Help me understand "average rolls"

[shadowlight]

Re: Re: Re: Help me understand "average rolls"

Is it? Look at the rest of the quote from the PHB (emphasis added):

"...so he will get a check result of 17 or 18 with his Perform checks."

It seems to assume that most of Devis' rolls will be in a certain range, which suggests frequency...

I disagree, to me this seems to be saying that on average he will get a check result of 17 or 18 which is exactly the case. I think the PHB writers know what they're talking about here and it seems pretty clear to me.

Looking at James Beach's article, I can't understand why he assumes that "On average, Devis will roll 10 or 11 on the d20.." is referring to frequency. It seems pretty clear that it's talking about long run averages.

Also, I had way too much stats in grad school so if you're interested in this kind of thing, I'd recommend you do a search on the Central Limit Theorem...

 

[Guilt Puppy]

Re: Re: Re: Help me understand "average rolls"

"...so he will get a check result of 17 or 18 with his Perform checks."

It seems to assume that most of Devis' rolls will be in a certain range, which suggests frequency.

In a sense, it does... You have to keep in mind that D&D checks are (typically) all-or-nothing... In these all-or-nothing circumstances, you have either success or failure. The 17 or 18 (again, not stated as 17.5 to avoid confusion) simply means that, on average (which is to say, more often than not), he will succeed at those perform checks.

Now, you'll note that this is somewhat misleading if you take it as 17.5: On DC's of "17.5" (if they could exist), there's a fifty-percent chance of success and failure (instead of "more often than not")... However, you'll note that this is accounted for in the mechanic... The result of 10 (which is what the example states), if successful, accounts for 55% of possible rolls (which are essentially identical, because they are successful). So, if he will succeed on rolling a 10, he will succeed more often than not -- which brings us back to mode, curiously.

Basically, the explanations may not be totally mathematically accurate, but that's because they're trying to explain it in terms which are easy to understand -- which is exactly what they should be doing. Any system that goes into as much detail as I just did (which isn't very much at all, really, but still too much) to explain a simple concept in its core rulebooks is not one I'd like to take the time to learn: Just get the general idea across so that I can understand and use the system, and if I'm curious, then I'll take the time to check up on the math.

 

[Darkness]

I prefer using 2d10 instead of 1d20 just because it cuts down on randomness (i.e., by giving more predictable results).
IMO, skill (and magical bonuses to same ) should be much more important than chance. YMMV, of course.

 

[Zappo]

I prefer using 2d10 instead of 1d20 just because it cuts down on randomness (i.e., by giving more predictable results).
IMO, skill (and magical bonuses to same ) should be much more important than chance. YMMV, of course.

Yeah, but "the d20 system" sounds a lot better than "the 2d10 system".

 

[Desdichado]

I've never done it, but I've also toyed with the idea of swapping the d20 for 2d10 for that same reason. Hmmm...

 

[Nine Hands]

I've never done it, but I've also toyed with the idea of swapping the d20 for 2d10 for that same reason. Hmmm...

I've had similar thoughts

 

[buzz]

Thanks and three d20's

I've had similar thoughts

First, thanks to everyone who helped clear this up for me. I still think the wording could have been more explicit, but that's me.

Anyway, besides the 2d10 option for you curve-lovers out there, one of the mroe interesting options I've heard of is to roll 3d20 and drop the highest and lowest results. It's creates a frequency curvem but not one that's steep enough to throw off the bonus system used in d20. A good option for those with large die collecitons.

 

[dcollins]

What a wierd article. "Technically one may arrive at a mathematical mean of 10.5, or find the median values of 10 or 11 on 1d20, but when speaking of dice and perhaps probabilities, what one desires to know is the mode."

I can't think of anyone who commonly uses the word "average" to mean "mode". In fact, it's the last meaning of "average" that anyone usually thinks of.

The average of a d20 roll is indeed around a 10 or 11. It's pretty odd to see someone rephrase that to say "most frequently" and then get irritated that the rephrased statement is incorrect.

 

[Drawmack]

I would not recomend using 2d10 instead of 1d20 for two reasons.

1) When selecting a DC it is very simply to calculat success ratio. (21 - Roll needed) * 5 = % chance of success. Makes designing adventures easy.

2) Drastic alteration to game balance. The rules were deisned with a d20 in mind not 2d10s when you use 2d10s you are changing the entire balance scenrio of the game. Also you could be doing away with critical failure and if you do not then you affect game balance even more drastically. Let's take a look at it from a statistical point of view.

When you roll two dice and add them together you begin to represent a bell curve. This anamoly happens because of the number of combinations that can make any given number.

When you take the set of possible results from adding 2d10 together it is 20, if you take the roll of 0,1 as a 1 and the roll of 0,0 as a 20. We will assume this for all future calculations since it is accepted practice to make 00 = 100 and 01 = 1 when using 2d10 for precentile rolls. You have 100 (10*10) possible rolls and only 20 possible out comes. However the number of combinations that make any given number are not equal which is where the bell curve representation comes from.

Variables
x = size of die (4,6,8,10,12,20)
y = target number
n = number of rolls that gives any result.
m = number of dice rolled.

I do not know the general formula but the formula for this particular is is

y < 11; 1 + y
y = 11; 8
y > 10; 1 + (20 - y)

The anamoly at 11 happens because we steal 2 11s to make 1s. So the odds of beating a given DC become very difficult to calculate and therefor a fair challenge becomes difficult to design. The benefit gained is very small for the complexity added therefor sticking with 1d20 is a better alternative then 2d10.
[/color]

 

[buzz]

The average of a d20 roll is indeed around a 10 or 11. It's pretty odd to see someone rephrase that to say "most frequently" and then get irritated that the rephrased statement is incorrect.

FWIW, the first time I read the Devis quote was long before I ever read the article, and I was a little confused. When I hear "average roll", I tend to think "most frequent result." It might also be that the "10 or 11" triggered an association (to me, at least) with 10 or 11 on 3d6, which is the top of the bell curve for that die combination.