D&D 5E Point Buy vs Rolling for Stats

[Hussar]

But, [MENTION=29398]Lanefan[/MENTION], when your curve is completely outside the range of believablility, then it's not realistic, is it? Just because there happens to be a bell curve doesn't make it more realistic, just coincidental since the bell curves for anything remotely close to realism ISN'T 3d6. Again, unless you believe that 10% of your population is physically or mentally challenged.

So, right off the bat, arguing that it's "more realistic" is two smurfs arguing over who's more blue. Is a standard array "realistic"? Nope. But, it also doesn't pretend to be. A 3d6 bell curve isn't remotely realistic either. That it might be slightly closer to realism than a standard array doesn't change that fact.

So, no, no facts are being ignored here. You're pretending that a tiny movement towards realism makes the system "realistic". That's like saying Donkey Kong is more realistic than Pac Man because it has gravity. Neither games are anywhere in the neighbourhood of realistic.

And AGAIN, in 5e, the range is NOT 3-18. It's not. There is not a single piece of evidence you can point to to support that claim. The charts go 1-20. PC chargen taps out at 20 if you die roll.

5e does not use a 3-18 scale. And since it doesn't use a 3-18 scale, then any other completely arbitrary scale we choose to use works. If you use point buy or standard array, the scale is 8-15 FOR PC's. And PC's only. Because ALL NPC'S have their stats dictated by the DM with absolutely no requirement for random generation at all and absolutely no requirement that they need stats in the first place.

Now, all that being said, you certainly can try to extrapolate game rules onto the game world. That's fine and groovy. But, pretending that it's anything other than personal preference, that there is some sort of concrete, objective advantage in doing so is pointless. It's a personal preference, pure and simple. Do you want to focus more on game balance or on a sort of Gygaxian naturalism?

Whatever floats your boat. Both methods have elements that appeal to their users. Fair enough. I'm just really tired of watching people try to claim that there is some sort of objective advantage to either system.

 

[Harzel]

And AGAIN, in 5e, the range is NOT 3-18. It's not. There is not a single piece of evidence you can point to to support that claim.

The abilities ... typically range from 3-18 for most adventurers.

"Typically" leaves it loose, but the idea is there.

 

[Harzel]

Just because there happens to be a bell curve doesn't make it more realistic, just coincidental since the bell curves for anything remotely close to realism ISN'T 3d6.

It's not a coincidence at all; it's just that reality uses more dice.

 

[Harzel]

With my limited mathematical abilities, that looks like it conforms pretty well to a normal distribution, certainly better than 3d6. It seems a little bulgy at two standard deviations, similar to 3d6 in that respect (slightly worse actually), but at least it doesn't have the problem 3d6 does, which is that it produces 100% of results well within three standard deviations, whereas a normal distribution would have only 99.7% of "results" within three standard deviations, following the 68-95-99.7 rule.

As long as your dice rolls are independent and identically distributed (which we always assume, even if it's not precisely correct), xdn will look more and more normal-ish as x gets larger. In fact, in a (very informal) sense, that's what the normal distribution is* and why it is interesting / useful.

* xdn is a special case; it's actually much more general. Google 'central limit theorem' if interested; the proof is kind of math-y, but the statement is really pretty straightforward.

 

[Tony Vargas]

In that system, perhaps; but in the game as a whole the range is and always has been 3-18.

It goes to 20 in 5e, and has gone higher in other eds. 3-18 wasn't even the whole range in the classic games: 19s were possible in a few ways, and STR could be magical boosted as high as 24.

dice rolling in any form using more than one die is going to give a bell curve across a range

Nod. A bell-curve just means the middle stats like, oh, once you consider 4d6k3, ~8-15, are a lot more likely to come up than the extreme ones. Really, both systems are gunning for the same thing - reasonably good stats for PCs - random is just, obviously, less consistent in delivering on it.

 

[Harzel]

dice rolling in any form using more than one die is going to give a bell curve across a range

The distribution for one die is approximately a bell curve also; it's just not a very good approximation.

 

[Harzel]

A bell-curve just means the middle stats like, oh, once you consider 4d6k3, ~8-15, are a lot more likely to come up than the extreme ones.

Since 'bell curve' is a fairly informal term, I can't say that's wrong, but it's a bit looser than what a lot of people would mean. At minimum, symmetry and unimodality (a single high point) are also usually implied. If it's not symmetric, just 'unimodal' might be a better description. To be fair, I guess 'middle stats are more likely' implies sorta, kinda symmetric (else they wouldn't be 'middle'), and you were probably thinking of unimodal. That said, a statistician might look at you a little askance if you gave 4d6k3 as an example of a bell curve.

 

[Hussar]

I have no problem with someone saying the like die rolling because it feels more realistic or believable to them. No problem.

I do have a problem with flat statements claiming that die rolling is more realistic.


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[Lanefan]

Since 'bell curve' is a fairly informal term, I can't say that's wrong, but it's a bit looser than what a lot of people would mean. At minimum, symmetry and unimodality (a single high point) are also usually implied. If it's not symmetric, just 'unimodal' might be a better description. To be fair, I guess 'middle stats are more likely' implies sorta, kinda symmetric (else they wouldn't be 'middle'), and you were probably thinking of unimodal. That said, a statistician might look at you a little askance if you gave 4d6k3 as an example of a bell curve.

It's still a bell curve, only skewed by a known amount and thus asymmetrical.

Many bell curves in nature end up looking like this, only the amount of skew isn't so nicely predictable - this happens a lot in weather observations.

 

[Lanefan]

I have no problem with someone saying the like die rolling because it feels more realistic or believable to them. No problem.

I do have a problem with flat statements claiming that die rolling is more realistic.

The stats resulting from die rolling are undeniably going to be more realistic than those resulting from either point buy or standard array.

Neither point but nor array gives any kind of curve (array gives no curve at all but instead gives a series of straight lines) that has a mathematically-predictable highest occurrence at or near the average, lowest occurrences at the extremes, and predictable levels of occurrence between these points.

However, when it comes to modelling a population note that "more realistic" doesn't mean 3d6 dice rolling is anywhere near "fully realistic" with the results it gives - you need a tighter bell curve for that, as various here (including me) have noted. Rolling is, however, a lot further along the realism spectrum than the other options: if 0 is completely unrealistic and 10 is a perfect mirror of reality then point-buy might get a 1, standard array a 0 and straight 3d6 maybe a 5. Using 5d4-2 for the 3-18 range might get this over to a 6...maybe even a 7.

Lanefan