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Message: <blockquote data-quote="Mercule" data-source="post: 6875295" data-attributes="member: 5100">There seems to be a basic misunderstanding of statistics, here. We're discussing the final results. If you discard some rolls, that's part of the method. Any sets that are discarded are explicitly outside the sample, which means they don't factor into the average. It's true that there is no difference in the odds of a particular result being rolled. There is a definite difference in the odds of a given result being used, which changes the sample mean.To determine what the average scores under a given method are, you must include only those scores that are accepted as part of that method. For ease of math, let's talk about the 1d6, reroll 1s method.Using a d6, the probability of rolling a "1" is 16.6%. The probability of having a result of 1 is 0% -- because 1s are explicitly excluded from the sample. The probability of rolling a 6 is 16.6%, but the probability of having a result of a 6 is 20%. You've just turned the d6 into a functional d5+1 for actual results and you'd probably be better served by using a d10 with results of 6-10 counted as 1-5. The meaningful results are identical.Because we really only care about results, trying to separate the mid-point rolls is pointless pedantry. In fact, most folks don't give a rip about the rolls, as such, and are just as happy to use the term "roll" to refer to the final results because that's the only meaningful point of conversation.If you exclude all sets (a.k.a. rolls) that have any scores lower than 8 or have two scores below 10 or have an average of under 12, then those sets are, well, excluded from the sample. That means the mean is going to be different (higher) than a table that has different rules for discards.Yes, it's true that statistics tend to suck with a small sample size. Any given table could have quirky luck, up or down. With sets of dice, however, we aren't limited to a small sample of a theoretic infinite population. We have quantum, identifiable values that can be projected out over that theoretic infinite population. The more times we use a method the more it will tend to have cumulative results that fit the infinite curve.You raise an excellent point about the coin flip for whether a given roll is discarded, though. This, IME, is one of the biggest issues with rolling for stats: There's almost always an arbitrary threshold for rerolls. By "arbitrary", I mean that it generally isn't a hard-and-fast, explicit rule. The DM looks at the set and rules. That makes the actual impact pretty much impossible to calculate because it can't be measured.I don't mind some randomness in my character generation -- in fact, I think I'd prefer it. I just think that's its really important to be able to know three things: 1) the mean, 2) the distribution range, 3) the standard deviation.I can live with an average result of 10.5 or 12 or 16, but each is going to give me slightly different expectations. Also, how much could I suck compared to the "average" (or best) character in the group? I don't really want to be relegated to sidekick status, and definitely not to page for the sidekick. Finally, what are my odds of having an unusually good or bad character? I'm not comfortable with having a high likelihood or playing that lackey, but it might be fun to get stuck with it once.Ideally, I think I'd like to see a mean around 12, maybe slightly higher. I wouldn't want the range to be too broad; maybe +/-4 (8-16), for most characters. The standard deviation is key, though; having mathematic sameness isn't ideal, but it's a lot better than archmages and grogs.Just as a gut reaction, using 4 FATE dice might give the right spread. It might also be too tight to use for all stats.</blockquote>

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