We can start our scientific inquiry by examining the distributions of both IQ and 3d6 statistics. Both IQ and 3d6 statistics are based around a standard distribution of scores. Given a 3d6 distribution having a mean of 10.5 and a standard deviation of 3.0 and IQ having a mean of 100 and a standard deviation of 15 it is possible to convert between the two via simple z-score formula [z= (score - M)/s)].
Using this formula we could determine a few things:
Int 18 = 137.5 IQ
Int 15 = 122.5 IQ
Int 12 = 107.5 IQ
Int 10.5 = 100 IQ
Int 7 = 82.5 IQ
Int 5 = 72.5 IQ
Int 3 = 62.5 IQ
The breakdown comes when one has character stat scores above 18 as well as as the IQ scores start to climb. This is because in the norming distribution there are few characters whom would actually have a stat score of 18 (0.539% of the population if using a z-table given an error of 0.05).
The ultimate problem is that one has to assume that the construct of intelligence (as defined by D&D) is the same as the construct of IQ (as defined by Wechsler or Stanford Binet) and that it differs from Achievement. It is my opinion, that the D&D statistic of intelligence really combines IQ and Achievement into a single statistic which is a methodological flaw from a social science perspective. However, its functionality in D&D really makes this point moot because WotC did not base ability score modifiers (i.e., bonuses) off normative distribution qualities. If they had, one would have had a bonus distribution that was something like the following:
| 3d6 Gaming Stat | Modifier |
|---|---|
| 20 | +3 |
| 19 | +2 |
| 18 | +2 |
| 17 | +2 |
| 16 | +1 |
| 15 | +1 |
| 14 | +1 |
| 13 | +0 |
| 12 | +0 |
| 11 | +0 |
| 10 | +0 |
| 9 | +0 |
| 8 | +0 |
| 7 | -1 |
| 6 | -1 |
| 5 | -1 |
| 4 | -2 |
| 3 | -2 |
Ultimately, I think it is fair to say that TSR/Wotc did not consult a applied statistician or social scientist when constructing their gaming tools. Therefore, they based it upon what sounded good or seemed logical. I would suggest taking this same perspective when gaming because most (if not all) gaming rules will not hold up to historical or scientific inquiry. Additionally, we do not want our gaming to be completely accurate because if it is held to the same scientific/historical accuracy then new products would take years to come out. One would also have to operationally define magic, a construct by its definition fail to appear in our reality.
