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<blockquote data-quote="tomBitonti" data-source="post: 1003772" data-attributes="member: 13107">Some calculationsThis is all off-the-cuff.&nbsp; My apologies for mistakes.Some calculations appear below ... the upshot appears immediately:I have only included in my calculations details for CR 18-20,19-20, and 20.&nbsp; Unfortunately, when the CR becomes wide,the calculations become a bit messy.For total damage expectation:When you have a small (5%) chance to hit, a (20 x4) weaponis better than a (20, x3) weapon, and a (20 x3) weaponis better than either a (19-20 x2) or a (18-20 x2) weapon.This is of course, as in this case the critical multiplier is allthat matters.The 10% chance to hit case is somewhat messy.When you have a (15%) or better chance to hit a (20 x3)weapon is the same as a (19-20 x2) weapon, and a (20 x4)weapon is the same as a (18-20 x2) weapon.The calculations show that, aside from changes to theshape of the damage curve, that increasing either thecritical range with a critical multiplier of 2, or increasingthe critical multipler (with a critical range of 20) are thesame.The calculations suggest that increasing --both-- thecritical range and the critical multipler is a bad idea, asthe benefits multiply.&nbsp; As the pattern of values fromthe PHB suggests, the initial weapons do not ever havea CM of anything by x2 when the CR is wider than 20,and the CR is always 20 when the CM is more than x3.Note that there is an alternative way to do the critical rollswhich gives the same critical results.&nbsp; Always roll two dice,and if the first dice is a hit, the hit is a critical hit if the seconddie is in the critical range.&nbsp; I'm still thinking this through, butit does seem to give the same results.============================================================Here are the summary charts:AQ&nbsp; == &quot;Attack Quotient&quot; == Chance to hitCM&nbsp; == Critical MultiplierCR&nbsp; == Critical Range == Chance to threaten a criticalBDE == Base Damage ExpectationThere are two cases:When:&nbsp; &nbsp; (AQ == 5) or ((AQ == 10) &amp;&amp; (CR &gt; 5))&nbsp; &nbsp; &nbsp; &nbsp; TDE == ((AQ - AQ * AQ) + (AQ * AQ) * CM)) * BDE&nbsp; &nbsp; &nbsp; &nbsp; TDE == (AQ + ((AQ * AQ) * (CM - 1))) * BDE&nbsp; &nbsp; (AQ &gt; 10) or ((AQ == 10) &amp;&amp; (CR == 5))&nbsp; &nbsp; &nbsp; &nbsp; TDE == ((AQ - CR * AQ) + (CR * AQ * CM)) * BDE&nbsp; &nbsp; &nbsp; &nbsp; TDE == (AQ + ((AQ * CR) * (CM - 