D&D 5E (2014) Is Point Buy Balanced?

[Lanefan]

I had a much longer spiel here, but I think it's better to be pithy: I think for something to be a "dump" stat, it requires player intent.

Agreed. And if it's 11 or higher it isn't really a dump stat in any case.

 

[EzekielRaiden]

OK so far - I see no problem with someone starting with an 18.

You're missing the forest for the trees.

The person doing point buy cannot start with 18. It's not possible. The absolute best they can start with is 15. As a result, when you cut off the bottom low-roll results, there is no cost paid for this potential, and it's pretty damn high potential too--with just 4d6k3, there's a 9.3% chance to get an 18, and a further (separate) 20.7% chance to get 17. More than half the time, your highest stat with six rolls of 4d6k3 will be 16, 17, or 18 (56.76%, to be precise).

Using our usual 5d6drop2 I've seen a pretty good number of 7s and 6s - and even lower - over the years

Obviously if you watch enough cases you'll always see such values. I'm wondering how much as "a pretty good number", because statistically, it really shouldn't be that high.

including two 4s rolled almost simultaneously by different players; both players put the 4 into Int and the party's overall thinking capacity dropped like a stone when those two came into play).

That, however, is shocking to the point of looking suspicious. The odds of any player getting a 4, even as their lowest stat, is only 0.08%. Hence, the odds of two players both rolling that at the same time are 0.0046^(2) = 0.00002116, or 0.002116%. That's a 1 in 47259 chance. (Rounding up because it's only the tiniest bit shy of that value.)

You are much more likely, as in literally 7.7x more likely, to see a player get all six stats being 16+: (0.2342)^6 = 0.000165, or about 1 in 6060.

Ideally the power curve is already flexible enough that this doesn't matter in the slightest. It's the same issue, from a different direction, as having uneven character levels within the party: the math should be more than forgiving enough to allow it and if it isn't, there's a problem.

Any math that is that forgiving is math that makes strategy worthless.

Agreed that it's easier to unbalance things than to balance them. The more important questions, though, are how much imbalance - particularly imbalance in the immediate here-and-now - is acceptable, and-or whether anyone at the table really cares.

I see the former requirement as shortsighted. Even a fair amount of imbalance can be fine, if and only if it is truly for a moment. But games are not for a moment. They are for hours and hours and hours. Designers cannot afford to think only about the here-and-now. They have to think about the long haul.

As for the latter, I was given to understand we have fairly robust statistical evidence that players do in fact notice when the power difference gets beyond, very roughly, 15% performance. Which, I'd say, makes sense. If one person is doing, say, 20%-25% more than anyone else, you're gonna notice over time. You won't notice in one single instant, because that's not how distributions work, but you'll get the feel over time. Just like how a small scatterplot may not have any visible pattern, but a long-term scatterplot with millions of points will usually have a clear pattern if there is any pattern to observe. (Consider, for instance, the famous scatterplot of airplane bullet holes on returning aircraft. The naive conclusion from that is to put armor on the places where lots of bullet holes are; the correct conclusion is to put armor on all of the places where the bullet holes aren't...because those are the places where, if you get shot there, you ain't coming back.)

And that's why I generally use, very roughly, a +/- 10% range for what I consider equivalent. If two results cannot be brought within 10% of one another, something is wrong and one or the other needs to be tweaked. This is, of course, quite complicated--but there are ways to get usable data even in places you might not expect. (E.g. you can quantify the benefit of crowd control by looking at it as a form of damage prevention--every attack a monster doesn't get to make because it's CC'd is equivalent to having spent resources on healing that damage, after all.)

 

[Lanefan]

You're missing the forest for the trees.

The person doing point buy cannot start with 18. It's not possible. The absolute best they can start with is 15. As a result, when you cut off the bottom low-roll results, there is no cost paid for this potential, and it's pretty damn high potential too--with just 4d6k3, there's a 9.3% chance to get an 18, and a further (separate) 20.7% chance to get 17. More than half the time, your highest stat with six rolls of 4d6k3 will be 16, 17, or 18 (56.76%, to be precise).

Again, someone starting with one or two high (as in, 16+) scores is fine with me.

Obviously if you watch enough cases you'll always see such values. I'm wondering how much as "a pretty good number", because statistically, it really shouldn't be that high.

