here's the output:


Top scores: 18, 18, 18, 17, 16, 16
Mid scores: 16, 14, 13, 12, 10, 9
Low scores: 9, 8, 6, 5, 3, 3
Ave scores: 15.6654, 14.18142, 12.96238, 11.76534, 10.42214, 8.5123

Top/Mid/Low refer to the highest, median, and lowest values in each position of the array. For instance, at least one array in the 50k had a 16 as its lowest score, and none had a value above 16 as their lowest score.

The median array is 16/14/13/12/10/9, which corresponds to 28 point buy. But if you round numbers down more aggressively, you end up with 15/14/13/12/10/8, which is the (25PB) "elite array."

Edit 2: Oh right, being on topic. E6 has a sliding point-buy scale based on level adjustment. It assigns point buy to each character based on LA using the following:



LA
Points


+0
32


+1
25


+2
18


+3
10


+4
0


The averages would be higher than that. You'd need to have it drop arrays that wouldn't be used (ie no stat of 14 or higher).

[bekeleven]

You're right. I hacked in a required max of 14 and re-ran with 50k more sims. (I didn't add the required +1 modifier because that will be a real pain.)

New output:

Top scores: 18, 18, 18, 17, 16, 16
Mid scores: 16, 14, 13, 12, 11, 9
Low scores: 14, 8, 7, 6, 3, 3
Ave scores: 15.88538, 14.32676, 13.08226, 11.8639, 10.48566, 8.549

The median 4th score has moved to 11, although the mean still rounds to 10 (10.49 instead of the previous 10.42). According to my fractional point-buy trendline I presented on page 1, this moves the point-buy value from 27.971 to 29.086. A whole point gained!

I predict adding the positive modifier rule would make a less dramatic impact, because most points were gained on the high end and that rule would impact mostly the lower 5 (since the top is locked at 14 or higher), and because the top guarantees a +2 to start, and also because I don't want to code it.