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Message: <blockquote data-quote="delericho" data-source="post: 2356475" data-attributes="member: 22424">That last term should be PpDb - the probability on the second roll is irrelevant to this term, as this represents the damage that is not multiplied on a critical hit.Additionally, Ps is a variable used to represent a number somewhere between 0.05 and 0.95 which in every case matches the numerical value of the number represented by Pp. We're not assuming the results are the same here, but the probabilities are.The representation of two rolls comes from that Pc term, which is the probability of a critical threat, which is the smaller of Pp and the probability generated from the weapon's threat range.So, the formula:A = PD + PDPc(M-1) + PDbwhereA is the average damage scoredP is the probability of a hitPc is the probability of the die landing in the threat range and the attack being a hitM is the critical multiplier of the weaponD is the damage caused that is multiplied on a critical hitDb is the damage caused that is not multiplied on a critical hitwill give numerically correct results.Of course, this can be reduced to:A = P{D[1+Pc(M-1)]+Db}Getting back to the analysis of the feats for the moment, what if the probabilities on the attack and confirmation roll were not the same? What if, instead of increasing the threat range, the Improved Critical feat gave a +4 bonus to the confirmation roll (or change the bonus to suit)? This could then be allowed to stack with a Keen weapon without making critical threats so common as to be mundane, and yet prevent the disappointment that comes from rolling a threat only to fail to confirm.Edit: of course, what I've just described in the paragraph above is the Power Critical feat from Complete Warrior. Oh, well.</blockquote>

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