1))) * BDE&nbsp; &nbsp; &nbsp; &nbsp; TDE == (AQ * (1 + CR * (CM - 1))) * BDEIn the first case the critical range has no effect.The sole benefit from criticals is due to the critical multiplier.In regards to the second case, note the multiplication:&nbsp; &nbsp; CR * (CM - 1)This is interesting, being linear in both critical range and criticalmultiplier:CF (Critical Factor):&nbsp; &nbsp; CF == CR * (CM - 1)(CF * 100) Chart:&nbsp; &nbsp; CM:&nbsp; 2&nbsp; 3&nbsp; 4&nbsp; 5&nbsp; 6CR:&nbsp; 5&nbsp;&nbsp; 5 10 15 20 25&nbsp; &nbsp; 10&nbsp; 10 20 40&nbsp; &nbsp; 15&nbsp; 15 30&nbsp; &nbsp; 20&nbsp; 20&nbsp; &nbsp; 25&nbsp; 25&nbsp; &nbsp; 30&nbsp; 30When&nbsp; &nbsp; (20; x2)&nbsp; &nbsp; &nbsp; &nbsp; TDE == AQ * (1.05) * BDE&nbsp; &nbsp; (20; x3)&nbsp; &nbsp; &nbsp; &nbsp; TDE == AQ * (1.10) * BDE&nbsp; &nbsp; (20; x4)&nbsp; &nbsp; &nbsp; &nbsp; TDE == AQ * (1.15) * BDE&nbsp; &nbsp; &nbsp; &nbsp; (19-20; x2)&nbsp; &nbsp; &nbsp; &nbsp; TDE == AQ * (1.10) * BDE&nbsp; &nbsp; (18-20; x2)&nbsp; &nbsp; &nbsp; &nbsp; TDE == AQ * (1.15) * BDEBDE Multiplier Chart:&nbsp; &nbsp; CM:&nbsp; 2&nbsp; &nbsp; &nbsp;&nbsp; 3&nbsp; &nbsp;&nbsp; 4&nbsp; &nbsp; &nbsp;&nbsp; 5&nbsp; &nbsp; &nbsp; 6CR:&nbsp; 5&nbsp;&nbsp; 1.05 1.10 1.15 1.20 1.25&nbsp; &nbsp; &nbsp; 10&nbsp;&nbsp; 1.10 1.20 1.30 1.40&nbsp; &nbsp; &nbsp; 15&nbsp;&nbsp; 1.15 1.30 1.45 1.60&nbsp; &nbsp; &nbsp; 20&nbsp;&nbsp; 1.20 1.40 1.60 1.80&nbsp; &nbsp; &nbsp; 25&nbsp;&nbsp; 1.25 1.50 1.75 2.00&nbsp; &nbsp; &nbsp; 30&nbsp;&nbsp; 1.30============================================================Here are the original calculations:Representative Weapons:&nbsp; &nbsp; Dagger&nbsp;&nbsp; 1d4&nbsp;&nbsp; 19-20&nbsp;&nbsp; x2&nbsp; &nbsp; Sword&nbsp; &nbsp; 1d8&nbsp;&nbsp; 19-20&nbsp;&nbsp; x2&nbsp; &nbsp; BAxe&nbsp; &nbsp;&nbsp; 1d8&nbsp;&nbsp; 20&nbsp; &nbsp; &nbsp; x3&nbsp; &nbsp; Scim&nbsp; &nbsp;&nbsp; 1d6&nbsp;&nbsp; 18-20&nbsp;&nbsp; x2&nbsp; &nbsp; Scythe&nbsp;&nbsp; 2d4&nbsp;&nbsp; 20&nbsp; &nbsp; &nbsp; x4DB (Damage Bonus):Representative Damage Bonus Range:&nbsp; &nbsp; -2&nbsp; 0 +2 +4 +6 +8 +10BDE (Base Damage Expectation):&nbsp;&nbsp; 1d4&nbsp;&nbsp; 1d6&nbsp;&nbsp; 1d8&nbsp;&nbsp; 2d4DE (Damage Expectation):DE Chart:&nbsp; &nbsp; BDE:&nbsp;&nbsp; D4&nbsp; &nbsp; D6&nbsp; &nbsp; D8&nbsp; &nbsp;&nbsp; 2D4DB: -2&nbsp; &nbsp;&nbsp; 1.25&nbsp; 2.00&nbsp; 2.825&nbsp; 3.25&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 2.50&nbsp; 3.50&nbsp; 4.50&nbsp;&nbsp; 5.00&nbsp; &nbsp; +2&nbsp; &nbsp;&nbsp; 4.50&nbsp; 5.50&nbsp; 