This is more of a brief rant than a full-fledged discussion topic.

I hate bad statistics.  Or, put another way, a little knowledge can be dangerous.

I was reading through an otherwise good (if dangerously Narrative) roleplaying game I won in a contest recently, and I got to the following passage explaining the statistics of rolling a single d12:

QuoteThe Narrator should keep in mind that a modest Virtue (3) should succeed in an average task requiring a roll about half the time. Let’s work backwards from a successful roll (i.e., 13) and see what modifier would be required to allow a Virtue of 3 to succeed half the time. Since an average roll on a d12 is about 7 (6.5 actually), a good base modifier for an average task is +3 or +4 to insure those kinds of odds...

I was slapping my forehead red.  Of course, the average roll on a d12 -- or any single die -- is even odds for any single face.  D'uh!  You don't start to get "average" results until you combine the result of two or more dice.  What the author was referring to is the median, an awfully basic element of statistics, and it occurs no more regularly than 1 or 12, or any of the other possible numbers.  Why didn't the author realise this?  Why did no one point this out before the book went to print?

Yeah, sure, it's kind of a minor point, but if you're going to work with numbers, really, really try to understand what the numbers mean and how they work.

!i!

[Edit:  Oops.  I left off part of the quoted passage.]

Not to be nitpicky back, but an "average" can be the mean, median or mode. So yes, the average should be the median on a single die.

Right, right.  When I put the word "average" in quotation marks, I meant to imply that what the author appeared to be looking for was an arithmetic mean.  His apparent assumption was that 6 or 7, the two numbers smack-dab in the middle of the 1-12 array, were the most commonly occurring results.

Now, looking at his mechanic a little closer, what he's asking for is a 50% success rate from a d12+stat+modifier roll against a target number of 13.  When it's couched in these terms, I have to be more forgiving.  If a typical character stat is 3, and the typical modifier is 3, then the range of results will be 7 to 18, with no single result being more likely than another, but, yes, half of the rolled results will meet or exceed the target number of 13.

It was just the wording of the author's statement that seemed to suggest a disconnect between his understanding of how his mechanic worked and how the results of a die roll are really generated.

!i!

Quote from: Ian Absentia;267990Now, looking at his mechanic a little closer, what he's asking for is a 50% success rate from a d12+stat+modifier roll against a target number of 13.

Okay, now, picking at this a little more closely, if you want your typical rolled result on a d12 to meet or exceed 13, why have a modifier at all?  If you'd typically modify every roll by +3 to achieve that 50% success rate, why not just raise the typical stat value from 3 to 6?  That way, an unmodified roll for your typical character's stats will generally beat the target number of 13 50% of the time.

You know what the problem was?  The author was going for this thematic use of the numbers 3, 7, and 13 -- common numbers encountered in fairy tales.  Every character has three stats, and the value of those stats is determined by dividing 13 points between them, with a maximum value of 7 (and a minimum of 1).  The net effect is that the over-weening desire to adhere to a theme ends up complicating otherwise simple mechanics.  Bah.

!i!

Ian, I think you're being too hard on the author, because you started from the assumptino that he was trying to work from the "most common" result on the dice. Instead he was trying to find the modifier that gave a close to 50/50 chance.

IMO it's perfectly reasonable to write "average" for the mean of a random variable. (The sum of any number of dice can be thought of as a discrete random variable.)

Also, the arithmetic mean of a die is the same as the mean of the values on its faces, which is also the same as the median if the faces are numbered consecutively.

That said, you're right that it's pretty dumb to give rules for back-calculating the modifier for attempting an average task with an average ability. I'd call that bad rules engineering.

In context, it makes no difference, since the authour's talking about how big a bonus to give to a roll to make it more likely that a particular result will come about.

What annoyed me was that they wanted to "insure those kinds of odds."

You insure against things happening, and you can ensure that something happens. But you cannot insure odds. It's like the affect/effect confusion.

Of course you missed that, Ian. So if you were writing, then I'd be annoyed by what you'd written. Lesson learned? Cut them some slack

Quote from: Elliot Wilen;268015Also, the arithmetic mean of a die is the same as the mean of the values on its faces, which is also the same as the median if the faces are numbered consecutively.

Ah, true.  "Average" is one of those words that's come to have a common connotation that leads to confusion when you intend a less common one.  And, yeah, I'm being too hard on the author.  The mechanic works, but I found the commentary confounding.

!i!

If I have said it once, I have said it a million times:

Statistics are like nuclear weapons.  If you don't know what you are doing, don't fuck around with them.

I think you're nitpicking a problem that doesn't actually exist. There's a difference between 'Doesn't understand' and 'Not getting overly technical'. It's an RPG, not a high-school math book.