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<blockquote data-quote="TheCosmicKid" data-source="post: 7138642" data-attributes="member: 6683613">Both you and&nbsp; @<a href="http://www.enworld.org/forum/member.php?u=6787650" target="_blank">Hemlock</a> are right about this. The 3E point buy values, and plausible extrapolations from the 5E values, do overvalue 17s and 18s. But even if you drop those values really low, the average of the random roll comes out ahead. The high scores simply aren't probable enough for their value to have a huge effect on the average: most of that figure is determined by the 8-15 range. It's almost the same situation for the low scores. Now, because you can give them negative values and go as low as you want, it is possible to push the random average to the same point value as the base array, or lower. But because those low numbers are really improbable, you have to go really low -- indisputably putting your thumb on the scale.However, when you stop playing with point buy values and just look at the raw probabilities, you find that the average scores of 4d6k3, from highest to lowest, are [15.66, 14.17, 12.96, 11.76, 10.41, 8.50]. That's pretty darn close to [15, 14, 13, 12, 10, 8]. Average difference of about +0.24. Yeah, rolling is better, and if I really wanted to make the standard array fair compared to rolling I'd probably round up instead of down on that 15.66. But even as-is, it's not like the standard array sucks compared to the average rolls. The gap is pretty small, and I suspect Hemlock is overinterpreting it. It's literally a rounding error.</blockquote>

[QUOTE="TheCosmicKid, post: 7138642, member: 6683613"] Both you and @[I][B][U][URL="http://www.enworld.org/forum/member.php?u=6787650"]Hemlock[/URL][/U][/B][/I] are right about this. The 3E point buy values, and plausible extrapolations from the 5E values, do overvalue 17s and 18s. But even if you drop those values really low, the average of the random roll comes out ahead. The high scores simply aren't probable enough for their value to have a huge effect on the average: most of that figure is determined by the 8-15 range. It's almost the same situation for the low scores. Now, because you can give them negative values and go as low as you want, it [I]is[/I] possible to push the random average to the same point value as the base array, or lower. But because those low numbers are really improbable, you have to go [I]really[/I] low -- indisputably putting your thumb on the scale. However, when you stop playing with point buy values and just look at the raw probabilities, you find that the average scores of 4d6k3, from highest to lowest, are [15.66, 14.17, 12.96, 11.76, 10.41, 8.50]. That's pretty darn close to [15, 14, 13, 12, 10, 8]. Average difference of about +0.24. Yeah, rolling is better, and if I really wanted to make the standard array fair compared to rolling I'd probably round up instead of down on that 15.66. But even as-is, it's not like the standard array [I]sucks[/I] compared to the average rolls. The gap is pretty small, and I suspect Hemlock is overinterpreting it. It's literally a rounding error. [/QUOTE]

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