6.50&nbsp;&nbsp; 7.00&nbsp; &nbsp; +4&nbsp; &nbsp;&nbsp; 6.50&nbsp; 7.50&nbsp; 8.50&nbsp;&nbsp; 9.00&nbsp; &nbsp; +6&nbsp; &nbsp;&nbsp; 8.50&nbsp; 9.50 10.50&nbsp; 11.00&nbsp; &nbsp; +8&nbsp; &nbsp; 10.50 11.50 12.50&nbsp; 13.00&nbsp;&nbsp; +10&nbsp; &nbsp; 12.50 13.50 14.50&nbsp; 15.00CM: Critical Multiplier&nbsp; &nbsp; x2&nbsp; x3&nbsp; x4CDE (Critical Damage Expectation):&nbsp; &nbsp; CDE == BDE * CMCDE Charts may be slightly off for DB == -2.CDE (x2)&nbsp; &nbsp; BDE:&nbsp;&nbsp; D4&nbsp; &nbsp; D6&nbsp; &nbsp; D8&nbsp; &nbsp;&nbsp; 2D4DB: -2&nbsp; &nbsp;&nbsp; 2.50&nbsp; 4.00&nbsp; 5.65&nbsp;&nbsp; 6.50&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 5.00&nbsp; 7.00&nbsp; 9.00&nbsp; 10.00&nbsp; &nbsp; +2&nbsp; &nbsp;&nbsp; 9.00 11.00 13.00&nbsp; 14.00&nbsp; &nbsp; +4&nbsp; &nbsp; 13.00 15.00 17.00&nbsp; 18.00&nbsp; &nbsp; +6&nbsp; &nbsp; 17.00 19.00 21.00&nbsp; 22.00&nbsp; &nbsp; +8&nbsp; &nbsp; 21.00 23.00 25.00&nbsp; 26.00&nbsp;&nbsp; +10&nbsp; &nbsp; 25.00 27.00 29.00&nbsp; 30.00CDE (x3)&nbsp; &nbsp; BDE:&nbsp;&nbsp; D4&nbsp; &nbsp; D6&nbsp; &nbsp; D8&nbsp; &nbsp;&nbsp; 2D4DB: -2&nbsp; &nbsp;&nbsp; 3.75&nbsp; 6.00&nbsp; 8.475&nbsp; 9.75&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp;&nbsp; 7.50 10.50 13.50&nbsp; 15.00&nbsp; &nbsp; +2&nbsp; &nbsp; 13.50 16.50 19.50&nbsp; 21.00&nbsp; &nbsp; +4&nbsp; &nbsp; 19.50 22.50 25.50&nbsp; 27.00&nbsp; &nbsp; +6&nbsp; &nbsp; 25.50 28.50 31.50&nbsp; 33.00&nbsp; &nbsp; +8&nbsp; &nbsp; 31.50 34.50 37.50&nbsp; 39.00&nbsp;&nbsp; +10&nbsp; &nbsp; 37.50 40.50 43.50&nbsp; 45.00CDE (x4)&nbsp; &nbsp; BDE:&nbsp;&nbsp; D4&nbsp; &nbsp; D6&nbsp; &nbsp; D8&nbsp; &nbsp;&nbsp; 2D4DB: -2&nbsp; &nbsp;&nbsp; 5.00&nbsp; 8.00 11.30&nbsp; 13.00&nbsp; &nbsp;&nbsp; 0&nbsp; &nbsp; 10.00 14.00 18.00&nbsp; 20.00&nbsp; &nbsp; +2&nbsp; &nbsp; 18.00 22.00 26.00&nbsp; 28.00&nbsp; &nbsp; +4&nbsp; &nbsp; 26.00 30.00 34.00&nbsp; 36.00&nbsp; &nbsp; +6&nbsp; &nbsp; 34.00 38.00 42.00&nbsp; 44.00&nbsp; &nbsp; +8&nbsp; &nbsp; 42.00 46.00 50.00&nbsp; 52.00&nbsp;&nbsp; +10&nbsp; &nbsp; 50.00 54.00 58.00&nbsp; 60.00AC == Armor ClassAB == Attack BonusAQ (Attack Quotient):&nbsp; &nbsp; AQ == (5/100) * min(19, max(1, 10 - AC + AB)) &nbsp; &nbsp; AQ == chance to hit (decimal chance)AQ * 100 Chart:AC:&nbsp; &nbsp; &nbsp; 5 10 15 20 25AB:&nbsp; 0&nbsp; 25&nbsp; 5&nbsp; 5&nbsp; 5&nbsp; 5&nbsp; &nbsp;&nbsp; 5&nbsp; 50 25&nbsp; 5&nbsp; 5&nbsp; 5&nbsp; &nbsp; 10&nbsp; 75 50 25&nbsp; 5&nbsp; 5&nbsp; &nbsp; 15&nbsp; 95 75 50 25&nbsp; 