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3.5 Weapon question
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<blockquote data-quote="Patryn of Elvenshae" data-source="post: 5579243" data-attributes="member: 23094"><p>Thanks. <img src="https://cdn.jsdelivr.net/joypixels/assets/8.0/png/unicode/64/1f642.png" class="smilie smilie--emoji" loading="lazy" width="64" height="64" alt=":)" title="Smile :)" data-smilie="1"data-shortname=":)" /></p><p></p><p>There is, however, a slight error in your chart.</p><p></p><p>Succinctly, your equation is only true for those cases in which all possible threat rolls are also successful hit rolls (e.g., they hold for a scimitar only so long as an 18 or better hits).</p><p></p><p>However, your chart continues down into very low to-hit percentages, and is flexible enough to allow for Improved Crit / Keen weapons, which exacerbates the issue.</p><p></p><p>Accordingly, the proper way to calculate average damage per swing is:</p><p></p><p>Chance to Miss * Miss Damage + Chance to Hit but Not Crit * Normal Damage + Chance to Hit and Crit * Crit Damage</p><p></p><p>The first obviously drops out in 3.5 (most of the time, anyway) since Miss Damage is 0. Calculating the rest involves some fancier math (using MIN() statements).</p><p></p><p>As an concrete example, the average damage per swing for a scimitar with a +2 damage bonus (5.5 Normal Damage) that hits 50% of the time is, indeed, 3.1625 as indicated on your Base Calculator page.</p><p></p><p>However, change your "To Hit / Confirm" percentage to 10% - a foe which can only be hit on a 19 or 20, both of which threaten, and for which the threat is confirmed only 10% of the time. Your calculator returns 1.265 as the average damage per swing. The correct answer is 0.605 damage per swing - 10% of the time I'll hit, of which 10% will be crits. So the average damage per swing calc should be:</p><p></p><p>(90% * 0) + (9% * Normal Damage) + (1% * Critical Damage) =</p><p>0 + (9% + 5.5) + (1% * 11) = </p><p>0 + (0.485) + (0.11) = 0.605</p><p></p><p>It's not a huge change to your numbers, but it will have drastic effects when you start using this spreadsheet to review things like, "What if Keen and Improved Crit stacked?" or "What if I compare a Keen Scimitar +1 vs. Longsword +2?"</p></blockquote><p></p>
[QUOTE="Patryn of Elvenshae, post: 5579243, member: 23094"] Thanks. :) There is, however, a slight error in your chart. Succinctly, your equation is only true for those cases in which all possible threat rolls are also successful hit rolls (e.g., they hold for a scimitar only so long as an 18 or better hits). However, your chart continues down into very low to-hit percentages, and is flexible enough to allow for Improved Crit / Keen weapons, which exacerbates the issue. Accordingly, the proper way to calculate average damage per swing is: Chance to Miss * Miss Damage + Chance to Hit but Not Crit * Normal Damage + Chance to Hit and Crit * Crit Damage The first obviously drops out in 3.5 (most of the time, anyway) since Miss Damage is 0. Calculating the rest involves some fancier math (using MIN() statements). As an concrete example, the average damage per swing for a scimitar with a +2 damage bonus (5.5 Normal Damage) that hits 50% of the time is, indeed, 3.1625 as indicated on your Base Calculator page. However, change your "To Hit / Confirm" percentage to 10% - a foe which can only be hit on a 19 or 20, both of which threaten, and for which the threat is confirmed only 10% of the time. Your calculator returns 1.265 as the average damage per swing. The correct answer is 0.605 damage per swing - 10% of the time I'll hit, of which 10% will be crits. So the average damage per swing calc should be: (90% * 0) + (9% * Normal Damage) + (1% * Critical Damage) = 0 + (9% + 5.5) + (1% * 11) = 0 + (0.485) + (0.11) = 0.605 It's not a huge change to your numbers, but it will have drastic effects when you start using this spreadsheet to review things like, "What if Keen and Improved Crit stacked?" or "What if I compare a Keen Scimitar +1 vs. Longsword +2?" [/QUOTE]
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