Remember the "3d6 For Stats In Order" Thread? I'm doing it!

dnd4vr

Adventurer
I think you kind of hit it here: all strategies are viable with arrays the system can very well produce. As you point out, it will be rare to see an ideal array for some strategies (and especially multi-classing, which I am fine with). To know how rare would require some analysis. The tuning offered by race plays a big part.
This is based on an analysis I did for 1E a long time ago using 3d6, but includes ability score requirements, social class (from Unearthed Arcana), and alignment restrictions for that edition. (I was much younger then LOL so the numbers might be off a bit... ;) )

Cleric: 1 in 9.33
Druid: 1 in 1,080
Fighter: 1 in 2.5
Barbarian: 1 in 2,000
Ranger: 1 in 3,222
Cavalier: 1 in 10,900
Paladin: 1 in 8,125,300
Magic-Users: 1 in 5.5
Illusionist: 1 in 911
Thief: 1 in 3
Acrobat: 1 in 864
Assassin: 1 in 265
Bard: 1 in 246,425
Monk: 1 in 8,300

The interesting thing in 5E is that there really aren't any minimums, so every set of ability scores is viable for any class (it might rule out multiclassing, however).

So, my question to you is what is an ideal array? And exactly which method: straight 3d6, card method (yours with 2:5, 3:4, 4:4, 5:5), or something else?
 
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dnd4vr said:
The interesting thing in 5E is that there really aren't any minimums, so every set of ability scores is viable for any class
Well, legal. Stat mins in 1e served two functions: they 'balanced' special sub-classes by making them rare (I know that's not really balancing) and they eliminated particularly bad sets of stats - if you had two or more really low stats you might qualify for no class at all, so your get to roll stats again.


It is too bad because lower scores are not only a challenge, but make the character more "believable" to me.
Since 3e put all stats on the same bonus progression stats in the 12-15 range have been more meaningful.
The reason 3d6 worked okay in earlier editions, such as AD&D, was because ability scores weren't tied into things as invasive as they are since 3E and 5E in particular.
High STR, for instance, was very critical to melee, essentially a major fighter class feature required an 18 STR.
A 16 CON would about double your MU's hps. DEX heavily impacted AC and surprise/initiative.

And, 1e's 4 Methods of generation did not include 3d6, in order, one time.

When you consider the normal maximum modifier is +11, and nearly half of that from ability score, is it surprising that players aren't excited when the best they can maybe expect is +8 or +9 unless they forego feats and invest heavily in ASIs?
OK, yes, 5e BA magnifies the impact of high stats, but 5e also caps stats at 20, in 3e or 4e they could flirt with 30.
 
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dnd4vr

Adventurer
Since 3e put all stats on the same bonus progression stats in the 12-15 range have been more meaningful.
3E+ also made scores of 7-9 more meaningful as well, but in a negative way. Those are the scores most people complain about when doing 3d6, in order, IME.

High STR, for instance, was very critical to melee, essentially a major fighter class feature required an 18 STR.
A 16 CON would about double your MU's hps. DEX heavily impacted AC and surprise/initiative.
High STR was a boon, not a requirement, as it seems to be in 5E. I've played many fighters (and had others as well) with STR below 18. With magic items being prevalent at many tables, items such as Gauntlets of Ogre Power were more meaningful. In out current 5E game, when we found a set, we gave them to the cleric. Why? Because every battler-type already had a STR 19 or 20! We laughed about it.

A CON 16 will still about double your Wizard's HP in 5E and DEX still heavily impacts AC, surprise, and initiative.

The issue is more about how BA and the +11 normal maximum is impacted A LOT more by ability scores than those things were in 1E.

And, 1e's 4 Methods of generation did not include 3d6, in order, one time.
True, but people used it, and I was simply explaining why when it was used then it wasn't as big an issue if you had more average ability scores.

OK, yes, 5e BA magnifies the impact of high stats, but 5e also caps stats at 20, in 3e or 4e they could flirt with 30.
Sure, but I was not referring to 3E or 4E (never played it). I was simply talking about an edition of D&D when 3d6 in order wasn't a death sentence to making a character.
 

clearstream

Explorer
I would appreciate it if you didn't edit my words when you quote me, especially to the degree you did so. It may make others think I said something I did not say. Kindly Please remove that. Thanks!
That's a fair point and I shall be more mindful next time. What I am pondering is...

Don't lump me in with arguing against a weaker party. In fact, I don't think anyone has done that. The issue is simply that mad classes lose a lot more than single stat classes (or maybe I should say dual stat classes, everyone benefits from a good con)
Once losses that all (intentionally) suffer are removed, to focus on relative losses i.e. overshadowing, and by looking at ability arrays that provably can be generated, I feel like the question becomes one of scarcity, and not weakness.

