D&D General Normal Distribution Ability Scores

[Xeviat]

Hi everybody!

I've been fiddling with numbers and probability all day for a project, but as ADHD do I had a brain tangent and followed an idea.

I've been using point buy ever since 2001 when one of my players rolled considerably lower stats than everyone else (but good enough to pass under the auto reroll). I ended up letting him reroll, and he proceeded to roll two 18s right in front of me. LOL. My next game just used point buy from the get go, and I haven't gone back to rolling.

But point buy has made me miss something about rolled characters; having unusual high scores. A fighter with a high int (who isn't an arcane trickster), a wizard with a high strength, or really almost anyone having high int that isn't a caster. Sure, there are some subclasses that reward having a different secondary stat, but having an unusual strength is fun.

Also, rolled stats can help you get a feel for "regular folk". But the 3d6 or 4d6 drop the lowest don't generate "normal distribution" curves. The more dice you roll, though, the closer you get to normal distribution. I poked the numbers around and found that 5d4-2 gets you 3-18, average 10.5, with a standard deviation of 2.5.

3d6 is also 10.5 average, but with a standard deviation of 2.96.
3d6 drop lowest is 12.24 average with standard deviation of 2.85
and 7d4 drop 2 lowest, minus 2 is 12.85 average with a deviation of 2.43

While I think about using rolled stats again, I rolled up some random stats in order to see if they produced playable characters. Back in 3E, rerolls were forced if sum of modifiers was 0 or lower, or if highest score is 13 or lower. Here's what I got:

Strength 13 +1
Dexterity 9 -1
Constitution 9 -1
Intelligence 9 -1
Wisdom 13 +1
Charisma 9 -1
Total Mod -2

Strength 13 +1
Dexterity 15 +2
Constitution 12 +1
Intelligence 14 +2
Wisdom 12 +1
Charisma 11 +0
Total Mod +7

Strength 15 +2
Dexterity 14 +2
Constitution 11 0
Intelligence 16 +3
Wisdom 16 +3
Charisma 10 0
Total Mod +8

Strength 13 +1
Dexterity 12 +1
Constitution 8 -1
Intelligence 14 +2
Wisdom 13 +1
Charisma 16 +3
Total Mod +7

Strength 14 +2
Dexterity 13 +1
Constitution 10 0
Intelligence 10 0
Wisdom 17 +3
Charisma 14 +2
Total Mod +8

Now these stats have some interesting spreads.
#2 is an all arounder that could work for a few different builds (especially when background bonuses are factored in)
#3 has high int and wis that won't synergize and a low con, but could make a different wizard with oddly high str and wis
#4 could be interesting, even with that low con; background could be used to bump up con, or the con could encourage a very sneaky/chicken rogue
#5's also good, could be a good cleric even with the average Con.

Would you try out 7d4, drop lowest 2, minus 2?

Alternatively, what if it was 5d4 with 2 rerolls; that makes it feel like a game (any 1s would be obvious rerolls, but rerolling a 2 would be a calculated risk). I don't know how to check the statistics on that unless I forced rerolling the 2 lowest.

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Another idea I had on the side was having players build their characters with point buy as normal, but then have them roll a 1d6. Based on what they roll, in order down the ability scores, I could give them a random boost worth 4 point buy points; Since the point buy costs seem to be a point per modifier of the new stat (13 is 5, 14 is 7, 15 is 9, so 16 is 12, 17 is 15, 18 is 19). If that falls on their 15, it only boosts it to 16, but if it falls on a 13 it would jump to 15, 11 or 12 to 14, 9 or 10 to 13, and 8 to 12.

Also, the 5d4-2 distribution looks like this:
76.36% are between 8 and 13
95.9% are between 6 and 15
99.8% are between 4 and 17

Only 0.10% of stats are a 3 or an 18, so really really rare. Oh, 6d4-4 would get a 2-20 spread with an average of 11... okay I'll put down the dice.

 

[mellored]

If you want usually high (or low) scores to happen more often, then you want bigger deviation. Not a smaller one.

I.e.
Middle 3 of 7d6
10.5 average and deviation of 2.70
 Vs
1d12+4
10.5 average and deviation of 3.45

And here is a good site to see what the rolls are. AnyDice

 

[GMMichael]

Would you try out 7d4, drop lowest 2, minus 2?

If the DM really wanted me to.

Alternatively, what if it was 5d4 with 2 rerolls; that makes it feel like a game (any 1s would be obvious rerolls, but rerolling a 2 would be a calculated risk). I don't know how to check the statistics on that unless I forced rerolling the 2 lowest.

I'd just roll the 5d4 and forfeit my rerolls. I'm not gonna cry if I get low scores - I'm going to think, "welp, I guess this character doesn't fight much." Or, "hey, I have a character who must overcome flaws to succeed. Why does that sound familiar?"

 

[Charlaquin]

With point buy you get a range of 8-15. What about a dice code that reproduces that range? Something like 1d4+2d3+6? That has a mean of 11.5 and a standard deviation of 1.6.

 

[GrimCo]

While point buy removes unusually high scores, it remove low ones also. And while occasional character with very low score can be fun, not everyone loves playing them, nor do they fit in all types of campaigns and playstyles. While my int 5 iliterate barbarian was fun in h&s campaign, it would be hard to pull of in current campaign where more well rounded characters shine.

Also, people used to roll stats first and stats were in good measure deciding factor in what class to chose. Now, people make concepts first, then use PB to generate scores they need for said concept.

In short, no, i wouldn't want any type of roll for stats.

