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Probability vs. Point Buy
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<blockquote data-quote="Christian" data-source="post: 1751674" data-attributes="member: 381"><p>Average score on 4d6, drop the lowest, is about 12.25. Roughly, an 'average' character on the standard method would have 4 1/2 12's and 1 1/2 13's; 4+4+4+4+4.5+5 = 25.5 points. So 25 is fairly close. Of course, there's the increased cost of higher stats, the extra control-there's a balancing act there that can't be solved mathematically.</p><p></p><p>Interesting tidbit I worked out once relating the point-buy levels to attribute levels rolled on 3d6 flat. Since this is the presumed default for common NPC's overall, you can compare the probability curves for those rolls to the results of the different point buys to see where the 'heroic' PC's stand in relation to the bulk of metahumankind ...</p><p></p><p>Point Buy Percentile</p><p>15 50</p><p>21 75</p><p>25 90</p><p>28 95</p><p>32 99</p><p></p><p>Interesting to note that the standard numbers correspond to mathematically 'natural' divisions in the normal distribution. (Everyone who thinks Jonathan Tweet had something to do with this, raise your hand. <img src="data:image/gif;base64,R0lGODlhAQABAIAAAAAAAP///yH5BAEAAAAALAAAAAABAAEAAAIBRAA7" class="smilie smilie--sprite smilie--sprite1" alt=":)" title="Smile :)" loading="lazy" data-shortname=":)" /> ) If you think, for example, that heroes should have natural ability levels overall in the top 5% of the population, then 28-point buy is the right number for you ...</p></blockquote><p></p>
[QUOTE="Christian, post: 1751674, member: 381"] Average score on 4d6, drop the lowest, is about 12.25. Roughly, an 'average' character on the standard method would have 4 1/2 12's and 1 1/2 13's; 4+4+4+4+4.5+5 = 25.5 points. So 25 is fairly close. Of course, there's the increased cost of higher stats, the extra control-there's a balancing act there that can't be solved mathematically. Interesting tidbit I worked out once relating the point-buy levels to attribute levels rolled on 3d6 flat. Since this is the presumed default for common NPC's overall, you can compare the probability curves for those rolls to the results of the different point buys to see where the 'heroic' PC's stand in relation to the bulk of metahumankind ... Point Buy Percentile 15 50 21 75 25 90 28 95 32 99 Interesting to note that the standard numbers correspond to mathematically 'natural' divisions in the normal distribution. (Everyone who thinks Jonathan Tweet had something to do with this, raise your hand. :) ) If you think, for example, that heroes should have natural ability levels overall in the top 5% of the population, then 28-point buy is the right number for you ... [/QUOTE]
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Probability vs. Point Buy
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