The deck I'm using is quite flat, so in some respects it advantages MAD classes more than it does one-core-ability classes. It's reasonably likely to have a few decent attributes (albeit all lower than what might be called decent with 4d6k3 or points-buy) and if those land in the right places the monk is as well supported as any other class. It's no worse for them than other chargen options.
 

clearstream

Explorer
This is based on an analysis I did for 1E a long time ago using 3d6, but includes ability score requirements, social class (from Unearthed Arcana), and alignment restrictions for that edition. (I was much younger then LOL so the numbers might be off a bit... ;) )

Cleric: 1 in 9.33
Druid: 1 in 1,080
Fighter: 1 in 2.5
Barbarian: 1 in 2,000
Ranger: 1 in 3,222
Cavalier: 1 in 10,900
Paladin: 1 in 8,125,300
Magic-Users: 1 in 5.5
Illusionist: 1 in 911
Thief: 1 in 3
Acrobat: 1 in 864
Assassin: 1 in 265
Bard: 1 in 246,425
Monk: 1 in 8,300

The interesting thing in 5E is that there really aren't any minimums, so every set of ability scores is viable for any class (it might rule out multiclassing, however).

So, my question to you is what is an ideal array? And exactly which method: straight 3d6, card method (yours with 2:5, 3:4, 4:4, 5:5), or something else?
Indeed, that is the relevant analysis. Or an alternative would be the probability for each array. And your question is of course the apposite one: we'd need to appoint each class an ideal array.

The deck I favour produces lower, flatter arrays, so my guess is that it favours classes like paladins more than 4d6k3, and is either equal or improved over points buy. Where it is less favourable is if a player comes with a burning need to play a paladin and only a paladin: if that is a group's intent then points-buy would be the better option.
 

dnd4vr

Adventurer
Indeed, that is the relevant analysis. Or an alternative would be the probability for each array. And your question is of course the apposite one: we'd need to appoint each class an ideal array.

The deck I favour produces lower, flatter arrays, so my guess is that it favours classes like paladins more than 4d6k3, and is either equal or improved over points buy. Where it is less favourable is if a player comes with a burning need to play a paladin and only a paladin: if that is a group's intent then points-buy would be the better option.
Well, it gets a bit tricky because the cards method is without replacement. However, as I pointed out, since there are no prerequisites for ability scores for classes, any method works just as well as another.

Your card method doesn't favor Paladins over using 4d6k3 or point-buy. Point-buy, for instance, will generate a total of 69 to 75 points for ability scores as where the cards method is 63. Being so much lower means you are less likely to have "viable" (whatever than means for you, me, whoever?) ability scores to play a Paladin, for instance.

Since 4d6k3 is arrange to taste, as is point-buy, you can put your best numbers where you want to make your character good where they "need" to be. The chart shows the probabiliy distribution for both 4d6k3 and cards. You can see the peaks for 4d6k3 is higher, as expected.

1568582532905.png


Ultimately, the truth is like you say, if someone has a burning desire to play a particular class, the other methods will guarantee it. With the cards method, you play the hand you were dealt. ;)
 

Blue

Orcus on a bad hair day
I think players with high-system mastery and an interest in optimising will not choose a sword bard unless they have the stats for it. Thus the situation one may fear in theory-crafting doesn't arise at the table.
Is this like saying that certain classes will become trap options unless the dice are very generous, and those with system mastery will avoid them.
 

iserith

Magic Wordsmith
With the cards method, you play the hand you were dealt. ;)
Hmm, that line alone as reinforcement for trying to make the best character you can and play as effectively as you can given the draw is almost enough for me to use the draw method sometime.
 

FrogReaver

Adventurer
That's a fair point and I shall be more mindful next time. What I am pondering is...


Once losses that all (intentionally) suffer are removed, to focus on relative losses i.e. overshadowing, and by looking at ability arrays that provably can be generated, I feel like the question becomes one of scarcity, and not weakness.

The deck I'm using is quite flat, so in some respects it advantages MAD classes more than it does one-core-ability classes. It's reasonably likely to have a few decent attributes (albeit all lower than what might be called decent with 4d6k3 or points-buy) and if those land in the right places the monk is as well supported as any other class. It's no worse for them than other chargen options.
Apparently we are talking about two different things. I'm talking about 3d6 roll in order.
 

clearstream

Explorer
Your card method doesn't favor Paladins over using 4d6k3 or point-buy. Point-buy, for instance, will generate a total of 69 to 75 points for ability scores as where the cards method is 63. Being so much lower means you are less likely to have "viable" (whatever than means for you, me, whoever?) ability scores to play a Paladin, for instance.
I think it does, relatively. Under points-buy, the one core ability class can sink their points into that and dump freely elsewhere, and they can choose their race to optimally boost their key stat. A paladin doesn't have that option. Under 4d6k3, it's far more likely to have an array with one very high roll, than with two or three. So the one core ability class is more frequently favoured.

