Game statistics tied to the value. You yourself mentioned how a given STR means you can lift a given amount, did you not? This is new information added to the ability score that is not present in the 3d6 roll. The 3d6 roll has not such information until and unless you transform it into an ability score. At that point, it loses it's rational nature, becomes ordinal or interval data (depending on application) and gains new meanings.
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The result of rolling 3d6 generates a number. That number is just a number, and has all of the meanings that just numbers have. An 18 is just the number 18. Six times greater than the number three, and one more than 17.
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Frex. I roll 3d6. I get a 12. I know that 12 is 4 times a 3, and one more than 11. If I continue to roll 3d6, I get a set of numbers that I can run a statistical model on. The parameters of this model happens to have a nice normal distribution.
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I decide to play D&D. I assign my roll of 12 to CON. Now, I do not know that as 12 CON is four times a 3 CON. I have lost information. Depending on the edition, I do know that the difference between a 12 CON and an 11 CON is the same as between a 12 CON and a 13 CON, though (both are half steps towards a new bonus).
The relevance of all this to the present discussion is lost on me.
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.
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: 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.
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.
3d6 doesn't measure anything. IQ attempts to rank intelligences, and so is a kind of measure (one that only says this is more than that as you go higher). So, how can you possibly compare the measurement of intelligence that is IQ to the total non-measurement of the 3d6 distribution?
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.
Sherlock Holmes is a genius, almost by definition. A 5 INT is not a genius. It's below average, by definition. Therefore, since a 5 INT cannot be a genius, and since Sherlock Holmes is a genius, it is objectively wrong to play a 5 INT as Sherlock Holmes.
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?