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Message: <blockquote data-quote="stephenh" data-source="post: 1754743" data-attributes="member: 8620">I'm not going to get into which method of stat generation is best, but here is a break down of some of the Stat rolling methods I have seen discussed on there boards.First some quick notes on the method. 1) All scores are calculated after applying the minimum viable character cut. This is defined (as per PHB or DMG - not sure which off the top of my head) as: a) must have at least 1 stat above 13 and b) total stat modifiers must add up to +1 or more.2) Randomly rolled stats of 8 or less are assigned 0 points.3) For all methods I generate a million random characters (actually a million and 1) and generate the statistics below based on this sample. This does not represent a complete sample for any of the methods below (i.e. covering every possible combination), but a sample of this size will have very small and well behaved errors, which I have also given where appropriate. The advantage of this method is that it is very simple to do and it is trivial to add in different (and arbitrarily complex) stat generation methods.4) For each method I calculate:  a) The mean (this is the average normally used) points obtained by that method (and error on the value I give).   b) The median. For those who don't know this is another sort of average, and in my opinion is a fairer representation of the average in this case. It is the value in which exactly half the values are larger than or equal to and half are less than or equal to. This will always be an exact integer in these tests. (I believe it is fairer because the points distributions are non linear).   c) I also give the 25th and 75th percentile of each method. Roughly speaking 1 in four randomly rolled characters will have a points value less than or equal to the 25th percentile and 1 in for will have a points value greater than or equal to the 75th percentile. i.e. in the "average" group of 4 characters, 1 will have a points value <= 25th percentile, 2 will have characters with points values between the 25th and 75th percentile, and one will have a character with a points value >=the 75th percentile.  d) Finally I give the average (mean) set of stats rolled using each of the given methods, in order from large to small. I can add other methods if anyone wants them.[code]3d6roll 3d6 and take the result.mean   = 24.685 +/- 0.005median = 2425th percentile 2175th percentile 28mean "stat array" 15.482 (+/- 0.001) 13.668 (+/- 0.001) 12.292 (+/- 0.001) 11.007 (+/- 0.001)  9.589 (+/- 0.001)  7.668 (+/- 0.002)4d6 drop lowroll 4d6 and drop the lowestmean   = 30.927 +/- 0.008median = 3025th percentile 2575th percentile 36mean "stat array" 15.949 (+/- 0.001) 14.455 (+/- 0.001) 13.228 (+/- 0.001) 12.022 (+/- 0.001) 10.659 (+/- 0.002)  8.720 (+/- 0.002)4d6 drop low -- best of 7 rollsroll 4d6 and drop the lowest -- do 7 times and keep the best 6mean   = 34.020 +/- 0.008median = 3325th percentile 2875th percentile 39mean "stat array" 16.020 (+/- 0.001) 14.624 (+/- 0.001) 13.516 (+/- 0.001) 12.480 (+/- 0.001) 11.403 (+/- 0.001) 10.140 (+/- 0.002)4d6 drop low -- reroll all 1sroll 4d6 and drop the lowest, but also reroll all 1s rolledmean   = 37.724 +/- 0.008median = 3725th percentile 3275th percentile 43mean "stat array" 16.310 (+/- 0.001) 15.077 (+/- 0.001) 14.061 (+/- 0.001) 13.064 (+/- 0.001) 11.937 (+/- 0.001) 10.341 (+/- 0.002)5d6 drop 2 lowestroll 5d6 and drop the 2 lowestmean   = 38.543 +/- 0.009median = 3825th percentile 3275th percentile 44mean "stat array" 16.486 (+/- 0.001) 15.251 (+/- 0.001) 14.185 (+/- 0.001) 13.102 (+/- 0.001) 11.836 (+/- 0.002)  9.963 (+/- 0.002)[/code]</blockquote>

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