 

[CreamCloud0]

I don’t really see why PB is capped, exponential cost of higher stats exists for a reason, and letting you ‘sell back’ stats to go below your starting 8’s

Doing either would be pretty cost inefficient IMO.

 

[Crimson Longinus]

I don’t really see why PB is capped, exponential cost of higher stats exists for a reason, and letting you ‘sell back’ stats to go below your starting 8’s

Doing either would be pretty cost inefficient IMO.

It would lead to even worse min maxing. A lot of people would feel that they "need" to have the highest possible score in their main stat, and they'd dump all stats not directly relevant to their class as low as possible in order to get it.

The issue with point buy is that all stats cost the same regardless of their usefulness to you. And with floating ASIs your main stats effectively cost even less than the other stats. This should be other way around, your main stats should cost more than the other stats, so that the trade-offs would be more meaningful. Like getting your wizard a two points less int so that you can get two points more of strength or even con sounds like a bad deal, but what if by getting that two point lower int would get you +2 to three or four other stats? At some point the balance is such that it is at least worth considering.

To OP. I like that you're rolling stats in order. That's the only way that randomisation makes any sense, as then you're actually randomising your concept, and not just the power of the concept like it is usually done.

 

[EzekielRaiden]

Another approach along these lines I have considered: using "forge dice"--aka d{-1,-1,0,0,1,1}, abbreviated dF--drifting away from a central point.

As an example, 10+8dF gives a 2-18 spread centered on 10, with 18s being extremely rare. If you instead change it to 10+10dFk8 (keep highest 8), values above 15 and below 9 are rare but still happen (~1 in 15 individual rolls), and values above 16 and below 7 are extremely rare but still possible (~1 in 50 individual rolls).

But you can instead do 12+6dF, which sets a higher floor (lowest stat is 6), making the most common scores decent (11-13) but not particularly powerful. This setup would actually be not too far off from a rolled version of 5e's point buy setup, as 17/18 and 6/7 are very rare (less than 1% chance each, per individual roll).

Or, if you want a spread which more closely resembles what WotC-era players are typically looking for, 14+4dF produces a very tight spread (10-18) and makes most scores good, but not reliably so--this is probably one of the only rolling methods where I'd accept strict rolling, for example, because it's essentially impossible to get a bad character with this setup. Or if you want something sort of midway between, here, then 12+7dFk6 is actually pretty similar to 4d6k3, but both 18s and sub-10 scores are rarer. Essentially, it becomes more "bunched up" around the 11-13 range; you get characters that usually have a +1 or better to most modifiers, but not to all modifiers. (In fact, according to AnyDice, the average lowest score on six sets of 12+7dFk6 is only 7.4, meaning most characters actually do have at least one "bad" score!)

 

[ezo]

@Xaviet are you looking for a normal distribution or do you want it skewed for higher scores like most methods?

 

[EzekielRaiden]

It would lead to even worse min maxing. A lot of people would feel that they "need" to have the highest possible score in their main stat, and they'd dump all stats not directly relevant to their class as low as possible in order to get it.

The issue with point buy is that all stats cost the same regardless of their usefulness to you. And with floating ASIs your main stats effectively cost even less than the other stats. This should be other way around, your main stats should cost more than the other stats, so that the trade-offs would be more meaningful. Like getting your wizard a two points less int so that you can get two points more of strength or even con sounds like a bad deal, but what if by getting that two point lower int would get you +2 to three or four other stats? At some point the balance is such that it is at least worth considering.

I mean, the even bigger underlying issue is that the stats themselves are not equally valuable, but their costs are. Dumping Charisma, unless you're a Cha-based caster, is a no-brainer for the vast majority of characters, because Cha has low defense value, zero offense value (again, barring Cha-casters), and is mostly redundant for utility so long as at least one person has good Cha and one or more associated skills. Likewise, for everyone but Wizard and Artificer, Int is a go-to dump stat. By comparison, nobody wants to dump Constitution or Dexterity ever, even if it's not as useful to them as other stats, and dumping Wisdom is a major major risk because of how dangerous Wis saves can be.

You'll never actually get people choosing stats the way you describe here unless you rework them so that they are at least loosely at parity. They emphatically are not even close to parity in 5e, they weren't in 3e or earlier, and the comparison is meaningless in 4e because of its heavy use of stat-swaps (e.g. Dragon Sorcerers using Str instead of Dex or Int for their AC bonus.)

There's no reason to sacrifice a point or two of Int for two points of Strength and Charisma as a Wizard or Artificer, because the value of one more point of Strength modifier is near zero for them, and Charisma isn't much better. Likewise, sacrificing a couple points of Strength to get an increase to, say, Int and Dex as a GWF Fighter is really not that useful--you just get so much more reliable value from Strength.

But if you try to tinker with those stats, be ready for the torches and pitchforks. D&D fans will defend its idiotic core design choices to the death.

To OP. I like that you're rolling stats in order. That's the only way that randomisation makes any sense, as then you're actually randomising your concept, and not just the power of the concept like it is usually done.

The big problem is, most players today don't want a randomized concept. They want to take a concept that has already inspired them and bring it to life. That's the real reason why random rolling has ceased to be a particularly compelling choice for most gamers today.

Of course, I do in fact agree with you--either you should embrace the randomness or you should move away from it. Naturally that decision is best left to each individual group, but those who do embrace the randomness should be forewarned that doing so may have consequences they don't care for. Not just the "your characters may be weaker," but also "there may be jealousy at the table" and "people may feel pressure to cheat/fudge their dice to get better results." We all know of the stories from ye olden dayse of Fighters who always miraculously showed up with 18/00 Strength.