Perhaps. I've seen a lot of characters come and go over the last 43+ years.

That, however, is shocking to the point of looking suspicious. The odds of any player getting a 4, even as their lowest stat, is only 0.08%. Hence, the odds of two players both rolling that at the same time are 0.0046^(2) = 0.00002116, or 0.002116%. That's a 1 in 47259 chance. (Rounding up because it's only the tiniest bit shy of that value.)

Perhaps, but I was standing there watching as they did it. Each rolling up (yet another - they went through a lot of 'em) replacement character. One rolled a 4, then within less than a minute (may have been just ten seconds or so, I forget now) the other one also rolled a 4 - and this is on 5d6drop2.

So, odds be damned, it happened.

They both put the 4 in Int., which meant they had to be Fighters as that's the only class that'll allow Int 4.

You are much more likely, as in literally 7.7x more likely, to see a player get all six stats being 16+: (0.2342)^6 = 0.000165, or about 1 in 6060.

I've never seen all 16+ but have seen, again rolled right in front of me, 18-18-17-17-15-15. The player - with every option open to him - went with Ranger for his class.

That Ranger didn't make it through his second combat. One of the Int-4 Fighters also didn't last very long. The other one, somewhat incredibly, survived and is still active in the setting, though his player retired him from adventuring a while back.

Any math that is that forgiving is math that makes strategy worthless.

Depends. For me, the best strategy comes before any dice get rolled as you attempt to mitigate the odds. Once you're rolling dice, however, it's all up to fate.

I see the former requirement as shortsighted. Even a fair amount of imbalance can be fine, if and only if it is truly for a moment. But games are not for a moment. They are for hours and hours and hours. Designers cannot afford to think only about the here-and-now. They have to think about the long haul.

Indeed. And in my view balance across the long haul can include, to use a hypothetical extreme example, one class sucking from levels 1-5 and being godlike from levels 6-10.

As for the latter, I was given to understand we have fairly robust statistical evidence that players do in fact notice when the power difference gets beyond, very roughly, 15% performance. Which, I'd say, makes sense. If one person is doing, say, 20%-25% more than anyone else, you're gonna notice over time.

IME 99+% of the time such things are connected with that person being the loudest and-or most persistent and-or most engaged talker rather than anything to do with character mechanics.

You won't notice in one single instant, because that's not how distributions work, but you'll get the feel over time. Just like how a small scatterplot may not have any visible pattern, but a long-term scatterplot with millions of points will usually have a clear pattern if there is any pattern to observe. (Consider, for instance, the famous scatterplot of airplane bullet holes on returning aircraft. The naive conclusion from that is to put armor on the places where lots of bullet holes are; the correct conclusion is to put armor on all of the places where the bullet holes aren't...because those are the places where, if you get shot there, you ain't coming back.)

And that's why I generally use, very roughly, a +/- 10% range for what I consider equivalent. If two results cannot be brought within 10% of one another, something is wrong and one or the other needs to be tweaked. This is, of course, quite complicated--but there are ways to get usable data even in places you might not expect. (E.g. you can quantify the benefit of crowd control by looking at it as a form of damage prevention--every attack a monster doesn't get to make because it's CC'd is equivalent to having spent resources on healing that damage, after all.)

That's already getting considerably deeper into the analytics than I care to bother with; and IMO analysing it to that degree isn't healthy for the game - it becomes too much an exercise in constrained math at cost of unconstrained roleplay and fun.

That was one thing I noticed when playing 3e - yes the numbers kept getting bigger but even with that it always felt a little too tightly constrained.

 

[TwoSix]

Obviously if you watch enough cases you'll always see such values. I'm wondering how much as "a pretty good number", because statistically, it really shouldn't be that high.

Chance of a 7- on 5d6k3 is 1.95%. So the chance for a 6 stat array to contain one value that is 7- is ~11.1%.

(I know you can calculate it, just adding for the audience.)

 

[TwoSix]

That, however, is shocking to the point of looking suspicious. The odds of any player getting a 4, even as their lowest stat, is only 0.08%. Hence, the odds of two players both rolling that at the same time are 0.0046^(2) = 0.00002116, or 0.002116%. That's a 1 in 47259 chance. (Rounding up because it's only the tiniest bit shy of that value.)

