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So 5 Intelligence Huh
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<blockquote data-quote="Hriston" data-source="post: 6864028" data-attributes="member: 6787503"><p>This is a good point, and it brings to my attention the fact that, with AD&D, Gygax abandons a straight 3d6 as a score generation method for any type of character and creates a firm distinction between what he calls "general" characters and the exceptional individuals that have a character class. Because an averaging d6 generates the set of numbers {2, 3, 3, 4, 4, 5}, instead of {1, 2, 3, 4, 5, 6}, general characters end up with scores between 6 and 15, with a much higher chance of a 10 or 11 (44.44% versus 25%) in a given ability. Furthermore, if we assume this is a clarificaton of Gygax's original intent (as I believe much of AD&D actually is), rather than a revision, then 3d6, as it is used in OD&D (not sure what Basic has to say on this matter), emerges as a method of generating scores for PCs that are more extreme (but not necessarily better) than the average character's, as it continues to do in AD&D for non-prime abilities in NPCs of an exceptional nature.</p><p></p><p>In fact, this gives me a great idea about doing a zero-level campaign where we roll our stats with averaging dice. </p><p></p><p>Changing this assumption about the distribution (or likelihood) of ability scores in the general population of a D&D world, of course, changes the relationship between the probability of a given ability score and the probability of a given IQ score. I've worked out the conversions for both methods of score generation, and the formula I've used to describe this relationship is: IQ=100+(Int-10.5)(15/s) where s is the standard deviation of the set of generated values. The standard deviation of 3d6 is about 2.96 whereas the standard deviation of 3 averaging d6 is about 1.66, so it changes the comparison significantly. To be clear, I'm using the definition of IQ that gives it a mean of 100 and a standard deviation of 15. You could, of course, as @<em><strong><u><a href="http://www.enworld.org/forum/member.php?u=23751" target="_blank">Maxperson</a></u></strong></em> has done in this thread, posit a type of <em>fantasy</em> IQ that has some other distribution.</p><p></p><p>I'm sharing the results for a few reasons. I think some might find it interesting, although I realize that @<em><strong><u><a href="http://www.enworld.org/forum/member.php?u=16814" target="_blank">Ovinomancer</a></u></strong></em> in particular seems to be rather disapproving of "mathturbation", as he calls it, although he does seem to enjoy talking about it, and the flatulence of certain fantasy creatures, quite a bit. I myself have been won over by the averaging dice method, which comes close enough, at least at the lower end, to @<em><strong><u><a href="http://www.enworld.org/forum/member.php?u=23751" target="_blank">Maxperson</a></u></strong></em>'s Int x 10 formulation that it seems likely that he'll be as satisfied with the results as I am and may even claim to be vindicated by them. I must point out, however, that while Intelligence 5 does actually equate to an IQ of 50 under this method, as the Intelligence score rises above 11 the divergence from the Int x 10 formulation becomes more and more apparent. Also of note is how using averaging dice comes a little closer to the design ethos behind 5e's Commoner NPC with its straight 10s (or 11s, taking human racial bonuses into consideration) across the board. I've rounded the IQ scores to the nearest whole number, and I've highlighted in green the range of IQ scores that each method of score generation would produce for members of the general population.