5&nbsp; &nbsp; 20&nbsp; 95 95 75 50 25AQ * 100 Range:&nbsp; &nbsp;&nbsp; 5 25 50 75 95CR: Critical RangeCR * 100 Chart:&nbsp; &nbsp; 20&nbsp; &nbsp; ==&gt; CR&nbsp; 5&nbsp; &nbsp; 19-20 ==&gt; CR 10&nbsp; &nbsp; 18-20 ==&gt; CR 15CQ (Critical Quotient):&nbsp; &nbsp; CQ == min(AQ, CR) * AQ&nbsp; &nbsp; CQ == chance to critical (decimal chance)When:&nbsp; &nbsp; AQ == 5:&nbsp; &nbsp; &nbsp; &nbsp; CQ == AQ * AQ&nbsp; &nbsp; AQ == 10:&nbsp; &nbsp; &nbsp; &nbsp; CR == 5:&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; CQ == CR * AQ&nbsp; &nbsp; &nbsp; &nbsp; CR &gt; 5:&nbsp; &nbsp; &nbsp; &nbsp; &nbsp; &nbsp; CQ == AQ * AQ&nbsp; &nbsp; AQ &gt; 10:&nbsp; &nbsp; &nbsp; &nbsp; CQ == CR * AQCQ * 100 Chart:AQ:&nbsp; &nbsp; &nbsp; 5&nbsp; &nbsp;&nbsp; 25&nbsp; &nbsp;&nbsp; 50&nbsp; &nbsp;&nbsp; 75&nbsp; &nbsp;&nbsp; 95CR:&nbsp; 5&nbsp;&nbsp; 0.25&nbsp;&nbsp; 1.25&nbsp;&nbsp; 2.50&nbsp;&nbsp; 3.75&nbsp;&nbsp; 4.75&nbsp; &nbsp; 10&nbsp;&nbsp; 0.25&nbsp;&nbsp; 2.50&nbsp;&nbsp; 5.00&nbsp;&nbsp; 7.50&nbsp;&nbsp; 9.50&nbsp; &nbsp; 15&nbsp;&nbsp; 0.25&nbsp;&nbsp; 3.75&nbsp;&nbsp; 7.50&nbsp; 11.25&nbsp; 14.25TDE (Total Damage Expectation):&nbsp; &nbsp; TDE == ((AQ - CQ) * BDE) + (CQ * CDE)&nbsp; &nbsp; TDE == ((AQ - CQ) * BDE) + (CQ * CM * BDE)&nbsp; &nbsp; TDE == ((AQ - CQ) + (CQ * CM)) * BDEWhen:&nbsp; &nbsp; (AQ == 5) or ((AQ == 10) &amp;&amp; (CR &gt; 5))&nbsp; &nbsp; &nbsp; &nbsp; TDE == ((AQ - AQ * AQ) + (AQ * AQ) * CM)) * BDE&nbsp; &nbsp; &nbsp; &nbsp; TDE == (AQ + ((AQ * AQ) * (CM - 1))) * BDE&nbsp; &nbsp; (AQ &gt; 10) or ((AQ == 10) &amp;&amp; (CR == 5))&nbsp; &nbsp; &nbsp; &nbsp; TDE == ((AQ - CR * AQ) + (CR * AQ * CM)) * BDE&nbsp; &nbsp; &nbsp; &nbsp; TDE == (AQ + ((AQ * CR) * (CM - 1))) * BDE&nbsp; &nbsp; &nbsp; &nbsp; TDE == (AQ * (1 + CR * (CM - 1))) * BDEVariations:AQ:&nbsp; 5 25 50 75 95CR:&nbsp; 5 10 15CM:&nbsp; 2&nbsp; 3&nbsp; 4</blockquote>

[QUOTE="tomBitonti, post: 1003772, member: 13107"] [b]Some calculations[/b] This is all off-the-cuff. My apologies for mistakes. Some calculations appear below ... the upshot appears immediately: I have only included in my calculations details for CR 18-20, 19-20, and 20. Unfortunately, when the CR becomes wide, the calculations become a bit messy. For total damage expectation: When you have a small (5%) chance to hit, a (20 x4) weapon is better than a (20, x3) weapon, and a (20 x3) weapon is better than either a (19-20 x2) or a (18-20 x2) weapon. This is of course, as in this case the critical multiplier is all