D&D (2024) First playtest thread! One D&D Character Origins.

[Cadence]

Working out a formula is a bit more time than I want to invest. I mean, for values from 1 to R, each value will occur R times; for values from R+1 to N, each value will occur N+R times, over a total population of values that's N^2. I'm sure it could be calculated from that, but seems much easier just to do analytically.

and @Bill Zebub

Ok, it was either this or do work I was supposed to do...

I think the easiest way to get the variances is to view it as a mixture distribution, where you have an R/N chance of having a discrete uniform from 1 to N (you rolled 1 to R the first time), and a 1-(R/N) chance of having a discrete uniform from (R+1) to N (you rolled a keeper the first time). That the mixture pretends you reroll the dice for keepers (to decide which keeper) doesn't matter since they have an equal probability either way.

So, putting the means and variances of the discrete uniform into the formulas for a mixture distribution I got:

m1=(1+N)/2
v1=(N^2-1)/12
w1=R/N

m2=(R+1+N)/2
v2=((N-R)^2-1)/12
w2=1-(R/N)

mmix=w1m1+w2m2
vmix=w1(v1+m1^2)+w2(v2+m2^2)-mmix^2

Insert algebra.

The mean comes out to be (RN+N+N^2-R^2)/2N, matching what you found.

The variance comes out to be gross, but just what you get by plugging things in. So we can calculate it pretty quickly for any given N and R. (I plopped those formulas right into R, and added taking a square root).

And the standard deviations are not what I was expecting!

It looks like when you get to rerolling the lowest half of the possible values that the variances start going up again, and can be larger than not dropping anything!

This seemed odd, so I calculated them out by getting the distributions in the d4 case, and they do look to be right.

Anyway, here are what I get for the ratios of the standard deviations for dropping 1s (and keeping the reroll) to the standard deviations of just keeping, for d3 to d100.

 

[Quartz]

So 1/20 times my Born on the Street uneducated Rogue can perform a successful brain surgery?

You only roll when the result is in doubt.

 

[Audiomancer]

No, but I also don't think Powerful Build is a particularly flavorful ability. It doesn't have to be all or nothing.

Your opinion is your opinion, and I’m not here to tell you you’re wrong, but…

I recently started playing a Firbolg Artificer with Powerful Build, and I’m absolutely loving it.

I envisioned the character as an inveterate tinkerer/packrat, and after every session I stock up on more mundane adventuring gear—the stuff you usually put down on your sheet at chargen and never look at again.

Pretty much every session, I manage to pull out something that makes the task at hand easier: Steel mirror? Got one. Crowbar? Grappling hook? Check and check. Portable ram? You bet your sweet bippie.

… plus the seven sets of tools I’m proficient with. All because Powerful Build gives me a carrying capacity of 450 pounds. It’s ridiculous and silly, and I kind of love it.

 

[MarkB]

Your opinion is your opinion, and I’m not here to tell you you’re wrong, but…

I recently started playing a Firbolg Artificer with Powerful Build, and I’m absolutely loving it.

I envisioned the character as an inveterate tinkerer/packrat, and after every session I stock up on more mundane adventuring gear—the stuff you usually put down on your sheet at chargen and never look at again.

Pretty much every session, I manage to pull out something that makes the task at hand easier: Steel mirror? Got one. Crowbar? Grappling hook? Check and check. Portable ram? You bet your sweet bippie.

… plus the seven sets of tools I’m proficient with. All because Powerful Build gives me a carrying capacity of 450 pounds. It’s ridiculous and silly, and I kind of love it.

 

[Parmandur]

Definitely incomplete. If you're going to call BECMI, RC, and Black Box Basic three different editions of D&D, then OD&D definitely had four separate editions. AD&D had at least two. 5E's had at least two, if not three. Etc.

Well, 5E hasn't had any type reset for the Core books. Difference between printings and editions.

 

[Bill Zebub]

and @Bill Zebub

Ok, it was either this or do work I was supposed to do...

Awesome work, @Cadence.

I was trying to (and still might) write a sim that would (or could) generate examples instead of probabilities, just because it seems that so many people don't understand the meaning behind purely mathematical results. But your analysis is great.

Then again, sometimes I wonder why I bother trying to persuade anybody:
1) I suspect no math will ever convert somebody who is just convinced that fixed racial ASIs are necessary.
2) It's clear which way WotC is going, and no argument here will change that.

 

[Cadence]

Awesome work, @Cadence.

I was trying to (and still might) write a sim that would (or could) generate examples instead of probabilities, just because it seems that so many people don't understand the meaning behind purely mathematical results. But your analysis is great.

Then again, sometimes I wonder why I bother trying to persuade anybody:
1) I suspect no math will ever convert somebody who is just convinced that fixed racial ASIs are necessary.
2) It's clear which way WotC is going, and no argument here will change that.

Sent you some simulation code in R that went a slightly different way that yours in a message too.

And no argument at all with your (1) or (2)!

 

[GMforPowergamers]

Well, to state my assumptions and arguments more clearly:

1. The range of ability scores for non-PC members of their races follows 3d6 plus racial ASIs. This approximates a normal distribution, and is one way to represent statements such as, "the average gnome is smarter than the average halfling".

2. Assuming a 4d6-1 plus racial ASI generation method for PCs, the PCs' ability scores still fall within the standard range for other members of their race, but are biased towards higher numbers. They are exceptional compared to the norm/mean, but they don't exceed the typical range of ability scores for their race and hence are not "atypical".

3. Using the standard array or point buy without racial ASI PC generation methods still creates PCs with ability scores that are higher than the norm/mean and fall within the standard range for their race (so still exceptional but not atypical), but a 17 Int halfling will be further along the bell curve for his race than a 17 Int gnome. This is not my preferred approach, but I can understand why WotC wants to adopt it.

Your assumptions about the distribution of non-PC ability scores seem to be different from mine, and that is fine. I am just stating my preferences and my conclusions if my assumptions are accepted.

the smartest halfing is a 20 int, the smartest gnome is 20 int

*In theory +magic

 

[GMforPowergamers]

I think most other RPGs actually follow more of a normal publishing world approach, honestly.

By my reckoning, which may be incomplete:

1. OD&D
2. Holmes Basic
3. AD&D
4. B/X
5. BECMI
6. AD&D 2E
7. Black Box Basic
8. Rules Cyclopedia Basic
9. AD&D 2E Skills & Powers
10. "Third Edition" just "Dungeons & Dragons
11. "3.5" (slightly worse than OneD&D even!)
12. "4E"
13. "4E" Essentials
14. "5E"
15. "OneD&D"

wow I knew people back in the 90's that called skills and powers 3rd edition... but now I want to start calling 1D&D 15th edition

 

[GMforPowergamers]

Having seen this kind of refresh happen in every edition, I think that intention is optimistic.

if we take it to be 100% honest the intent and belief of the dev and management team is this is it... the one and only edition going forward never to change again (and I don't buy that entirely) there is still the fact that someday the sales will drop and someone (maybe even someone new not in magement/dev team today) will say "I bet if we modernize this with a new edition we can up sales for a bit"