|
-
Young & Lawful Good
United Kingdom
Redhill
Surrey
Support comes in many forms: community involvement, forum posts, submitting data, word-of-mouth advertising, financial donations... All of these are vital to this site, and you have my sincere thanks for participating in any of them.
Currently: banned as per http://rpggeek.com/article/9104203#9104203
-
IQ has a statistical definition (in terms of a median value and standard deviation). In this article I apply this definition to the randomly generated Intelligence scores in various RPGs (original/basic D&D, Call of Cthulhu, WFRP 1&2, Rifts).
IQ (Intelligence Quotient) is a statistical measure of relative levels of intelligence within a population. It is important to note that by its definition it is not a fixed value. Any given IQ test is normalised by using a sample population that should be representative of the total population for which the test is aimed. The resultant IQ values are then set so that the median value is 100 and a single standard deviation is 15 IQ points.
So for the total population, half of the people should have an IQ of less than 100 and half should have an IQ of more than 100. If we assume a normal distribution of IQ then that means:
 About 68.3% of the population have an IQ in the range of 85 to 115 (plus or minus 1 standard deviation)
About 95.4% of the population have an IQ in the range of 70 to 130 (plus or minus 2 standard deviations)
About 99.7% of the population have an IQ in the range of 55 to 145 (plus or minus 3 standard deviations)
This definition of IQ (median 100, standard deviation 15) can be directly applied to measures of intelligence in some role-playing games that have randomly generated attributes.
Original and Basic Dungeons & Dragons
"Intelligence" (Int) is determined by rolling 3d6. This has a symmetrical distribution so the median is equal to the mean of 10.5. The variance is 8.75, giving a standard deviation of approximately 2.958.
Int Prob IQ
3 0.5% 62.0
4 1.4% 67.0
5 2.8% 72.1
6 4.6% 77.2
7 6.9% 82.3
8 9.7% 87.3
9 11.6% 92.4
10 12.5% 97.5
11 12.5% 102.5
12 11.6% 107.6
13 9.7% 112.7
14 6.9% 117.7
15 4.6% 122.8
16 2.8% 127.9
17 1.4% 133.0
18 0.5% 138.0
Call of Cthulhu and Basic Role-Playing
"Intelligence" (INT) is determined by rolling 2d6+6. This has a symmetrical distribution so the median is equal to the mean of 13. The variance is 5 5/6, giving a standard deviation of approximately 2.415.
INT Prob IQ
8 2.8% 68.9
9 5.6% 75.2
10 8.3% 81.4
11 11.1% 87.6
12 13.9% 93.8
13 16.7% 100.0
14 13.9% 106.2
15 11.1% 112.4
16 8.3% 118.6
17 5.6% 124.8
18 2.8% 131.1
Warhammer Fantasy Roleplay (1st/2nd edition)
"Intelligence" (Int) is determined by rolling 2d10+20. This has a symmetrical distribution so the median is equal to the mean of 31. The variance is 16.5, giving a standard deviation of approximately 4.062.
Int Prob IQ
22 1.0% 66.8
23 2.0% 70.5
24 3.0% 74.2
25 4.0% 77.8
26 5.0% 81.5
27 6.0% 85.2
28 7.0% 88.9
29 8.0% 92.6
30 9.0% 96.3
31 10.0% 100.0
32 9.0% 103.7
33 8.0% 107.4
34 7.0% 111.1
35 6.0% 114.8
36 5.0% 118.5
37 4.0% 122.2
38 3.0% 125.8
39 2.0% 129.5
40 1.0% 133.2
Rifts
"Intelligence Quotient" (I.Q.) is determined by rolling 3d6. If the resultant score is over 15, you roll and add an additional 1d6. This has an asymmetrical distribution; in this particular case the median is equal to the mean of 3d6, which is 10.5. The variance is approximately 11.370, giving a standard deviation of approximately 3.372.
I.Q. Prob IQ
3 0.5% 65.9
4 1.4% 70.4
5 2.8% 74.8
6 4.6% 79.3
7 6.9% 83.7
8 9.7% 88.2
9 11.6% 92.6
10 12.5% 97.1
11 12.5% 101.5
12 11.6% 106.0
13 9.7% 110.4
14 6.9% 114.8
15 4.6% 119.3
16 0.0% 123.7
17 0.5% 128.2
18 0.7% 132.6
19 0.8% 137.1
20 0.8% 141.5
21 0.8% 146.0
22 0.8% 150.4
23 0.3% 154.9
24 0.1% 159.3
Rifts Chaos Earth
"Intelligence Quotient" (I.Q.) is determined by rolling 3d6. If the resultant score is over 15, you roll and add an additional 1d6. If this additional die comes up as a 6, you roll and add a fifth d6. This has an asymmetrical distribution; in this particular case the median is equal to the mean of 3d6, which is 10.5. The variance is approximately 12.126, giving a standard deviation of approximately 3.482.
I.Q. Prob IQ
3 0.5% 66.9
4 1.4% 71.2
5 2.8% 75.5
6 4.6% 79.8
7 6.9% 84.1
8 9.7% 88.4
9 11.6% 92.7
10 12.5% 97.0
11 12.5% 101.3
12 11.6% 105.6
13 9.7% 110.0
14 6.9% 114.3
15 4.6% 118.6
16 0.0% 122.9
17 0.5% 127.2
18 0.7% 131.5
19 0.8% 135.8
20 0.8% 140.1
21 0.8% 144.4
22 0.3% 148.7
23 0.2% 153.0
24 0.1% 157.3
25 0.1% 161.6
26 0.1% 166.0
27 0.1% 170.3
28 0.1% 174.6
29 0.1% 178.9
30 0.0% 183.2
Other RPGs
I am happy to entertain requests for other RPGs as well. Note that this analysis cannot be performed on systems that use fixed values or an allocation of points (since there is no probability distribution to analyse). Suitable games are listed under the Random Attribute Generation (during Character Creation) mechanic (although not all of these necessarily include an intelligence attribute).
Some specific exclusions:
Other editions of Dungeons & Dragons and Pathfinder - There are several different methods of generating ability scores. Each of these gives different median values and standard deviations. Without specifying which one to use, or in which proportion to apply to all of the methods, a single mapping to IQ is not possible.
Warhammer 40,000 Roleplay - Each individual RPG uses a different calculation: Dark Heresy (2d10+20), Rogue Trader (2d10+25 modified by Origin Path), Deathwatch (2d10+30), Black Crusade (2d10+25 or 2d10+30). Since they are all part of the same setting, the measures for IQ cannot be derived without knowing the relative population proportions for each character type. But note that a straight 2d10+20 score has been covered above for Warhammer Fantasy Roleplay.
|
|
|
A brief answer for you is that standard deviation is a measure of how spread out a set of data is, with a low number indicating that the data set mostly lies very close to the mean. (I'll add this to the glossary...)
