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Message: <blockquote data-quote="EzekielRaiden" data-source="post: 6866284" data-attributes="member: 6790260">Uh...no, it's not anymore. You've changed the center of the data by changing the produced results--you're throwing out all arrays that don't meet certain standards, so the distribution of kept arrays is quite different from the average. It's quite easy to demonstrate the effect.For example, consider 4d6-L, where we throw out any set of 6 where the sum of the modifiers is 0 or less or the highest stat is 12 or less (inclusive or, there). I'll use Anydice to generate 3000 rolls of highest 3 of 4d6 (the equivalent of 500 test characters--plenty big enough for the kinds of numbers we want, and because I was going to do 1000 and got incredibly bored formatting the numbers so I could process them in Excel).Edit: Expected/"ideal" average of 4d6-L: 12.24Averages without any modification of 4d6-L: {12.328, 12.322, 12.32, 11.916, 12.114, 12.282} Net average 12.21367 (Note: not sure why the fourth column's average was so low--just a random fluke, I guess)Averages after removing all arrays with net mod of 0: {12.48812095, 12.4838013, 12.4924406, 12.03455724, 12.27861771, 12.49460043} Net average 12.37869Averages after removing all remaining arrays with max under 13: {12.49891068, 12.49673203, 12.50326797, 12.05228758, 12.28976035, 12.51198257} Net average 12.39216 (Note: this only appears to have removed 4 arrays at this point, which is probably why the impact is almost invisible. The two rules cover many redundant cases.)Incidentally, these changes also shifted the median of several of the columns up by 1--no trifling feat, since the median is supposed to be a robust statistic. So, no, it is not true that removing those arrays which don't meet the standards has no effect on the averages. It may not be a huge increase, but it's definitely an increase. And this doesn't even include any attempt to capture the "beg your DM to let you reroll because two 16s/17s isn't worth having two 4s/5s" kind of situation, where an array juuuuuust barely passes the minimum requirements but are still crappy. Being able to cajole the DM into letting you reroll a merely mediocre array will push these results even higher (since such things will almost exclusively apply sets near the low end). The exact effects are harder to estimate, since what exactly counts as "too crappy to keep" will vary a lot, but (for example) removing arrays with averages less than 11.5 results the averages shifting up another .25 or so--meaning an extra 1.5 stat points on average over the modified set, or very close to 4 extra points over the completely unmodified set. Small? Perhaps, but a statistically significant shift.(As a side note: 269/459 of the end-modified results contain at least one 16. That's approx. a 58.6% chance of getting at least one score better than you could possibly get in 5e's point-buy system, and only 89/459 = 19.4% chance of getting no stats better than what you could get via point-buy. 'Course, that means you'd expect about one player at every rolling-only table to lose out...but it's still clear that, if you're a minmaxer, you want to roll, not point-buy. Being able to cajole in the suggested manner--when the average stat is below 11.5--boosts the chances of getting at least one 16+ to almost exactly two-thirds, for example.)Edit: I've saved the Excel file, if you want to examine my math. I also have the original data set--6000 values, of which I only used the first 3000, arranged into sets of six to make 500 entries. You'll need to do some formatting to get most of the 500 unused sets to play nice with Excel (I strongly recommend TextPad if you're going to do that--Block Select is beautiful), but it's available if you want it.Edit II:Perhaps I should rephrase the "Uh, no it's not" comment. Yes, you're absolutely correct that the average result of 3d6 remains 10.5, even if you choose to ignore any result less than 8. No, you are not correct if you are trying to say that the average of the things you keep remains unchanged--which is what I was talking about.Rolls you could get from the dice, but which aren't acceptable for play, should not be counted in the average. But because it would be a statistics nightmare to try to account for those two rules (lowest max score must be 13+, net modifier must be > 0), people just go with the nice, easily-estimated results like AnyDice does. (Incidentally, the slightly-better "standard array" in 4e could be argued to have shifted to take into account the rules that boost the averages.)</blockquote>

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