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(Discussion) Character Points Change Issue
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<blockquote data-quote="orsal" data-source="post: 1597411" data-attributes="member: 16016"><p>OK, agreed, although to nitpick that should be 16^6. (Fenceposts again.)</p><p></p><p></p><p></p><p>That was exactly what I was referring to above when I wrote</p><p></p><p></p><p>My spreadsheet as it stands does not take that rule into effect. I could fix it to throw out characters with no score at least 14 (takes a little thinking, if you want I'll explain how and why it works, but mathematics is already boring most of our readers, and this would only make it worse), but I don't think I could fix it to require a net +1 or higher. However, if scores are rolled with 4d6, and the character is guaranteed at least one +2, it is very unlikely that the sum of the ability modifiers will be 0 or less, so that won't alter the average very much.</p><p></p><p></p><p></p><p>That doesn't matter. So long as I compute the average of the point buy counts, rather than the ability scores, of the individual abilities, I'll get the average of the sum of the point buy counts when I multiply by six. The reason is this: if you have any number of random variables (let's say six, call them S, D, C, I, W, X), the expected value (i.e. mean average) of (S+D+C+I+W+X) is the sum of the individual expected values. That's a theorem from probability theory.</p></blockquote><p></p>
[QUOTE="orsal, post: 1597411, member: 16016"] OK, agreed, although to nitpick that should be 16^6. (Fenceposts again.) That was exactly what I was referring to above when I wrote My spreadsheet as it stands does not take that rule into effect. I could fix it to throw out characters with no score at least 14 (takes a little thinking, if you want I'll explain how and why it works, but mathematics is already boring most of our readers, and this would only make it worse), but I don't think I could fix it to require a net +1 or higher. However, if scores are rolled with 4d6, and the character is guaranteed at least one +2, it is very unlikely that the sum of the ability modifiers will be 0 or less, so that won't alter the average very much. That doesn't matter. So long as I compute the average of the point buy counts, rather than the ability scores, of the individual abilities, I'll get the average of the sum of the point buy counts when I multiply by six. The reason is this: if you have any number of random variables (let's say six, call them S, D, C, I, W, X), the expected value (i.e. mean average) of (S+D+C+I+W+X) is the sum of the individual expected values. That's a theorem from probability theory. [/QUOTE]
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