</p><p></p><table style='width: 100%'><tr><td>Intelligence</td><td>IQ if using 3d6</td><td>IQ if using 3 avg d6</td></tr><tr><td>1</td><td>52</td><td>14</td></tr><tr><td>2</td><td>57</td><td>23</td></tr><tr><td>3</td><td><span style="color: #00FF00">62</span></td><td>32</td></tr><tr><td>4</td><td><span style="color: #00FF00">67</span></td><td>41</td></tr><tr><td>5</td><td><span style="color: #00FF00">72</span></td><td>50</td></tr><tr><td>6</td><td><span style="color: #00FF00">77</span></td><td><span style="color: #00FF00">59</span></td></tr><tr><td>7</td><td><span style="color: #00FF00">82</span></td><td><span style="color: #00FF00">68</span></td></tr><tr><td>8</td><td><span style="color: #00FF00">87</span></td><td><span style="color: #00FF00">77</span></td></tr><tr><td>9</td><td><span style="color: #00FF00">92</span></td><td><span style="color: #00FF00">86</span></td></tr><tr><td>10</td><td><span style="color: #00FF00">97</span></td><td><span style="color: #00FF00">95</span></td></tr><tr><td>11</td><td><span style="color: #00FF00">103</span></td><td><span style="color: #00FF00">105</span></td></tr><tr><td>12</td><td><span style="color: #00FF00">108</span></td><td><span style="color: #00FF00">114</span></td></tr><tr><td>13</td><td><span style="color: #00FF00">113</span></td><td><span style="color: #00FF00">123</span></td></tr><tr><td>14</td><td><span style="color: #00FF00">118</span></td><td><span style="color: #00FF00">132</span></td></tr><tr><td>15</td><td><span style="color: #00FF00">123</span></td><td><span style="color: #00FF00">141</span></td></tr><tr><td>16</td><td><span style="color: #00FF00">128</span></td><td>150</td></tr><tr><td>17</td><td><span style="color: #00FF00">133</span></td><td>159</td></tr><tr><td>18</td><td><span style="color: #00FF00">138</span></td><td>168</td></tr><tr><td>19</td><td>143</td><td>177</td></tr><tr><td>20</td><td>148</td><td>186</td></tr><tr><td>21</td><td>153</td><td>195</td></tr><tr><td>22</td><td>158</td><td>204</td></tr><tr><td>23</td><td>163</td><td>213</td></tr><tr><td>24</td><td>168</td><td>222</td></tr><tr><td>25</td><td>173</td><td>231</td></tr><tr><td>26</td><td>179</td><td>240</td></tr><tr><td>27</td><td>184</td><td>249</td></tr><tr><td>28</td><td>189</td><td>258</td></tr><tr><td>29</td><td>194</td><td>267</td></tr><tr><td>30</td><td>199</td><td>276</td></tr></table></blockquote><p></p>
[QUOTE="Hriston, post: 6864028, member: 6787503"] This is a good point, and it brings to my attention the fact that, with AD&D, Gygax abandons a straight 3d6 as a score generation method for any type of character and creates a firm distinction between what he calls "general" characters and the exceptional individuals that have a character class. Because an averaging d6 generates the set of numbers {2, 3, 3, 4, 4, 5}, instead of {1, 2, 3, 4, 5, 6}, general characters end up with scores between 6 and 15, with a much higher chance of a 10 or 11 (44.44% versus 25%) in a given ability. Furthermore, if we assume this is a clarificaton of Gygax's original intent (as I believe much of AD&D actually is), rather than a revision, then 3d6, as it is used in OD&D (not sure what Basic has to say on this matter), emerges as a method of generating scores for PCs that are more extreme (but not necessarily better) than the average character's, as it continues to do in AD&D for non-prime abilities in NPCs of an exceptional nature. In fact, this gives me a great idea about doing a zero-level campaign where we roll our stats with averaging dice. Changing this assumption about the distribution (or likelihood) of ability scores in the general population of a D&D world, of course, changes the relationship between the probability of a given ability score and the probability of a given IQ score. I've worked out the conversions for both methods of score generation, and the formula I've used to describe this relationship is: IQ=100+(Int-10.5)(15/s) where s is the standard deviation of the set of generated values. The standard deviation of 3d6 