Give the dragon stats and this is what he comes up with!

[davv]

Here's a silly thought.

The probability of getting a certain value when rolling a number of dice is given by the binomial distribution, which is kinda close to the normal distribution. D&D and other RPG stats are made by rolling a number of dice (I think). Thus the probability of getting a certain stat value is approximately normal (with mean and deviation that can be found out by knowing how many dice are in play).

So if we had a real world statistic that followed the normal distribution and was reasonably related to the RPG stat, and we made the assumption that probability of getting a certain roll would be the same as the probability of a random person having that value of the statistic, then we could map RPG stats to real world metrics.

Find a way of measuring strength, do so with lots of people, then map the resulting curve to the probability distribution given by the dice rolls and you have a STR mapping. CHA's going to be right out (how do you put a number on it?). INT... probably is the easiest to fit.

Still, it's a big assumption that the probabilities are equal - and without it, you got nothing.

And I'm really tired and should sleep! I just thought it was a funny thing to think about, and so I posted it. Yeah, this only makes me look stranger, I know :)

Comments

[lhexa]

You would probably run afoul of the Central Limit Theorem. In short, it says that if you take any smooth distribution (not just a normal one), sample it repeatedly and take the means of those samples, then look at the distribution of these means, then as the sample size increases this distribution-of-means will more and more resemble a normal distribution. This plagues demographic studies, and is one of the reasons why normal distributions are taken a bit more seriously than they should be.

[davv]

Well, true, the statistic you're linking the approximate normal to would have to be (approximately) normal, itself. This is part of why I mentioned INT in particular - the real world equivalent, the intelligence quotient, is pretty much defined to be normal (and that seems to be a good fit, at least as far as I know).

[lhexa]

That's not what I meant. The statistic could be something wildly different than a normal distribution, but the distribution of means-of-samples would still end up normal with large enough sample sizes.

[davv]

Then I don't see the problem, since I'm not comparing means. I'm comparing the shapes of the distributions themselves: as you keep adding dice, the binomial distribution goes to the normal distribution; not just as far as mean and standard deviation goes, but in shape as well.

So there are really two "leaps of fancy" here: first, that the binomial for the number of dice used in D&D is close enough, and second, that the designers intended say, the probability of rolling an upper 10 percentile INT to be similar to the probability of an upper 10 percentile IQ. (Or same with STR and whatever strength statistic you'd use.)

Or are you meaning that the statistic for actual real world strength, or intelligence, or whatnot, is actually rather different from normal, but is masked by taking means so that it looks like the normal too much? Then what I said in the previous message should apply, I think.

[lhexa]

More the latter, but in retrospect, you're right that the theorem wouldn't be a cause of worry in this particular matter.