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8 months ago ::
Sep 30, 2012 - 5:02PM
#41
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What's more, there is simply less control over the probability of success for most of the distribution. You slide very steeply from 90.7% to 16.2% in just seven discrete steps.
I'm not sure how you can categorically say there is no advantage to this system - it depends on what the goals of the system are. If the complaint is that a d20 roll is too "swingy", then making it so that more DCs have either a higher chance of success or a higher chance of failure is an advantage.
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8 months ago ::
Sep 30, 2012 - 5:37PM
#42
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Date Joined:
Jul 19, 2012
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Quite simply, there is no advantage to the Gaussian distribution for binary effects.
I just really like this line.
In my head, I hear C3PO saying that.
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8 months ago ::
Sep 30, 2012 - 5:39PM
#43
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I think it's important to simply accept the fact that at lower levels, combat is going to be a bit "swingy..."
This is the best point made in this thread. If "swingy" (I really hate that term, btw...) offends your "it's over 9000!!!!11!!" sensibilities, then simply start your campaign at a higher level. This way, everybody's happy--those of us who enjoy the "swinginess" of classic low-level play get what we want out of the core system, and the Dragonball types get their superpowered starting characters without breaking the system for the rest of us. How is this a bad plan?
And a base 50% "hit and deal damage" rate is still too damn low.
No it isn't. If anything, it's far too high. If a trained, unarmoured man is menacing you with a sword, and you strike at him with your own sword, your attack is probably much less than 50% likely to hit him because he's probably going to parry your stroke. Unfortunately, D&D has never been all that good at representing a character's skill at defending himself. I enjoyed using a variation of the 3E optional "defense roll" rule to represent this.
In the interest of keeping things simple, though, I'd prefer to see the base unarmoured "hit and deal damage" chance at somewhere around 30-40%. If we have to, however, I guess we can keep the classic 50% hit rate, but I'd like to see it modified by some sort of character base defense bonus...
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8 months ago ::
Sep 30, 2012 - 5:42PM
#44
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I think it's important to simply accept the fact that at lower levels, combat is going to be a bit "swingy..."
This is the best point made in this thread. If "swingy" (I really hate that term, btw...) offends your "it's over 9000!!!!11!!" sensibilities, then simply start your campaign at a higher level. This way, everybody's happy--those of us who enjoy the "swinginess" of classic low-level play get what we want out of the core system, and the Dragonball types get their superpowered starting characters.
While I understand and respect your playstyle and point of view here, could you have found a more offensive way to say this?
A little respect for others playstyles goes a long way towards preserving civility.
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8 months ago ::
Sep 30, 2012 - 6:00PM
#45
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What's more, there is simply less control over the probability of success for most of the distribution. You slide very steeply from 90.7% to 16.2% in just seven discrete steps.
I'm not sure how you can categorically say there is no advantage to this system - it depends on what the goals of the system are. If the complaint is that a d20 roll is too "swingy", then making it so that more DCs have either a higher chance of success or a higher chance of failure is an advantage.
You're making several incorrect assumptions here. Yes, what is technically superior is defined by whatever your goals are. However, even by the most broad set of goals for every skill resolution system as D&D understands them you'll find no coherent set that makes the normal distribution the better pick. Specifically, if you want to control difficulty in a manner that makes the system "less swingy," that can be done best through the manipulation of modifiers and DC's on a uniform distribution.
What makes a system "swingy" is the slope of the cumulative mass function (CMF) in relation to the range of bonuses and difficulties that player characters experience. The only numbers where 3d6 has a smaller slope are 3-7 and 15-18. That wouldn't be so bad except that those ranges of the distribution cover 100% through 90.7% and 9.26% through 0.46%. The designers, game masters, and players all have objectively less granular control over the probability between 90.7% and 9.26%. So unless your game is only about people who succeed 90-100% or 0-10% of the time you're using a very "swingy" system. Then the other problem is that if you wanted to focus on those probabilities, you could just have used a d20 distribution and restricted all the DC's to 1 to 4 and 17-20. You'll also notice that you're using about the same number of discrete steps with the uniform distribution as you did with the 3d6 distribution, so you really haven't lost any granularity and now you can intuitively know the probability value of each of those steps.
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8 months ago ::
Sep 30, 2012 - 6:41PM
#46
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In the post I wrote above the "swingyness" I'm addressing is the huge difference in effectiveness that crops up from a seemingly small situational penalty or benefit. That's a major problem in systems that use non-uniform distributions.