You are much more likely, as in literally 7.7x more likely, to see a player get all six stats being 16+: (0.2342)^6 = 0.000165, or about 1 in 6060.

To be fair, it's probably a little higher in context, since it was probably two players in a group of 4-6 making characters.

 

[Thomas Shey]

Er...that's...that's exactly what statistics is for?

As an overall set.*

Statistics do not actually tell you what will happen in a limited set of results though. They just tell you what to expect.

My whole point here is that the variance isn't all that significant,

It isn't all that significant when viewed as a population of rolls. That does not tell you how significant it will actually be in a given specific set of rolls, because outliers happen.

Then by definition every person always dumps at least one stat. Even if their stats are {18,18,18,18,18,17}. That seems...a pretty weak and impoverished definition of "dump stat", as it refers to behavior almost* everyone must engage in.

I think using a degenerate case here doesn't help your argument.

I had a much longer spiel here, but I think it's better to be pithy: I think for something to be a "dump" stat, it requires player intent. If you just happen to have already assigned your other scores and you're left putting the final, lowest value in the last open spot, it doesn't matter whether that value is 17 or 7 or 3. If, however, you intentionally put the lowest value in the place where you believe it will hurt you least, then yes, that's a dump stat. I might even call it that if it is a 17, though I do personally feel that degree of difference has some impact too.

Except I'm willing to bet few people do it that way; I'd be willing to put money on the fact most people assign the low stat first to that place they know is largely irrelevant to them. Because the higher rolls and the more valuable stats are the ones that will require some thought about priorities.

 

[Maxperson]

Well, that's where we're simply going to have to disagree. I did the rolling for groups with 5 people 10 times and got the results I got. It's similar to things I've seen in real life. If you have a house rule - whether you call it that or not - that if someone doesn't like the results they roll again but again I've been at a table where they were not allowed to do so. But if you do then it skews things.

I've seen worse disparity than my example and the DM did not allow a reroll. I don't think it's as uncommon to get the difference as you think. I don't really have anything else to add.

First, as I've said many times in many threads, bonuses in 5e don't mean a whole heck of a lot, so the skewing fear is overrated. Second, it doesn't really skew things much in practice. I've been doing this for years and over many campaigns and characters I've noticed that most of the PCs end up in the average range, with a few that are above average. It's rare for someone to roll really superawesomeuber stats, but even when that happens, they can't dominate anything in 5e because bonuses don't matter that much.

 

[Maxperson]

I don't disagree with any of this. This is pretty much how I learned to stop worrying and love the d20 System.

We should still appreciate that not everyone will notice the same things, or notice them to the same degree. Something barely noticeable to me could be obvious to the person on my left, and completely invisible to the person on my right. (shrug)

When I say not noticeable unless the DM tell them, it's literally not noticeable unless the DM tells them. If the players don't know the DC numbers, they can't know when in the many, many rolls they hit that one single number out of 20 where the +1 actually makes a difference.

It's only when the DM says the DC is 17(or whatever) that they can tell if the +1 made the difference or not. And even then it won't make the difference except for rarely.

 

[Maxperson]

Is there any way to arrange scores without dumping one?

If I have the following set to arrange: 18 17 16 15 14 13, then I must put the 13 somewhere - is that a dumped score?

In my opinion a dump score has to have a stat penalty. If the score is average or better, the number isn't dumped there. Dump implies trash in this context.

 

[AlViking]

First, as I've said many times in many threads, bonuses in 5e don't mean a whole heck of a lot, so the skewing fear is overrated. Second, it doesn't really skew things much in practice. I've been doing this for years and over many campaigns and characters I've noticed that most of the PCs end up in the average range, with a few that are above average. It's rare for someone to roll really superawesomeuber stats, but even when that happens, they can't dominate anything in 5e because bonuses don't matter that much.

I think doing double damage, one character having 1/3 less HP and so on from my examples are significant. It's even worse if those two both wanted to be barbarians, monks or any other class that relies on more than 2 stats.

Whether or not it matters to you or if you allow rerolls isn't the point. The point is that 4d6dl has inherent issues - a group of 10 tables having that extreme difference indicates it is not rare by any stretch. You can resolve those issues by allowing multiple rolls or other issues or simply using point buy. I prefer using point buy.