So my thoughts on points-buy is that it creates more relative disadvantage for paladins (cards using my mix creates absolute disadvantage for everyone). 4d6k3 just creates scarcity, which to be fair my cards mix does also. I suppose 4d6k3 could result in an overwhelmingly powerful paladin on the flip side, so there's that.
 

clearstream

Explorer
Is this like saying that certain classes will become trap options unless the dice are very generous, and those with system mastery will avoid them.
I guess one should first note that no option is a trap option, unless it is punished by the DM's game difficulty setting or some other ill like player-player overshadowing. That noted, yes, I think so. My experience with cards-in-order so far is that arrays often fall in ways that pull you in multiple directions, but one does tend to channel down the mechanically stronger pathways. Perhaps because the sub-optimal pathways end up even more horrible than they would under other methods.

That's why I have at every point in this conversation focused squarely on players with high-system mastery. I also would not use points-buy for players with low-system mastery: it's a very unfair system if one doesn't understand the mechanics (or have a guide that does). Noted its strengths for wider play where arrays must be self-validating. Standard array would be better I think (for low system mastery).

4d6k3 arrange at will would be my choice for low-system mastery, because the values are so generally high that the character will be strong relative to official material pretty much regardless. And it is easy to guide without being overbearing - "Oh, you want to be an X? Just put those two high rolls on S and C". The results of allocate in order are trickier "I see you have strong S and I so you might go X or maybe Z is better... I wonder what it looks lie after race..." etc.
 

dnd4vr

Adventurer
I think it does, relatively. Under points-buy, the one core ability class can sink their points into that and dump freely elsewhere, and they can choose their race to optimally boost their key stat. A paladin doesn't have that option. Under 4d6k3, it's far more likely to have an array with one very high roll, than with two or three. So the one core ability class is more frequently favoured.

So my thoughts on points-buy is that it creates more relative disadvantage for paladins (cards using my mix creates absolute disadvantage for everyone). 4d6k3 just creates scarcity, which to be fair my cards mix does also. I suppose 4d6k3 could result in an overwhelmingly powerful paladin on the flip side, so there's that.
I guess it depends on what you mean by favoring a class? As you say, the card method creates disadvantage for everyone, but if it is hard to get good scores for MAD classes, such as a Paladin, with 4d6k3 and point-buy, it is harder with the card method since it creates overall lower scores. Of course, this was by design so is not unexpected.

You are more likely to only have one good score with the card method, and by design if you happen to have two good scores or even three, you must have one or more low ones. The following table represents possible arrays with scores that would favor one, two, or three better scores using the card method.

ThreeTwoOneThree (balanced)Two (balanced)One (balanced)
141515121212
141411121211
131010121111
899101010
89991010
669889

This is because the distribution is even on both the high and low ends for the card method. Although 4d6k3 might have only one or two higher rolls, those relatively high rolls are more likely because the distribution is skewed towards the high end with more of the probability above 12 (over 60%) than below it..

With point-buy you can have two or even three +2 modifiers (three is impossible with the card method). To address point-buy, the table below shows three sets of ability scores depending on how many "high" scores they desire (even three for MAD classes, such as a paladin). None of these arrays have any negative modifiers.

ThreeTwoOne
141515
141512
141112
101012
101012
101010

The point is with 4d6k3 you are more likely to get rolls above the average than below, supporting MAD classes like the paladin. With point-buy, you can always build a set of scores that will support MAD classes. With the card method, because it is an even distribution, you are less likely to get multiple higher scores to support MAD, and if you happen to, you must have lower scores to offset the high ones.

So, although I like the idea of the card method and having overall lower scores, it really doesn't support a higher likelihood of MAD classes--it favors SAD ones.
 

clearstream

Explorer
ThreeTwoOneThree (balanced)Two (balanced)One (balanced)
141515121212
141411121211
131010121111
899101010
89991010
669889
Consider after race -

Three = 16 15 14 etc
Two = 16 16 etc
One = 16 etc

So what I am thinking of is that yes, scarcity, but no, not much overshadowing. Ms Three lost +1 compared with the others. A 15 doesn't payout more than a 14 (except in the most marginal of ways, like CC) until an ASI can be applied, but the efficiency of that ASI will vary depending on the precise array along with other factors (relevant skills, nature of campaign, sub-class choices, etc).

With point-buy you can have two or even three +2 modifiers (three is impossible with the card method). To address point-buy, the table below shows three sets of ability scores depending on how many "high" scores they desire (even three for MAD classes, such as a paladin). None of these arrays have any negative modifiers.