that matters. The 10% chance to hit case is somewhat messy. When you have a (15%) or better chance to hit a (20 x3) weapon is the same as a (19-20 x2) weapon, and a (20 x4) weapon is the same as a (18-20 x2) weapon. The calculations show that, aside from changes to the shape of the damage curve, that increasing either the critical range with a critical multiplier of 2, or increasing the critical multipler (with a critical range of 20) are the same. The calculations suggest that increasing --both-- the critical range and the critical multipler is a bad idea, as the benefits multiply. As the pattern of values from the PHB suggests, the initial weapons do not ever have a CM of anything by x2 when the CR is wider than 20, and the CR is always 20 when the CM is more than x3. Note that there is an alternative way to do the critical rolls which gives the same critical results. Always roll two dice, and if the first dice is a hit, the hit is a critical hit if the second die is in the critical range. I'm still thinking this through, but it does seem to give the same results. ============================================================ Here are the summary charts: AQ == "Attack Quotient" == Chance to hit CM == Critical Multiplier CR == Critical Range == Chance to threaten a critical BDE == Base Damage Expectation There are two cases: When: (AQ == 5) or ((AQ == 10) && (CR > 5)) TDE == ((AQ - AQ * AQ) + (AQ * AQ) * CM)) * BDE TDE == (AQ + ((AQ * AQ) * (CM - 1))) * BDE (AQ > 10) or ((AQ == 10) && (CR == 5)) TDE == ((AQ - CR * AQ) + (CR * AQ * CM)) * BDE TDE == (AQ + ((AQ * CR) * (CM - 1))) * BDE TDE == (AQ * (1 + CR * (CM - 1))) * BDE In the first case the critical range has no effect. The sole benefit from criticals is due to the critical multiplier. In regards to the second case, note the multiplication: CR * (CM - 1) This is interesting, being linear in both critical range and critical multiplier: CF (Critical Factor): CF == CR * (CM - 1) (CF * 100) Chart: CM: 2 3 4 5 6 CR: 5 5 10 15 20 25 10 10 20 40 15 15 30 20 20 25 25 30 30 When (20; x2) TDE == AQ * (1.05) * BDE (20; x3) TDE == AQ * (1.10) * BDE (20; x4) TDE == AQ * (1.15) * BDE (19-20; x2) TDE == AQ * (1.10) * BDE (18-20; x2) TDE == AQ * (1.15) * BDE BDE Multiplier Chart: CM: 2 3 4 5 6 CR: 5 1.05 1.10 1.15 1.20 1.25 10 1.10 1.20 1.30 1.40 15 1.15 1.30 1.45 1.60 20 1.20 1.40 1.60 1.80 25 1.25 1.50 1.75 2.00 30 1.30 ============================================================ Here are the original calculations: