Ability points PC vs. NPCs

[frisbeet]

DMG 3.5, p. 170.

6). Customized Average Characters: Roll 3d6 six times and arrange scores as desired. This method produces characters more like average people but still allows customization.

Therefore it’s a 3d6 world you’re all playing in.

Question: how frequently on average would you expect to bump into an NPC with at least one 18?

One answer, which many claim is a consensus opinion (stemming from the 1st ed. of D&D), is: virtually never; extremely rare.

Rubbish!

Either that or “rare” is an extremely relative term.

Here’s why.

There’s just 1 way of rolling an 18 with 3 d6 dice: all 3 dice are sixes. Genius.

There are 6^3 = 216 total ways of rolling 3 dice. That’s 6 ways to roll the 1st die x 6 ways to roll the next die x 6 ways to roll the last die.

The probability of rolling an 18 by 3d6 is therefore 1/216. There is but 1 in 216 ways of rolling an 18 with 3 dice.

Maybe that’s rare to some people. I dunno, most villages a PC traipses through will have this many occupants. Is one prodigy/village so rare?

But I’m not done. 1/216 is really the probability of an NPC having an 18 Int, or 18 Str, or 18 in any one specified attribute. That doesn’t answer the question. The question, again: how frequently on average would you expect to bump into an NPC with at least one 18, without requiring it be one particular attribute?

That probability is found by the simple trick of subtracting from 1 the probability of not having any 18s. Probabilities are always between and including 0 and 1, incidentally; 1 represents the probability that the NPC will have 6 attributes, each between and including 3 to 18 (well, duh).

The probability of not having any 18s = probability of rolling 17 or less for Str x probability of rolling 17 or less for Dex x … = P(17 or less) ^ 6. That’s because a law of probability requires that if N independent things must happen to get a certain outcome, the P(outcome) = P(thing 1 happening) x P(thing 2 happening) x … x P(thing N happening). The probability of rolling a 17 or less is 215/216. There is 1 way to roll an 18 out of 216 total ways of rolling 3d6. Therefore there’s 215 ways of not rolling an 18. Then the probability of not having any 18s among 6 stats = P(17 or less) ^ 6 = (215/216)^6 = 0.972541746577387.

The probability of having at least one 18 among 6 stats is, again, 1 minus this. 1-(215/216)^6 = 1 - 0.972541746577387 = 0.0274582534226134 If you’re accustomed to percentile, that’s 2.75% of the time.

The answer to the question, the frequency, is defined as 1 over the probability:
1 / (1 – (215/216)^6) = 1 / 0.0274582534226134 = 36.418922376776

So, a PC will bump into one NPC with at least one 18 in a crowd of 36 NPCs, on average.

That’s rare????

Ergo, you’d better give your PCs an advantage. 4d6-drop-lowest analysis shows the answer to be 1 / (1 – ((1296 – 21)/1296)^6) = 10.7103209606842. A little fewer than 1 in 11 PCs (created by 4d6 drop method) will have at least one 18, on average.

18 isn’t that spectacular, IMO.

 

[Eremite]

(snip) I often don't use the NPC classes as I find them a bit too weak for my taste. (snip)

I avoid the NPC classes, not so much because they're weak, but because they don't make sense past a certain point (with the exception of Aristocrats and Experts).

IMO, the common-ness of a Commoner does not support this class being used for more than about 3-5 levels. If a Warrior is good enough to reach, say, 5th level, he has gone past being a Warrior and really is a proper Fighter, IMO. Anyway, I limit both of these to 3rd level IMC and I don't use Adepts at all because they don't fit the flavour of the games I run.

I've been disappointed with Eberron's overuse of high-level NPC classes. If you're high level, especially in a world like Eberron which is still at the Gray Box stage of pre-outrageousness, then surely you're more likely to be one of the "real" classes than one of the NPC classes.

 

[Darkness]

4d6-drop-lowest analysis shows the answer to be 1 / (1 – ((1296 – 21)/1296)^6) = 10.7103209606842. A little fewer than 1 in 11 PCs (created by 4d6 drop method) will have at least one 18, on average.

Did you account for hopeless PCs? (I.e., reroll your stats if sum of modifiers is 0 or lower, or if highest score is 13 or lower.)
Having an 18 at all means a character can only be rerolled under the first clause, never the second, and makes the second less likely.
I.e., the percentage of PCs with an 18 should be a little higher since the bottom is cut off (rerolled) and they usually aren't in it.

 

[frisbeet]

Did you account for hopeless PCs?

Nope. Good point. Also doesn't say anything about standard point buy distribution either, which is a really hard thing to gauge.

 

[Li Shenron]

Bof! So many DMs seems to precise for my taste... Why bothering with lots of methods for generating npc stats? When making an NPC I never roll, I just make it up like I want. If I need a strong fighter, I give it a Str score between 14 and 18 for example; if I need a good alchemist, I may give it +X in Alchemy and that's it, who cares about the other skills if they're not going to be used?

When an NPC is going to last longer than a battle, and there are good chances that the players interact with it a lot (beside talking), I have it all statted out, but I still don't mind if I'm following a "rule" or whatever. For myself it's a waste of time that I'd better spend improving my stories instead, which so much often suck...

 

[Darkness]

Why bothering with lots of methods for generating npc stats?

Because it's easier for me.

 

[Li Shenron]

Because it's easier for me.

Ok, if it's easier for you In my case it feels even easier to assign stats quite arbitrarily

 

[Darkness]

Ok, if it's easier for you In my case it feels even easier to assign stats quite arbitrarily

Agreed, what works best for someone varies by the individual. I desire some consistency and want to avoid stat inflation. (Which I have a tendency to indulge in if I don't limit myself. Also, I play in the FR and I want to tone down some NPCs' silly 2e-style uber-stats anyway.)

Of course, if I see that my guidelines prevent something that's necessary for my campaign, I expand them to make it work. They're more of a work in progress than a set of absolute rules.

 

[Gez]

IMC, the women are strong, the men are good looking, and all the children who survive to breed are above average.

So, you're saying that the average stat is above average?

 

[Sammael]

IMC:

Nameless monsters, templated monsters, or monsters with a few class levels - 11, 11, 11, 10, 10, 10
BBEG mooks - 13, 12, 11, 10, 9, 8
NPCs meant to actually challenge the party, cohorts, friendlies, etc. - 15, 14, 13, 12, 10, 8
Major NPCs - 4d6 drop lowest, repeat up to three times until satisfied