D&D 5E Point Buy vs Rolling for Stats

[Maxperson]

That's really interesting, and quite unexpected mathematically.

15-14-12-11-10-8 gives a total of 70 and an average of 11.67, over half a point lower than the 12.24 mathematical average of 4d6x1 that leads one to expect a total of about 73.44 - for simplicity let's round this down to 73 - which means on average there's over three stat points missing. Where did they go?

Rounding error is a possibility for some of it, I suppose, and if the difference in averages was less than half a point it could represent all of it. But the difference is over half a point - .57 to be more precise - meaning this variance can't all be attributed to simple rounding error.

Did your app by any chance record the actual "rolls" so as to give a total of how many times each number from 3 to 18 came up, what the average was, etc.? If the average of all the actual rolls was 12.24 or very close (with a sample size of 6 million it should be about bang on) then there must be some sort of way-beyond-my-pay-grade statistical weirdness that makes those three points vanish into thin air.

Curious.

Lanefan

The actual average is 16, 14, 13, 12, 10, 9. There are two of the missing three points.

 

[Sadras]

Lanefan doesn't play 5e. They just pop in from time to time confirm that we are still doing it wrong.

To be fair, first sentence applies to Lanefan, second sentence is more Pemerton

 

[Sadras]

There can be no rational assumption that people are going to use optional rules, and it's stupid to balance the game around optional rules.

Playing devil's advocate here, but we are constantly trying to balance the game using optional rules (Feats) - at least on this forum.

 

[Maxperson]

Playing devil's advocate here, but we are constantly trying to balance the game using optional rules (Feats) - at least on this forum.

Yes, but that's because at this point, I think the vast majority of people use feats. I'm really not sure why they made feats optional in the first place. That said, the fact that the game really doesn't balance for an optional rule like feats very well, indicates that they aren't really balancing the game around options. There's another balance point and they try(or maybe not) to ballpark the options near that point, rather than balance for them.

 

[Satyrn]

So what races fit this concept or can it only be successfully build with one or two? And what are the final stats for this concept?

Well, for this specific character, in my specific campaign, with my specific party, the only races that would really work would be human, half-elf or dwarf, as those are the races that could reasonably be knights.

But mechanically, any race will work - if you're okay with a wizard starting with a 14 or 15 Intelligence.

My stats, as a variant human are
15 s
10 d
12 c
16 I
13 w
8 charisma.

 

[Oofta]

That's really interesting, and quite unexpected mathematically.

15-14-12-11-10-8 gives a total of 70 and an average of 11.67, over half a point lower than the 12.24 mathematical average of 4d6x1 that leads one to expect a total of about 73.44 - for simplicity let's round this down to 73 - which means on average there's over three stat points missing. Where did they go?

Rounding error is a possibility for some of it, I suppose, and if the difference in averages was less than half a point it could represent all of it. But the difference is over half a point - .57 to be more precise - meaning this variance can't all be attributed to simple rounding error.

Did your app by any chance record the actual "rolls" so as to give a total of how many times each number from 3 to 18 came up, what the average was, etc.? If the average of all the actual rolls was 12.24 or very close (with a sample size of 6 million it should be about bang on) then there must be some sort of way-beyond-my-pay-grade statistical weirdness that makes those three points vanish into thin air.

Curious.

Lanefan

The app rolled 4d6 drop lowest 6 times sorted the numbers lowest to highest and then added the number to the appropriate entry in an array. I ran it 10,000,000 times an then divided the totals by 10,000,000. It's possible the sorting/bucketing skewed the results somewhat but I'm not enough of a mathematician to tell you that answer.

Percentages
3: 45698 for 0.46%
4: 185435 for 1.85%
5: 463554 for 4.64%
6: 970876 for 9.71%
7: 1759450 for 17.59%
8: 2870240 for 28.7%
9: 4213181 for 42.13%
10: 5649762 for 56.5%
11: 6849121 for 68.49%
12: 7726461 for 77.26%
13: 7964239 for 79.64%
14: 7408369 for 74.08%
15: 6068077 for 60.68%
16: 4351651 for 43.52%
17: 2501156 for 25.01%
18: 972730 for 9.73%

overall average: 12.2450446333333

Of course if anyone wants to independently verify I'm open. Grab some friends and start rolling, by end of the year you should have a similar sample size.

 

[Oofta]

The actual average is 16, 14, 13, 12, 10, 9. There are two of the missing three points.

Where did you get those numbers?

 

[Satyrn]

The app rolled 4d6 drop lowest 6 times sorted the numbers lowest to highest and then added the number to the appropriate entry in an array. I ran it 10,000,000 times an then divided the totals by 10,000,000. It's possible the sorting/bucketing skewed the results somewhat but I'm not enough of a mathematician to tell you that answer.