D&D's "swingyness" is a slightly different problem that I want to address. One of the other traits that make a system seem swingy is where the average difficulty is centered at. In 4e it was centered around 55%. I felt that was too low because it created a relatively steep relationship with effect that encouraged the "Tyranny of Accuracy" as Mearls eloquently named it. In 5e apparently it's shifted to about 60%-65%, but that's not a significant improvement yet.
One of the problems with a location near the mean is the amount of variance in the expected frequency of success. Consequently, this translates to high variance in the number of rounds that any character or monster is effective in a given encounter. This is the other "swingyiness" in D&D that both players and DM's commonly complain about.
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8 months ago ::
Sep 30, 2012 - 6:42PM
#47
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Quite simply, there is no advantage to the Gaussian distribution for binary effects.
Which is why almost all systems emplying a gaussian distribution is not binary but use graded successes and failures, something that just does not work as well with a flat distribution.
The problem you state lies in the binary effect rather than the gaussian distribution, especially as you speak about game-design in general and not D&D in particular.
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8 months ago ::
Sep 30, 2012 - 6:59PM
#48
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What makes a system "swingy" is the slope of the cumulative mass function (CMF) in relation to the range of bonuses and difficulties that player characters experience.
I think we're suffering from a difference of definition here. And of the two of us, you're the first one to articulate your definition, so mea culpa. Let me clarify. When you read "swingy", you take that to mean that a change in the DC of a roll causes a large change (or "swing") in the probability of success on that roll. I'm using "swingy" in a bigger-picture sense: the experience of success or failure in an encounter resting on a roll whose probability falls in the 40-60%, which can result in a player feeling uncertain and out of control, because the encounter "swings" on the result of an effective coin toss. I'm certainly not contesting what you're saying about the effect of a normal distribution on the CMF. What I'm pointing out is that a normal distribution pushes the probability more quickly out of that uncertain middle ground and towards probabilities that players can feel more assured about. In short, it is exactly the feature that you call "swingy" that I say alleviates "swinginess". Weird, huh?
Now, you're right in principle that this same assurance-raising effect can be achieved with a uniform distribution by forcing all the DCs into low and high numbers. But this only works when you're dealing with one character with a known and fixed bonus to their roll. When comparing multiple characters with different bonuses, I don't see how you can make this idea work without the DM massaging the math on a character-by-character basis. With a normal distribution, the DM can take any DC, and the distribution itself will naturally push it into the low- or high-probability range (unless it's very close to the character's bonus). This, again, strikes me as an advantageous feature, if keeping most rolls in those ranges is your goal.
EDIT: I see you ninja'ed me in bringing up this "other swinginess".
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8 months ago ::
Sep 30, 2012 - 7:00PM
#49
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Quite simply, there is no advantage to the Gaussian distribution for binary effects.
Which is why almost all systems emplying a gaussian distribution is not binary but use graded successes and failures, something that just does not work as well with a flat distribution.
The problem you state lies in the binary effect rather than the gaussian distribution, especially as you speak about game-design in general and not D&D in particular.
Yes, normal distributions are acceptable in systems where there are degree of success without a cut-off chance for failure. That's basically why normal distributions are acceptable as means of generating earnings or damage. But frustratingly the vast majority of all RPG resolution systems really just boil down to a binary outcome. And a huge proportion of RPG's are using Guasian distributions to determine those outcomes.
For instance, FATE actually could have allieviated some of this issue by having it so all difficulties are centered on 0 and have it so that skill determined the number of dice you rolled and difficulty determined the acceptable range of deviance from 0. However, this is not how their system works. My point is this mistake is rampant in the gaming industry.
I've yet to encounter a system in the industry that is actually using complex distributions to implement degrees of success in a reasonable manner.
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8 months ago ::
Sep 30, 2012 - 7:34PM
#50
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Date Joined:
Aug 27, 2012
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I have read all this conversation and understood all the math, so when I skip talking about what you have been talking, know that it has been on purpose, because I am lazy.
I believe that no level of "swingyness" is universally fair for all types of checks in the D&D game. By "swingyness" I use TheCosmicKid's definition.
Anyway, I think it makes more sense to realize that certain ability scores are more reliable than others, so I'm thinking I will house rule like this:
Attack Rolls-> Use 1d20
Strenght Checks (non-combat, maybe grapple) -> use 3d6
Dexterity, Constitution or Intelligence[knowledge] checks -> use 2d10
Intelligence[not knowledge], Wisdom, Charisma -> use 1d20
Prolonged use of Charisma (extended debate that you want to resume in one roll, for instance) -> Use 3d6
I guess in some cases, 4d4 might even be an acceptable substitution.
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