D&D 5E Point Buy vs Rolling for Stats

[Maxperson]

When we invoke 'realism,' that's exactly what we're doing (and, yes, that one word can neatly invalidate everything associated with it if not used very carefully, indeed), we're bringing in RL standards. In this specific case, the idea that rolling is more 'realistic,' it's even in the exact sense that Hussar brought up - the sense of what the character controls mapping closely to what the player controls. The character can't choose his parents, for instance, so the player shouldn't be able to just take a background like Noble. You're either born into a noble family or not - usually not - so roll on this table....

No you're not. Real life is one extreme and pure chaos in another dimension with no realism whatsoever is at the other end. Everything in-between is a grade of realism. People talk about things being more realistic than other things all the time without saying it mirrors real life. Attempting to force realism to only mean real life is to engage in a False Dichotomy.

 

[Hriston]

And yet tons and tons of NPCs had 3-18 in basic, 1e, 2e, and 3e. Methinks you are incorrect about that. I can't imagine that the game creators and later the designers would all get that so very wrong.

Were those NPCs members of the "general population", i.e. peasants, laborers, men-at-arms, and the like? Or were they classed NPCs, the NPC equivalent of adventurers? I would guess that the overwhelming majority of them were the latter.

That isn't to say, however, that a "general" character never had an 18. I can think of at least one example from a module off the top of my head. The point is that the distribution of such scores is far more rare than 3d6 would suggest. Averaging dice produce a distribution in which 1 in 216 rolls is a 15, rather than an 18, and any score above 15 is so vanishingly rare that it falls outside the mathematical model. The same is true, of course, of scores below 6.

 

[Lanefan]

Now, for that first question. I'm not deliberately making an illogical world, but it is a likely side effect of my decisions, I admit. Because, again, "creating a logical world" is not one of my goals. See, my platonic ideal of a D&D game is Xena: Warrior Princess, a show that throws facts and logic right out the window in order to tell a fun little story of fighting. Each episode might be internally logical, but if you try to make sense of the show as a whole, you'd fail horribly.

Actually, you might be surprised.

Its History, for example, is horrendous. Xena is friends with Helen of Troy and an enemy of Julius Caeser, for example - two people who lived a thousand years apart.

Which makes it ring truer to most D&D games than any other show out there, as most D&D settings take variants on historical real-world cultures from all sorts of eras - ancient Sumerians, classical Greeks, Romans, Vikings, Druidic-era Celts, Aztecs/Incans, right through middle-ages crusaders all the way up to early-Renaissance European - and put them all on the same world at the same time. Then for good measure they chuck a bunch of non-Human races and cultures on top of it all; so it's X:WP with Dwarves and Elves and Orcs and Aboleths. And dinosaurs. And occasional crashed spacecraft.

My ideal game also hews very close to X:WP-meets-Tolkein, yet it still has a strong internal logic and consistency to it. That this internal logic and consistency doesn't completely agree with real-world historical logic and consistency is nigh-irrelevant; it's still consistent, and it still works.

Lan-"Joxer the Mighty is proof positive that a low-stat character can blunder his way to survivability"-efan

 

[Lanefan]

Like I said, it seems to be a widely held misconception. I think I retroactively assumed 3d6 was for commoners because 4d6 drop lowest was for adventurers. I think a lot of people make the same mistake. If you look at the history of the game, it turns out that 3d6 is for adventurers too. 4d6 drop lowest just makes sure you don't get a really bad adventurer.

3d6 straight was for adventurers in 0e. By 1e it had gone to 3d6 straight for commoners and various other methods (best six of 12 3d6 rolls, or 4d6x1, etc.) for adventurers.

 

[Hussar]

I'm pretty sure you could. Charisma isn't required for firefighting or catching a football, and I've seen plenty of football players who rubbed people the wrong way. In any case, adventurers are not chosen based on stats. Any Tom, Dick or Lowstat can pick up a sword and go out to kill dragons. If there were some organization that selected individuals to be adventurers, you'd have a point.

Not sure, but, I'm pretty sure that organization is called the Darwin something or other.

 

[Harzel]

Update to this post.

This is the first batch of results; I have a few more things planned. Suggestions are welcome.

Also, @Oofta’s numbers again for reference.

AKA, yes it looks like I was accidentally using integer math.
The real numbers:
15.6627465
14.1746176
12.9559838
11.76172
10.4118873
8.5048237

Below are the frequency distributions for each ranked value in attribute arrays generated by 6 x 4d6k3 – that is, highest value, 2^nd highest, …, down to lowest. Below each distribution are the mean, median, and mode, which are all identical, excepting one case. The number of Big Surprises is, well, pretty much 0. Note that Oofta’s sample means are good to ‘only’ five digits; yeah, that there sampling worked pretty good.

