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<blockquote data-quote="Cadence" data-source="post: 8518552" data-attributes="member: 6701124">Certainly, there is no reason a location shift by a constant should work that well for modeling the difference between two arbitrary distributions.Does it work sort of ok for going between heights of adult men and adult women as they are roughly normal and the standard deviations aren't ridiculously far apart? (With any truncation for biological constraints so far out it doesn't particularly come in to play for general modeling.)On the other hand, it is ludicrous for going between the height of 3yo boys and adult human males.&nbsp; Not only is the mean very different, but so are the standard deviations.Is the case of halfling strength vs. human strength vs. Goliath strength better modeled for the die rolling case by using different dice?&nbsp; Maybe the Halfling is 2d4+d6, the human 3d6, and the Goliath d6+2d8 (or whatever).&nbsp; Perhaps let each roll an extra of the most common die type and discard the lowest roll.&nbsp; That gives the means and standard deviations both growing with size, as well as the maximums but not minimums.Coming up with a percentile based table for STR point buy based on that shouldn't be hard if the goal is maintaining percentiles.&nbsp; If the goal of point buy is to control total modifiers, then it could be done by limiting Halflings to, say 14, Humans to 18, and Goliaths to 24.If it's of concern the distributions are skewed you could take best of some dice, or disregard some numbers rolled, but that seems a lot of work to model only that approximately.Assuming one isn't capping things or using extra dice, is a location shift down for halflings (minimum 3) and location shift up for goliaths (maybe not capping) closer than doing nothing?</blockquote>

[QUOTE="Cadence, post: 8518552, member: 6701124"] Certainly, there is no reason a location shift by a constant should work that well for modeling the difference between two arbitrary distributions. Does it work sort of ok for going between heights of adult men and adult women as they are roughly normal and the standard deviations aren't ridiculously far apart? (With any truncation for biological constraints so far out it doesn't particularly come in to play for general modeling.) On the other hand, it is ludicrous for going between the height of 3yo boys and adult human males. Not only is the mean very different, but so are the standard deviations. Is the case of halfling strength vs. human strength vs. Goliath strength better modeled for the die rolling case by using different dice? Maybe the Halfling is 2d4+d6, the human 3d6, and the Goliath d6+2d8 (or whatever). Perhaps let each roll an extra of the most common die type and discard the lowest roll. That gives the means and standard deviations both growing with size, as well as the maximums but not minimums. Coming up with a percentile based table for STR point buy based on that shouldn't be hard if the goal is maintaining percentiles. If the goal of point buy is to control total modifiers, then it could be done by limiting Halflings to, say 14, Humans to 18, and Goliaths to 24. If it's of concern the distributions are skewed you could take best of some dice, or disregard some numbers rolled, but that seems a lot of work to model only that approximately. Assuming one isn't capping things or using extra dice, is a location shift down for halflings (minimum 3) and location shift up for goliaths (maybe not capping) closer than doing nothing? [/QUOTE]

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