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*Pathfinder & Starfinder
Superior Xbow/Greatbow dpr
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<blockquote data-quote="DracoSuave" data-source="post: 5180047" data-attributes="member: 71571"><p>The easy way to compare the math is quite simple.</p><p></p><p>Take the number of outcomes where the bow hits. Multiply that by 1 in pre-epic, and 2 in epic. This is how much more damage those outcomes would generate if you used a bow instead of a xbow.</p><p></p><p>Take the average damage on a hit of a xbow. This is how much damage that extra outcome (the +1 to hit) grants you.</p><p></p><p>Divide both by 20 to get the DPR. This gives you the equation:</p><p></p><p>(p = number of outcomes, x = 1 or 2 depending on tier, d = average damage of the great bow)</p><p></p><p>GreatBow is superior if and only if:</p><p></p><p>px/20 > d/20</p><p></p><p>or</p><p></p><p>px > d</p><p></p><p>Really simple math to do, actually.</p><p></p><p>So, let's take level one, with a 20 dex.</p><p></p><p>1d10+5+1d6 = 7-21 damage = 14 damage on an average hit. </p><p></p><p>1p > 14</p><p></p><p>p > 14</p><p></p><p>Now p is equal to 21 minus what you need to roll on the d20 to hit. Well call that number t for target number.</p><p></p><p>21 - t > 14</p><p></p><p>7 > t</p><p></p><p>Which means the greatbow is only superior if you can hit with anything less than a 7 with it. So:</p><p></p><p>Your attack bonus is +7, so that would mean the AC would have to be less than 14.</p><p></p><p>How many level 1 monsters have an AC less than 14? Most 'theorycraft' around D&D 4th edition revolves around the 50% attack assumption, which doesn't apply in practical use. A more practical examination looks at the AC break-even point, and considers whether or not you encounte that AC often.</p><p></p><p>In this case, the AC in question -never happens- and SupXBow is superior across all monsters. However, if examination shows the AC break point occurs often, then either weapon is good. And if the breakpoint is above what you normally shoot at, greatbow is better for damage.</p><p></p><p>EDIT: The math actually works out to AC 15 because of the extra point of critical damage. But the rest is still as much a wash.</p><p></p><p>EDIT2: Load minor is only a concern to characters who use minor actions to do their shtick....</p><p></p><p>...oh wait... Hunter's Quarry...</p><p></p><p>EDIT3: I flipped xbow and gbow around. It's correct now: The more accurate wepaon does more damage even at level 1. More static bonuses favor accuracy over damage.</p></blockquote><p></p>
[QUOTE="DracoSuave, post: 5180047, member: 71571"] The easy way to compare the math is quite simple. Take the number of outcomes where the bow hits. Multiply that by 1 in pre-epic, and 2 in epic. This is how much more damage those outcomes would generate if you used a bow instead of a xbow. Take the average damage on a hit of a xbow. This is how much damage that extra outcome (the +1 to hit) grants you. Divide both by 20 to get the DPR. This gives you the equation: (p = number of outcomes, x = 1 or 2 depending on tier, d = average damage of the great bow) GreatBow is superior if and only if: px/20 > d/20 or px > d Really simple math to do, actually. So, let's take level one, with a 20 dex. 1d10+5+1d6 = 7-21 damage = 14 damage on an average hit. 1p > 14 p > 14 Now p is equal to 21 minus what you need to roll on the d20 to hit. Well call that number t for target number. 21 - t > 14 7 > t Which means the greatbow is only superior if you can hit with anything less than a 7 with it. So: Your attack bonus is +7, so that would mean the AC would have to be less than 14. How many level 1 monsters have an AC less than 14? Most 'theorycraft' around D&D 4th edition revolves around the 50% attack assumption, which doesn't apply in practical use. A more practical examination looks at the AC break-even point, and considers whether or not you encounte that AC often. In this case, the AC in question -never happens- and SupXBow is superior across all monsters. However, if examination shows the AC break point occurs often, then either weapon is good. And if the breakpoint is above what you normally shoot at, greatbow is better for damage. EDIT: The math actually works out to AC 15 because of the extra point of critical damage. But the rest is still as much a wash. EDIT2: Load minor is only a concern to characters who use minor actions to do their shtick.... ...oh wait... Hunter's Quarry... EDIT3: I flipped xbow and gbow around. It's correct now: The more accurate wepaon does more damage even at level 1. More static bonuses favor accuracy over damage. [/QUOTE]
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Superior Xbow/Greatbow dpr
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