Representative Weapons: Dagger 1d4 19-20 x2 Sword 1d8 19-20 x2 BAxe 1d8 20 x3 Scim 1d6 18-20 x2 Scythe 2d4 20 x4 DB (Damage Bonus): Representative Damage Bonus Range: -2 0 +2 +4 +6 +8 +10 BDE (Base Damage Expectation): 1d4 1d6 1d8 2d4 DE (Damage Expectation): DE Chart: BDE: D4 D6 D8 2D4 DB: -2 1.25 2.00 2.825 3.25 0 2.50 3.50 4.50 5.00 +2 4.50 5.50 6.50 7.00 +4 6.50 7.50 8.50 9.00 +6 8.50 9.50 10.50 11.00 +8 10.50 11.50 12.50 13.00 +10 12.50 13.50 14.50 15.00 CM: Critical Multiplier x2 x3 x4 CDE (Critical Damage Expectation): CDE == BDE * CM CDE Charts may be slightly off for DB == -2. CDE (x2) BDE: D4 D6 D8 2D4 DB: -2 2.50 4.00 5.65 6.50 0 5.00 7.00 9.00 10.00 +2 9.00 11.00 13.00 14.00 +4 13.00 15.00 17.00 18.00 +6 17.00 19.00 21.00 22.00 +8 21.00 23.00 25.00 26.00 +10 25.00 27.00 29.00 30.00 CDE (x3) BDE: D4 D6 D8 2D4 DB: -2 3.75 6.00 8.475 9.75 0 7.50 10.50 13.50 15.00 +2 13.50 16.50 19.50 21.00 +4 19.50 22.50 25.50 27.00 +6 25.50 28.50 31.50 33.00 +8 31.50 34.50 37.50 39.00 +10 37.50 40.50 43.50 45.00 CDE (x4) BDE: D4 D6 D8 2D4 DB: -2 5.00 8.00 11.30 13.00 0 10.00 14.00 18.00 20.00 +2 18.00 22.00 26.00 28.00 +4 26.00 30.00 34.00 36.00 +6 34.00 38.00 42.00 44.00 +8 42.00 46.00 50.00 52.00 +10 50.00 54.00 58.00 60.00 AC == Armor Class AB == Attack Bonus AQ (Attack Quotient): AQ == (5/100) * min(19, max(1, 10 - AC + AB)) AQ == chance to hit (decimal chance) AQ * 100 Chart: AC: 5 10 15 20 25 AB: 0 25 5 5 5 5 5 50 25 5 5 5 10 75 50 25 5 5 15 95 75 50 25 5 20 95 95 75 50 25 AQ * 100 Range: 5 25 50 75 95 CR: Critical Range CR * 100 Chart: 20 ==> CR 5 19-20 ==> CR 10 18-20 ==> CR 15 CQ (Critical Quotient): CQ == min(AQ, CR) * AQ CQ == chance to critical (decimal chance) When: AQ == 5: CQ == AQ * AQ AQ == 10: CR == 5: CQ == CR * AQ CR > 5: CQ == AQ * AQ AQ > 10: CQ == CR * AQ CQ * 100 Chart: AQ: 5 25 50 75 95 CR: 5 0.25 1.25 2.50 3.75 4.75 10 0.25 2.50 5.00 7.50 9.50 15 0.25 3.75 7.50 11.25 14.25 TDE (Total Damage Expectation): TDE == ((AQ - CQ) * BDE) + (CQ * CDE) TDE == ((AQ - CQ) * BDE) + (CQ * CM * BDE) TDE == ((AQ - CQ) + (CQ * CM)) * BDE When: (AQ == 5) or ((AQ == 10) && (CR > 5)) TDE == ((AQ - AQ * AQ) + (AQ * AQ) * CM)) * BDE TDE == (AQ + ((AQ * AQ) * (CM - 1))) * BDE (AQ > 10) or ((AQ == 10) && (CR == 5)) TDE == ((AQ - CR * AQ) + (CR * AQ * CM)) * BDE TDE == (AQ + ((AQ * CR) * (CM - 1))) * BDE TDE == (AQ * (1 + CR * (CM - 1))) * BDE Variations: AQ: 5 25 50 75 95 CR: 5 10 15 CM: 2 3 4 [/QUOTE]

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