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<blockquote data-quote="Xeriar" data-source="post: 759456" data-attributes="member: 4116">You can use the standard deviation formula, inputting it into Excel or some other program, say.For example, 3d6 has a mean of 10.5 and a Standard Deviation of ~2.95.&nbsp; This is a little rough, but you can verify it for yourself.Over 2/3rds of the population is within one Standard deviation of the mean (7.55-13.45), another 2/7ths are between one and two deviations (4.6-7.55 and 13.45-16.4), 2/46ths (1.65-4.6, 16.4-19.35)...As you can see, this is an approximation, and it also extrapolates beyond what the dice can physically represent.&nbsp; This can be useful for determining what a given ability score should mean (if you're paying careful attention to detail <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f61b.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":-p" title="Stick out tongue&nbsp; &nbsp; :-p"&nbsp; data-smilie="7"data-shortname=":-p" /> )As more deviations get factored in, the probabilities get drastically smaller, of course - one in a billion for being six standard deviations above the mean, even (which would equate to a half dozen people on earth with an intelligence score of 28 - maybe one with a 29).</blockquote>

[QUOTE="Xeriar, post: 759456, member: 4116"] You can use the standard deviation formula, inputting it into Excel or some other program, say. For example, 3d6 has a mean of 10.5 and a Standard Deviation of ~2.95. This is a little rough, but you can verify it for yourself. Over 2/3rds of the population is within one Standard deviation of the mean (7.55-13.45), another 2/7ths are between one and two deviations (4.6-7.55 and 13.45-16.4), 2/46ths (1.65-4.6, 16.4-19.35)... As you can see, this is an approximation, and it also extrapolates beyond what the dice can physically represent. This can be useful for determining what a given ability score should mean (if you're paying careful attention to detail :-p ) As more deviations get factored in, the probabilities get drastically smaller, of course - one in a billion for being six standard deviations above the mean, even (which would equate to a half dozen people on earth with an intelligence score of 28 - maybe one with a 29). [/QUOTE]

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