Percentages
3: 45698 for 0.46%
4: 185435 for 1.85%
5: 463554 for 4.64%
6: 970876 for 9.71%
7: 1759450 for 17.59%
8: 2870240 for 28.7%
9: 4213181 for 42.13%
10: 5649762 for 56.5%
11: 6849121 for 68.49%
12: 7726461 for 77.26%
13: 7964239 for 79.64%
14: 7408369 for 74.08%
15: 6068077 for 60.68%
16: 4351651 for 43.52%
17: 2501156 for 25.01%
18: 972730 for 9.73%

overall average: 12.2450446333333

Of course if anyone wants to independently verify I'm open. Grab some friends and start rolling, by end of the year you should have a similar sample size.

I'm confused by those percentages. Shouldn't they add up to 100%?

 

[Tony Vargas]

That statement made by [MENTION=6909244]Razamis[/MENTION] is provably false. 4d6 drop the lowest is not just the first stat creation method, it's the default method with the other two specifically being optional rules.

Well, second or third after 3d6-in-order and 4d6-in-order, if I may split that particular hair.
The 5e default is random-and-arrange, but it also allows the player who doesn't want to roll to just use the standard array -
and I'll spin that a little now - by default.

Point-buy is the side-bar variant.

That makes the array seem like the logical thing to balance around - since it's available by default, is apparently really close to the perplexing ranked-average of 4d6, and since you can't balance against the distribution of 4d6...

There can be no rational assumption that people are going to use optional rules, and it's stupid to balance the game around optional rules.

Sure, like feats & multi-classing and PCs getting ahold of magic items...


But, really, the game isn't that balanced, anyway. Balancing the game wasn't a high priority. Evoking the classic game was. Fast combat was. DM Empowerment was. None of those need balance - heck, balance can get in their way.

The average roll is 12-13, so they probably balanced it against those numbers rather than an array of numbers that will probably be incorrect when rolled individually. That array will only be true when rolled a large number of times, which isn't going to happen in any campaign. By balancing it against a 12, they avoid that issue.

Straight 12s have the same problem, they're very unlikely to actually happen to every PC in a party of 5

That statement made by [MENTION=6909244]Razamis[/MENTION] is provably false. 4d6 drop the lowest is not just the first stat creation method, it's the default method with the other two specifically being optional rules.

Well, second or third after 3d6-in-order and 4d6-in-order, if I may split that particular hair.
The 5e default is random-and-arrange, but it also allows the player who doesn't want to roll to just use the standard array -
and I'll spin that a little now - by default.

Point-buy is the side-bar variant.

That makes the array seem like the logical thing to balance around - since it's available by default, is apparently really close to the perplexing ranked-average of 4d6, and since you can't balance against the distribution of 4d6...

There can be no rational assumption that people are going to use optional rules, and it's stupid to balance the game around optional rules.

Sure, like feats & multi-classing and PCs getting ahold of magic items...


But, really, the game isn't that balanced, anyway. Balancing the game wasn't a high priority. Evoking the classic game was. Fast combat was. DM Empowerment was. None of those need balance - heck, balance can get in their way.

The average roll is 12-13, so they probably balanced it against those numbers rather than an array of numbers that will probably be incorrect when rolled individually. That array will only be true when rolled a large number of times, which isn't going to happen in any campaign. By balancing it against a 12, they avoid that issue.

Straight 12s have the same problem, they're very unlikely to actually happen to every PC in a party of 5...

Yes, but that's because at this point, I think the vast majority of people use feats. I'm really not sure why they made feats optional in the first place.

They were no part of the classic game. Presumably, they're there for a bit of optional 3.x feel.

But, yes, on the assumption that the game is 'balanced' for default chargen, feats are balance-poison.

That said, the fact that the game really doesn't balance-

That's really all that needs be said on the subject.

for an optional rule like feats very well, indicates that they aren't really balancing the game around options. There's another balance point and they try(or maybe not) to ballpark the options near that point, rather than balance for them.

The one nearly-explicit attempt at balance is the 6-8 encounter day. Not that there aren't plenty of folks who don't accept that, either.

 

[Oofta]

As far as the balance thing, I don't see how you could possibly "balance" the game perfectly. I've been running a home campaign and a couple of people got swapped out (people moving to a different part of the country does that) and I had to redo my expectations. Similar characters, same rules, new people that are fun to play with but not very tactical. Suddenly my "difficulty multiplier" when from 1.5 to 1.0 or a little less.

There's no way you can have 1 guideline for everyone, any guidelines are a starting point that need to be adjusted, tweaked, twisted and modified to fit your style and group. I don't see how people could reasonably expect any formula that could take into account DM style, player tactical acumen, feats/no feats, differing methods to get ability scores, etc. Unlike a video game there are just too many variables, and even then most games have several difficulty levels (or adjust difficulty on the fly).

However, I will say that if you go with 6-8 encounters and don't have a gonzo group the basic guidelines are a decent starting point in my experience.