ThreeTwoOne
141515
141512
141112
101012
101012
101010
Consider after race and first ASI -

Three = 16 15 14 etc >> 18 15 14 etc
Two = 17 16 etc >> 17 18 etc
One = 17 etc >> 19 etc

So, although I like the idea of the card method and having overall lower scores, it really doesn't support a higher likelihood of MAD classes--it favors SAD ones.
I think with your helpful analysis I am drawn to saying that cards and points-buy are the same for MAD. It might be that the card mix should be tuned further, but I am not sure how to approach the probability analysis. For instance, are those arrays with 15s that are serving One and Two, more or less probable than the array with two 14s?

I continue to suspect that 4d6k3 will usually put one and two ability classes further ahead of three than the more constrained systems. Compare the likelihood of one super-score to that of three. Sometimes the 4d6k3 MAD character will be fine or, very occasionally, amazing.
 

dnd4vr

Adventurer
I think with your helpful analysis I am drawn to saying that cards and points-buy are the same for MAD. It might be that the card mix should be tuned further, but I am not sure how to approach the probability analysis. For instance, are those arrays with 15s that are serving One and Two, more or less probable than the array with two 14s?
Well, I am glad to help and find it interesting. Point-buy is perfect for MAD classes as you can build a character with three good abilities and no penalties. You can draw a three score decent MAD character with cards, but because it is balanced out, you will have two penalties.

As far as those three arrays, the single 15 (one) is the most likely, two is next, and three with the 14's is least likely. This is because of how the draws have to happen. For a single 15, you only need one score to draw 3 of the 5's. For array "two", the fives are required as well as one of the 4's. But for 2 14's in three, four of the 5's and all of the fours have to be in those scores. So, even with the card system, it is hard to get MAD class scores supported if you want them to be higher scores. If you are happy with a more balanced, but decent scores, such as {12, 12, 12, 10, 9, 8} that is not hard to get and prior to racial adjustments would be perfectly acceptable to me.

I continue to suspect that 4d6k3 will usually put one and two ability classes further ahead of three than the more constrained systems. Compare the likelihood of one super-score to that of three. Sometimes the 4d6k3 MAD character will be fine or, very occasionally, amazing.
Actually, no, 4d6k3 is more likely to have more "better" scores because it has replacement. In the card method, if you get a 15, those 5's are not available later and consequently your scores will be lower. When rolling 4d6k3, if I roll a 15, all the numbers are still available later on for me to roll another.

If you recall a while ago, this was one reason why I asked if your idea was with replacement or not. With replacement in 4d6k3, I could get an array of all 13's, all scores above average of 12.45. With cards, I can't get an array of all 11's, with all scores above the average of 10.5.

FYI, here are the probabilities for the individual scores as there are 816 combinations you can draw for a single result. Later draws are dependent on earlier ones, but ultimately the probabilities remain consistent because if you draw certain numbers first, others are available later, and vice versa.

ScoreNProb.
6100.0123
7400.0490
8700.0858
91340.1642
101540.1887
111540.1887
121340.1642
13700.0858
14400.0490
15100.0123
TOTAL =816
 

clearstream

Explorer
Actually, no, 4d6k3 is more likely to have more "better" scores because it has replacement.
I'm guessing that of six 4d6k3 rolls, the probability that up to two will be say 16+ is better than the probability that three or more will be. That could be wrong: have you analysed it?
 

dnd4vr

Adventurer
I'm guessing that of six 4d6k3 rolls, the probability that up to two will be say 16+ is better than the probability that three or more will be. That could be wrong: have you analysed it?
Oh, sure, of course. You are always less likely to get more higher rolls than fewer, but that is true with point-buy and cards as well. And as I wrote, with point-buy and cards, since there is no replacement, having good scores necessitates having poor ones. With 4d6k3, it is theoretically possible, however unlikely, to have all six scores be 18.

The more important issue you might be wondering about is are you more likely to get a 16 with 4d6k3 or a 13 with cards? We know cards generated lower numbers, so what are the equivalents? They are roughly these:

4d6k3 = Cards
5 = 6
6 = 7
8 = 8
10 = 9
11 = 10
13 = 11
14 = 12
16 = 13
17 = 14
18 = 15
 

Ratskinner

Adventurer
High STR was a boon, not a requirement, as it seems to be in 5E. I've played many fighters (and had others as well) with STR below 18.
This is precisely the opposite of my experience. From what I can tell, the AD&D exceptional strength bonus is a tremendous incentive for fighter-players to "cheat"* on stat rolls. I don't know that I've ever seen a single-class AD&D fighter without exceptional strength...which flies in the face of all this "tough guy" OSR rhetoric that I hear so much...and statistics.

*"cheat" here meaning everything from flat-out: "No, I rolled it straight up, honest!" To lobbying for more bizarre rolling methods to suicide by fighters without exceptional strength.
 

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