Ovinomancer
No flips for you!
I've been clear all along: you cannot compare IQ distributions to 3d6 distributions. Despite both claiming to have normal distributions, 3d6 is the only one of the two that has a legitimate normal distribution; IQ has an artificial, forced normal distribution. The two are just fundamentally different things.The relevance of all this to the present discussion is lost on me.
No, you can't. A 100 IQ is not twice a 50 IQ. That's like saying 100th place in a marathon is twice 50th place in the same marathon -- it's nonsensical. This is because the numbers used for IQ are rankings, not values. 50 IQ is less than 100 IQ, and that's all that can be noted. You can expand that and compare to each step between, but that's it. You can't even say how much 50 IQ is less than 100 IQ because the distance between the rankings isn't uniform, like the distance between race finishes isn't uniform.Yes, natural numbers have various properties and relationships to one another. But that is equally true of the numbers used to label IQ score eg if my IQ is 50, and yours 100, we can both note that 100 is twice 50, that 75 is as much greater than 50 as it is less than 100, etc.
YES! FINALLY! IQ tells us a bit about the difference between our intelligences, 3d6 tells us nothing, and INT (if real) would also tell us something. None of them measure intelligence, though. So you can't go from a ranking of intelligence (IQ) to a pure chance distribution of real numbers (3d6) and then to another ranking/sometimes interval of intelligence (INT). The transitions make no sense -- you can't do it.Those observations about the properties of numbers tell us little or nothing about the relationship between my intelligence and yours. Similarly, the various observations you are making about the relationships between numbers generated by rolling 3d6 tell us little or nothing about ability scores in D&D, and the personal attributes that they notionally measure. That is why I am puzzled by your calling the association of mechanical stats with ability scores arbitrary. It's not arbitrary, as far as I can tell - the point of rolling scores is to establish those mechanical stats!
Bottom line -- this is false. This is like saying there's .5% of people that finish first in a race, so if you roll an 18 on 3d6, you also finish first the race. It makes no sense to say this, yet this is what you're trying to say when you try to equate the two. That they have similar percentages doesn't mean that they're actually the same thing, or can or should be compared.Bottom line: the likelihood of rolling an 18 on 3d6 is a bit less than .5%. There are IQ scores whose incidence in the population is, by definition, a bit less than .5%. If a player of D&D wants to say that rolling 18 for INT is a marker of having that degree of IQ, and puts forward as his/her reason for that that the likelihood of the dice roll result correlates to the incidence of the IQ score, that seems fine to me. If done accurately, this technique can be expected to yield a distribution of IQ scores among randomly generated D&D characters that at least approximates to the distribution of such scores in the general population.
THIS is the trap of statistics. You've heard the old saw 'there's lies, damned lies, and statistics.' There's a reason for this other than the general feeling that stats you don't like are suspect. It's because statistics lies to you by transforming data into a common language and letting your forget that the data aren't the stats -- that what you've done with your mathemagic isn't the reality. In this case, you're allowing the fact that someone abused reality to do math that doesn't mean what it appears to say -- the IQ distribution is false and arbitrary. The functions performed to create it should not be done with that data. While you can plug the numbers into a calculator and perform the process of determining the mean of IQ scores, the fact that IQ scores are ranks, not values, and lack any defined interval means that the result is meaningless. It's like taking all of the place finishes in a race, averaging them, and declaring that this has meaning -- it clearly doesn't because the average of 1st place through nth place isn't meaningful. IQ data, similarly, doesn't have a meaningful mean.
So, why then do researchers do it? Again, an old saw "all models are wrong, but some are useful." The IQ distribution is wrong, but it's useful in some ways. It's useful to compare points within the IQ distribution. It has no use outside of that (because it's too wrong to be useful outside of that). This is agreed with in many studies on IQ.
So, because of this, comparing the IQ set to 3d6, despite the fact that they have similar words and apparently similar values, is meaningless because the IQ data is of a completely different nature than 3d6 rolls. There's no transferable meaning.
Maxperson's method is exactly as valid as Hriston's method. Both are making arbitrary claims that are not backed by anything valid.The point that [MENTION=6787503]Hriston[/MENTION] was making to [MENTION=23751]Maxperson[/MENTION] and others, though, is that in their attempt to make a move along these lines they have failed to achieve a correlation of likelihoods. The reply was that they are aware of this, but are prepared to tolerate errors in approximation. Hriston then pointed out that the errors are so significant that they cast the whole project (of treating INT as corresponding to IQ/10) into doubt.
The result of the 3d6 roll is a number, which is intended to be a type of measure - not a measure of the quantity of some determinable property that is present (as I posted already, that makes no sense) but a type of ranking measure where position in the rank also corresponds, roughly at least, to population frequency of that degree of ability/aptitude.
No, the result of 3d6 roll is a number, it is not a measurement of any kind. That we then take it to use as a measure means it transforms from just a number into a new kind of data and loses some of it's properties along the way. For instance, if I roll a 3 and an 18 on 3d6, then those numbers are just numbers -- 18 is six times greater than 3, for instance. If I then use those numbers as INT scores, they change. 18 INT is no longer six times greater than 3 INT. It is greater, for sure, and I can (depending on edition) even state how many intervals greater it is, but I've lost the ability to say that it is six times greater.
The means that you can't map the distribution of 3d6 the roll to INT scores. The distribution of 3d6 requires you to take the mean of the rolls and the SD of the rolls, and that only has meaning if they are rational (you can do something similar on interval data, but INT isn't solely interval data). That math requires certain properties of the data to be meaningful. Those properties are missing with the ordinal data of INT.
We use the roll of 3d6 (sometimes) to generate a random number to assign to a measurement of an ability. This is a fine use for a random generator if we wish to have a random measurement within the range. What we should be careful of it mistaking the properties of the random generator for the properties of the measurement we wish to randomize. They are not the same thing.
This argument completely discounts character generation as meaningful declaration by the player. My problem with any argument that holds that the only factors that are important are only made during gameplay is that it ignores that character creation is a factor that also occurred during gameplay. It's special pleading that the ability scores and other factors chosen by the player have only a limited meaning while action declarations are superior to all other choices. I can't agree with this.I don't follow this either.
In D&D, being Sherlock Holmes is a consequence of action declaration and resolution. That is to say, the player can't just declare "I'm a genius who solves the mystery": rather, the GM frames the PC (and thereby the player) into some sort of challenging situation or other, the player declares action, adjudication takes place and we then learn what exactly has happened in the fiction.
If the player whose PC has 5 INT declares actions that turn upon intelligence, and the GM adjudicates them in such a way as the PC is revealed to be a genius, why is that the player's fault?