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Message: <blockquote data-quote="ECMO3" data-source="post: 9836430" data-attributes="member: 7030563">That is balance in a white room it is not balance in play and if imbalance in play causes problems at your table in play, equal ability scores will not minimize or solve it to any degree.It can, although the chance decreases rapidly with every roll.Ok so then you are fine if the game is not balanced in play.  So am I.  I have no problem with this.When I hear complaints about imbalance in play it is because one player supposedly feels bad or "useless", because another player has more success in play.  I say hear about it, because I have never actually seen this personally.  But as you note any time there is randomness this will happen.Yep and that variance will almost always cause imbalance in play.  Giving them the same ability scores will not change that.Neither of these are factually true when you are talking about the bonuses from ability scores and random die rolls.To start with the discussion of Variance is not accurate because the population is not a continuous distribution.  It doesn't fluctuate around the mean.  A 1st level PC with a 16 strength swinging a longsword against a 16 AC has a mean damage of 3.975, but the most common damage rolled (mode) is 0, not 4 and it does not fluctuate around 3-4.  Your chance of doing 0 damage is 50%.  Your chance of doing 4 damage is 5.63% and all numbers from 5-11 are slightly more likely than 4 damage even though 4 is already higher than the mean.  You have a better chance of doing 19 Damage (0.7%) than you do of doing 3 damage (0%).Bias also does not mean outcomes are consistently shifted in one direction, it means there is an inclination or prejudice in one direction.Exactly!  You are discounting "rare events" that are far more likely to occur when you say: "The player with significantly lower modifiers will experience more frequent failure"You can't ignore rare events (i.e. the chance the low score character does better).I agree it is overwhelmingly unlikely the low 8 stat player will be more successful than the high 18 stat player, but in a session it is more likely than getting that disparity in scores you are talking about in the first place.  A weak player with an 8 as their highest stat consistently outperforming a player with an 18 as their highest stat is a "rare event" and you can't ignore it or act like it is impossible when you consider it possible to have that disparity in ability scores to begin with.Replace the 8 and 18 with 12 and 16:The chance of one player having a high of 12 or lower and another player having a high of 16 or higher is 0.78%.  That is not common at all, it is very rare.  Not unheard of like 8 and 18, but still rare.I would say an average combat-heavy session is around 12 rounds of combat.  If both PCs are 1st level and fight enemies with a 16AC and have longswords there is a 16% chance the PC with the 12 strength outperforms the PC with the 16 strength in terms of damage over that session.  So yes it is more common for a PC with a high of 12 to outperform a PC with a high of 16 than it is to have that disparity in ability scores.The other examples you cited:14 and 18:Chance for this disparity - 2% (rare)Chance 14 Strength PC doing more damage during session than 18 strength PC - 16% (uncommon)15 and 17:Chance for disparity - 13% (uncommon)Chance of 15 strength PC doing more damage during session 17 Strength PC - 31% (common)In all of these cases the low scores are less likely to result in poor performance for the low score player than they are to even exist in the first place.I don't think either of them are a problem, but only one of those actually happens at the table.I never said this.  I said multiple times on this post that ability scores do matter and do affect play.I said they will not make gameplay more balanced, or to use your verbiage (which I do like by the way) - they will not lead to balanced outcomes.</blockquote>

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