is about 2.96 whereas the standard deviation of 3 averaging d6 is about 1.66, so it changes the comparison significantly. To be clear, I'm using the definition of IQ that gives it a mean of 100 and a standard deviation of 15. You could, of course, as @[I][B][U][URL="http://www.enworld.org/forum/member.php?u=23751"]Maxperson[/URL][/U][/B][/I] has done in this thread, posit a type of [I]fantasy[/I] IQ that has some other distribution. I'm sharing the results for a few reasons. I think some might find it interesting, although I realize that @[I][B][U][URL="http://www.enworld.org/forum/member.php?u=16814"]Ovinomancer[/URL][/U][/B][/I] in particular seems to be rather disapproving of "mathturbation", as he calls it, although he does seem to enjoy talking about it, and the flatulence of certain fantasy creatures, quite a bit. I myself have been won over by the averaging dice method, which comes close enough, at least at the lower end, to @[I][B][U][URL="http://www.enworld.org/forum/member.php?u=23751"]Maxperson[/URL][/U][/B][/I]'s Int x 10 formulation that it seems likely that he'll be as satisfied with the results as I am and may even claim to be vindicated by them. I must point out, however, that while Intelligence 5 does actually equate to an IQ of 50 under this method, as the Intelligence score rises above 11 the divergence from the Int x 10 formulation becomes more and more apparent. Also of note is how using averaging dice comes a little closer to the design ethos behind 5e's Commoner NPC with its straight 10s (or 11s, taking human racial bonuses into consideration) across the board. I've rounded the IQ scores to the nearest whole number, and I've highlighted in green the range of IQ scores that each method of score generation would produce for members of the general population. [TABLE="class: grid, width: 500"][TR][TD]Intelligence[/TD][TD]IQ if using 3d6[/TD][TD]IQ if using 3 avg d6[/TD][/TR][TR][TD]1[/TD][TD]52[/TD][TD]14[/TD][/TR][TR][TD]2[/TD][TD]57[/TD][TD]23[/TD][/TR][TR][TD]3[/TD][TD][COLOR=#00FF00]62[/COLOR][/TD][TD]32[/TD][/TR][TR][TD]4[/TD][TD][COLOR=#00FF00]67[/COLOR][/TD][TD]41[/TD][/TR][TR][TD]5[/TD][TD][COLOR=#00FF00]72[/COLOR][/TD][TD]50[/TD][/TR][TR][TD]6[/TD][TD][COLOR=#00FF00]77[/COLOR][/TD][TD][COLOR=#00FF00]59[/COLOR][/TD][/TR][TR][TD]7[/TD][TD][COLOR=#00FF00]82[/COLOR][/TD][TD][COLOR=#00FF00]68[/COLOR][/TD][/TR][TR][TD]8[/TD][TD][COLOR=#00FF00]87[/COLOR][/TD][TD][COLOR=#00FF00]77[/COLOR][/TD][/TR][TR][TD]9[/TD][TD][COLOR=#00FF00]92[/COLOR][/TD][TD][COLOR=#00FF00]86[/COLOR][/TD][/TR][TR][TD]10[/TD][TD][COLOR=#00FF00]97[/COLOR][/TD][TD][COLOR=#00FF00]95[/COLOR][/TD][/TR][TR][TD]11[/TD][TD][COLOR=#00FF00]103[/COLOR][/TD][TD][COLOR=#00FF00]105[/COLOR][/TD][/TR][TR][TD]12[/TD][TD][COLOR=#00FF00]108[/COLOR][/TD][TD][COLOR=#00FF00]114[/COLOR][/TD][/TR][TR][TD]13[/TD][TD][COLOR=#00FF00]113[/COLOR][/TD][TD][COLOR=#00FF00]123[/COLOR][/TD][/TR][TR][TD]14[/TD][TD][COLOR=#00FF00]118[/COLOR][/TD][TD][COLOR=#00FF00]132[/COLOR][/TD][/TR][TR][TD]15[/TD][TD][COLOR=#00FF00]123[/COLOR][/TD][TD][COLOR=#00FF00]141[/COLOR][/TD][/TR][TR][TD]16[/TD][TD][COLOR=#00FF00]128[/COLOR][/TD][TD]150[/TD][/TR][TR][TD]17[/TD][TD][COLOR=#00FF00]133[/COLOR][/TD][TD]159[/TD][/TR][TR][TD]18[/TD][TD][COLOR=#00FF00]138[/COLOR][/TD][TD]168[/TD][/TR][TR][TD]19[/TD][TD]143[/TD][TD]177[/TD][/TR][TR][TD]20[/TD][TD]148[/TD][TD]186[/TD][/TR][TR][TD]21[/TD][TD]153[/TD][TD]195[/TD][/TR][TR][TD]22[/TD][TD]158[/TD][TD]204[/TD][/TR][TR][TD]23[/TD][TD]163[/TD][TD]213[/TD][/TR][TR][TD]24[/TD][TD]168[/TD][TD]222[/TD][/TR][TR][TD]25[/TD][TD]173[/TD][TD]231[/TD][/TR][TR][TD]26[/TD][TD]179[/TD][TD]240[/TD][/TR][TR][TD]27[/TD][TD]184[/TD][TD]249[/TD][/TR][TR][TD]28[/TD][TD]189[/TD][TD]258[/TD][/TR][TR][TD]29[/TD][TD]194[/TD][TD]267[/TD][/TR][TR][TD]30[/TD][TD]199[/TD][TD]276[/TD][/TR][/TABLE] [/QUOTE]
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