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Message: <blockquote data-quote="Arial Black" data-source="post: 6877877" data-attributes="member: 6799649">Sorry, I was called away before I could explain properly. I'll try again.I can't use 1d6 as my example because it doesn't produce a bell curve, so I'll use 2d6 because it produces a well-known bell curve which has the easiest maths.2d6 generates results of between 2 and 12, where both the average roll AND the most common roll equals 7. Specifically, out of 36 rolls, we expect:-1 result of 22 results of 33 results of 44 results of 55 results of 66 results of 75 results of 84 results of 93 results of 102 results of 111 result of 1236 total resultsThis is the bell curve.Now, if you were to be generating a character for an RPG where, instead of having six ability scores generated by rolling 3d6, you instead you have one ability score generated by rolling 2d6....The average set (of one score in this case) will be 7. Also, as it happens, the most common score for a table full of PCs will also be observed to be 7 (we would expect).If you were to add a rule to character creation such that any set (of one stat) that was less than, say, 6 had to be re-rolled, what effect would this rule have on the stats of the PCs?Well, it's totally true that the average observed stats of a group of PCs will be...8.15, if my calculations are correct. Indisputably higher than 7.Why? If players roll 6+, does the discard rule improve what they roll if that is the result? No, they roll what they roll!What if they roll 5 or less? Then they roll again, and if that re-roll is 6+ then the fact that this is a re-roll does not change what they roll, and if it's 5 or less then the re-roll again. At no point in this process does any previous re-roll improve any score of 6+, and those are the only rolls that are played.So the average observed is over (but close to) 8, but does this mean that the most common roll is 8 under a system that includes discards while a no-discard method remains at 7?No!If you discard rolls of less than 6, this doesn't change the bell curve at all! Low rolls are just as likely as they ever were, 7 remains the most common result (six times out of every 36 rolls) and results of 6 or 8 remain joint second at 5 rolls out of 36 each. 7 remains the most likely stat because it is not discarded! 2 or 12 remain the joint least likely results, and while 2 cannot be played (because it must be re-rolled), 12 doesn't suddenly become more likely to be rolled than it was before! It's still only a 1 in 36 chance to be a result of 12, still a six in 36 chance to be a 7, and 7 remains exactly six times more likely to be played than a 12, unchanged whether or not there is a discard rule in place.This is why DMs should not fear that a discard rule skews stats towards higher results, because the proportion of average stats to max stats remains totally identical either way! The only difference is the lack of low sets, not a greater proportion of high sets over medium sets than there would have been without a discard rule!Now, this breaks down if you discard the average rolls as well as the low rolls, but not because the proportions of high to medium sets have changed but simply because you are no longer allowed to play medium sets!TL;DR: with or without a discard rule, the proportion of high to medium sets remains totally identical as long as you don't discard medium sets.I hope that this explains my position more clearly.</blockquote>

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