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<blockquote data-quote="Patryn of Elvenshae" data-source="post: 2140791" data-attributes="member: 23094"><p>Which is, of course, disproven by a simple mathematical analysis.</p><p></p><p>You need to have a pretty large bonus to damage before the low-damage, high-crit weapon even begins to pull even against an un-enhanced high-damage, low-crit weapon.</p><p></p><p>Take, for instance, the following three weapons:</p><p></p><p>1. Falchion +1, Keen and Improved Crit Stacking</p><p>2. Greatsword +1, Flaming</p><p>3. Greataxe +1, Flaming</p><p></p><p>Each has a bonus to damage of +16 - +1 enhancement, +15 from other sources (equivalent to a 30 Strength score). Every non-1 roll hits.</p><p></p><p>Expected damage per attack?</p><p></p><p>1. Falchion: 28.9</p><p>2. Greatsword: 27.4</p><p>3. Greataxe: 26.8</p><p></p><p>So, the Falchion wielder has given up an additional feat to be, on average, 1.8 points per attack better than his standard weapon buddies.</p><p></p><p>If the GS and GA wielders likewise pick up Improved Critical, they pull back ahead of the Falchion wielder, but they are roughly equal.</p><p></p><p>If the GS and GA also benefit from stacking, and give up the Flaming enhancement to pick up keen, then they are worse than the Falchion by 0.8 points per attack.</p><p></p><p>Again, all of this assumes that only a 1 misses.</p><p></p><p>If the miss range increases - to, say, 13 or better required to hit - the initial setup now looks like:</p><p></p><p>1. Falchion: 11.8</p><p>2. Greatsword: 11.5</p><p>3. Greataxe: 11.3</p><p></p><p>So, after paying a feat, the falchion is just *barely* ahead of the standard weapon types. He falls behind as soon as you need a 14 or better to hit.</p><p></p><p>Again, all of this is done at +16 damage per hit.</p><p></p><p>At, say, +31 damage per hit (+1 Enhancement, +30 from other sources), given the intial setup (anything but a 1 hits):</p><p></p><p>1. Falchion: 49.6</p><p>2. Greatsword: 43.0</p><p>3. Greataxe: 42.5</p><p></p><p>Egads! Once you get to +31 damage on your attacks, the Falchion is better by a whole 7 points per average attack than a Greatsword against trivial opponents! Holy cow!</p><p></p><p>Note, however, that expected damage on a normal attack is 5 points lower, and expected damage on a critical is 7 points lower. It is, likewise, 5 points lower and <strong>40 points lower</strong> than the greataxe, respectively. The only reason it is comparing favorably is the higher number of critical hits.</p><p></p><p>The falchion's lead, however, quickly evaporates once you consider cases where you can only hit on reasonable numbers (2 points over GS and GA at 13 or better to hit, 0.5 points over GS and GA at 15 or better to hit).</p><p></p><p>In short, letting them stack is mathematically fine, and all objections to the contrary need to bring some hard numbers before I'll start believing them.</p></blockquote><p></p>
[QUOTE="Patryn of Elvenshae, post: 2140791, member: 23094"] Which is, of course, disproven by a simple mathematical analysis. You need to have a pretty large bonus to damage before the low-damage, high-crit weapon even begins to pull even against an un-enhanced high-damage, low-crit weapon. Take, for instance, the following three weapons: 1. Falchion +1, Keen and Improved Crit Stacking 2. Greatsword +1, Flaming 3. Greataxe +1, Flaming Each has a bonus to damage of +16 - +1 enhancement, +15 from other sources (equivalent to a 30 Strength score). Every non-1 roll hits. Expected damage per attack? 1. Falchion: 28.9 2. Greatsword: 27.4 3. Greataxe: 26.8 So, the Falchion wielder has given up an additional feat to be, on average, 1.8 points per attack better than his standard weapon buddies. If the GS and GA wielders likewise pick up Improved Critical, they pull back ahead of the Falchion wielder, but they are roughly equal. If the GS and GA also benefit from stacking, and give up the Flaming enhancement to pick up keen, then they are worse than the Falchion by 0.8 points per attack. Again, all of this assumes that only a 1 misses. If the miss range increases - to, say, 13 or better required to hit - the initial setup now looks like: 1. Falchion: 11.8 2. Greatsword: 11.5 3. Greataxe: 11.3 So, after paying a feat, the falchion is just *barely* ahead of the standard weapon types. He falls behind as soon as you need a 14 or better to hit. Again, all of this is done at +16 damage per hit. At, say, +31 damage per hit (+1 Enhancement, +30 from other sources), given the intial setup (anything but a 1 hits): 1. Falchion: 49.6 2. Greatsword: 43.0 3. Greataxe: 42.5 Egads! Once you get to +31 damage on your attacks, the Falchion is better by a whole 7 points per average attack than a Greatsword against trivial opponents! Holy cow! Note, however, that expected damage on a normal attack is 5 points lower, and expected damage on a critical is 7 points lower. It is, likewise, 5 points lower and [b]40 points lower[/b] than the greataxe, respectively. The only reason it is comparing favorably is the higher number of critical hits. The falchion's lead, however, quickly evaporates once you consider cases where you can only hit on reasonable numbers (2 points over GS and GA at 13 or better to hit, 0.5 points over GS and GA at 15 or better to hit). In short, letting them stack is mathematically fine, and all objections to the contrary need to bring some hard numbers before I'll start believing them. [/QUOTE]
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