The attached spreadsheet also has tables of cumulative probabilities both ascending and descending. (For convenience. They are equivalent to the values in the table below.) A few data points from those:

• Probability of # of values ≤ 5: 1 – 7%
• Probability of # of values ≤ 7: 1 – 30%; 2 – 4%
• Probability of # of values ≤ 9: 1 – 69%; 2 – 28%; 3 – 7%
• Probability of # of values ≥ 14: 1 – 93%; 2 – 69%; 3 – 36%; 4 – 12%
• Probability of # of values ≥ 15: 1 – 72%; 2 – 42%; 3 – 14%; 4 – 3%
• Probability of # of values ≥ 16: 1 – 57%; 2 – 18%; 3 – 3%
• Probability of # of values ≥ 17: 1 – 30%; 2 – 4%
• Probability of # of values = 18: 1 – 9%

FWIW, my sort of rough feeling based on all of this is that there are maybe 10-12% of the arrays that I would be somewhat loathe to play as a player and for which as a DM I would feel obliged to let the player reroll. On the other end, I think there are maybe around 20% which would feel like an embarrassment of riches as a player and would look out of whack as a DM. Overall, I think this makes me more favorably inclined than I was toward point buy even though both I and my players like rolling for stats just as a mini-game.

Probabilities of value by rank
Value	Highest	2nd	3rd	4th	5th	Lowest
3	0.0000	0.0000	0.0000	0.0000	0.0000	0.0046
4	0.0000	0.0000	0.0000	0.0000	0.0002	0.0183
5	0.0000	0.0000	0.0000	0.0000	0.0017	0.0445
6	0.0000	0.0000	0.0000	0.0004	0.0088	0.0880
7	0.0000	0.0000	0.0001	0.0029	0.0312	0.1417
8	0.0000	0.0001	0.0014	0.0148	0.0822	0.1886
9	0.0000	0.0008	0.0089	0.0527	0.1597	0.1992
10	0.0004	0.0057	0.0383	0.1303	0.2274	0.1627
11	0.0028	0.0273	0.1085	0.2204	0.2290	0.0973
12	0.0149	0.0875	0.2100	0.2576	0.1616	0.0415
13	0.0540	0.1885	0.2699	0.1980	0.0744	0.0114
14	0.1340	0.2685	0.2217	0.0942	0.0206	0.0018
15	0.2264	0.2431	0.1086	0.0252	0.0030	0.0001
16	0.2669	0.1355	0.0293	0.0033	0.0002	0.0000
17	0.2073	0.0392	0.0033	0.0002	0.0000	0.0000
18	0.0934	0.0038	0.0001	0.0000	0.0000	0.0000
Mode	16	14	13	12	11	9
Mean	15.6618863	14.1742279	12.9551079	11.7609295	10.411357	8.50408450
Median	16	14	13	12	10	9

Note: Entries that appear to be 0 are just values < 10^-4. I just thought it was easier to read with fewer digits and I have an irrational aversion to scientific notation.

 

[Harzel]

[MENTION=6857506]Harzel[/MENTION], in the last line of the table in post 1534 (just above this one) I think it wants to say "Some < 8; Some > 15" - you have an extra '=' in there.

Otherwise, good stuff; and I'm curious as to what your further number-crunching will show.

Lanefan

Yes, good catch. Thank you.

 

[Hriston]

3d6 straight was for adventurers in 0e. By 1e it had gone to 3d6 straight for commoners and various other methods (best six of 12 3d6 rolls, or 4d6x1, etc.) for adventurers.

Based on what? Certainly not the DMG, which gives the averaging method for commoners. 3d6 was for "special" characters.

 

[Maxperson]

Not sure, but, I'm pretty sure that organization is called the Darwin something or other.

Heh. Except that we know that not all low stat characters die, because we've played them in basic, 1e, 2e, 3e, etc. Some died, just as some PCs with high stats died. Darwin applies to all adventurers.

 

[Arial Black]

I'm gonna start with your last question, because I think it illustrates what I was saying from the start: My strange decision doesn't help anyone decide which stat generation method is best. It doesn't help you since you want to judge how realistic it is and you can't. And it doesn't help me because I don't care about that at all.

Now, for that first question. I'm not deliberately making an illogical world, but it is a likely side effect of my decisions, I admit. Because, again, "creating a logical world" is not one of my goals. See, my platonic ideal of a D&D game is Xena: Warrior Princess, a show that throws facts and logic right out the window in order to tell a fun little story of fighting. Each episode might be internally logical, but if you try to make sense of the show as a whole, you'd fail horribly. Its History, for example, is horrendous. Xena is friends with Helen of Troy and an enemy of Julius Caeser, for example - two people who lived a thousand years apart.

Logic is simply not relevant to me the way it is to you.

More specifically: 1) I don't care if the stats model the world logically, and 2) I'm not using the stats to model the world, anyway.

Ahhh! Xena: Warrior Princess! Hercules! Great shows! Typical D&D fodder!

Who were the 'player characters' here? Hercules, Iolus, Xena, Gabrielle, Joxer, a few others.

Would anyone like to try to convince me that Hercules and Xena were made to the same point-buy total as Joxer? Or even Gabrielle?