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Power Attack and Statistics
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<blockquote data-quote="KarinsDad" data-source="post: 306354" data-attributes="member: 2011"><p>Some of the math above is extremely suspect. I will attempt to simplify this for you (with a lot of examples, just go to the bottom of the post to get the bottom line).</p><p></p><p>There are basically two cases here, full round attack and single attack. So, for each of these cases, we look for when your average damage = average to hit (including criticals).</p><p></p><p>Full Round Attack:</p><p></p><p>AC 22 is the break even point where one point of Power Attack helps.</p><p></p><p>AC 22 = 95% hit + 75% hit + 50% hit or 220% chance to hit = 220% damage or 2.2 * (18.5) * 1.2 = 48.84.</p><p></p><p>If you add one for Power Attack here, you would get:</p><p></p><p>AC 22 = 95% hit + 70% hit + 45% hit or 210% chance to hit = 210% damage or 2.1 * (19.5) * 1.2 = 49.140.</p><p></p><p>But, if you add two for Power Attack here, you would get:</p><p></p><p>AC 22 = 90% hit + 65% hit + 40% hit or 195% chance to hit = 195% damage or 1.95 * (20.5) * 1.2 = 47.97.</p><p></p><p>So, adding one point at AC 22 helps, adding 2 points hurts (ever so slightly).</p><p></p><p>Anything AC 23 or higher can only be hurt by Power Attack.</p><p></p><p>AC 23 = 95% hit + 70% hit + 45% hit or 210% chance to hit = 210% damage or 2.1 * (18.5) * 1.2 = 46.62.</p><p></p><p>If you add one for Power Attack here, you would get:</p><p></p><p>AC 23 = 90% hit + 65% hit + 40% hit or 195% chance to hit = 195% damage or 1.95 * (19.5) * 1.2 = 45.63.</p><p></p><p>Basically, once you decrease all 3 chances to hit by 5% (in this case), you are doing more harm than adding slightly less than a 5% increase to 3 sets of damage.</p><p></p><p></p><p>Now, the other side of the coin here is to figure out how much Power Attack to add to ACs lower than 22. The answer for this case is real simple. Every 2 points of AC below 22 should have one more added to Power Attack since you are increasing the overall to hit by 20% while increasing the damage by almost 15% (5% times 3 attacks, at least for the higher ACs).</p><p></p><p>So, a nice rule of thumb for this character is:</p><p></p><p>(23 - AC) / 2 round up = points to add to Power Attack OR</p><p>(24 - AC) / 2 round down, depending on your preference</p><p></p><p>To illustrate this, let’s take an AC of 10.</p><p></p><p>AC 10 = 95% hit + 95% hit + 95% hit or 285% chance to hit = 285% damage or 2.85 * (18.5) * 1.2 = 63.27.</p><p></p><p>If you add 7 for Power Attack here (as per the rule of thumb), you would get:</p><p></p><p>AC 10 = 95% hit + 95% hit + 75% hit or 265% chance to hit = 265% damage or 2.65 * (25.5) * 1.2 = 81.09.</p><p></p><p>If you add 6 for Power Attack here, you would get:</p><p></p><p>AC 10 = 95% hit + 95% hit + 80% hit or 270% chance to hit = 270% damage or 2.7 * (24.5) * 1.2 = 79.38.</p><p></p><p>If you add 8 for Power Attack here, you would get:</p><p></p><p>AC 10 = 95% hit + 90% hit + 70% hit or 255% chance to hit = 255% damage or 2.55 * (26.5) * 1.2 = 81.09.</p><p></p><p>So, this is one of those weird cases where adding 7 to power attack is the same as adding 8 to power attack. Adding 9 to power attack will, yet again, decrease the average damage.</p><p></p><p>In any case, for the ACs that your character will encounter, the full round rule of thumb above is accurate enough to give you really good information as to what to add once you figure out your opponents AC.</p><p></p><p>Whew!!! <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></p><p>Single Attack:</p><p></p><p>AC 23 is also the point at which it does not help to add for a single attack.</p><p></p><p>AC 23 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09.</p><p></p><p>If you add one for Power Attack here, you would get:</p><p></p><p>AC 23 = 90% chance to hit = 90% damage or 0.90 * (19.5) * 1.2 = 21.06.</p><p></p><p>The equation is similar to full round attack:</p><p></p><p>23 - AC = points to add to Power Attack</p><p></p><p></p><p>AC 22 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09.</p><p></p><p>If you add one for Power Attack here, you would get:</p><p></p><p>AC 22 = 95% chance to hit = 95% damage or 0.95 * (19.5) * 1.2 = 22.23.</p><p></p><p>If you add two for Power Attack here, you would get:</p><p></p><p>AC 22 = 90% chance to hit = 90% damage or 0.90 * (20.5) * 1.2 = 22.14.</p><p></p><p>Taking an AC 12 example since 11 is the most you can add to Power Attack:</p><p></p><p>AC 12 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09.</p><p></p><p>If you add 11 for Power Attack here (the maximum), you would get:</p><p></p><p>AC 12 = 95% chance to hit = 95% damage or 0.95 * (29.5) * 1.2 = 33.63.</p><p></p><p>If you add 10 for Power Attack here, you would get:</p><p></p><p>AC 12 = 95% chance to hit = 95% damage or 0.95 * (28.5) * 1.2 = 32.49.</p><p></p><p>If you add 12 for Power Attack here (if it were allowed), you would get:</p><p></p><p>AC 12 = 90% chance to hit = 90% damage or 0.9 * (30.5) * 1.2 = 32.94.</p><p></p><p></p><p>So, the answer for this specific character is:</p><p></p><p>Full Round Attack:</p><p></p><p>(23 - AC) / 2 round up = points to add to Power Attack OR</p><p>(24 - AC) / 2 round down, depending on your preference</p><p></p><p>Single Attack:</p><p></p><p>23 - AC = points to add to Power Attack</p><p></p><p>One other note on this: Criticals are totally irrelevant to the conversation. As you can see above, it does not matter what percentage a critical increases your average damage. Power Attack does not change that percentage. What matters is the "to hit" to "damage" ratio and getting those two numbers as close as possible. A square 4x4 has 16 square units. A square 3x5 has 15 square units. The closer you get a rectangle to a square (by adding a unit to the smaller side and subtracting it from the larger side), the more square units you get. Ditto for this. It's the same type of math.</p></blockquote><p></p>
[QUOTE="KarinsDad, post: 306354, member: 2011"] Some of the math above is extremely suspect. I will attempt to simplify this for you (with a lot of examples, just go to the bottom of the post to get the bottom line). There are basically two cases here, full round attack and single attack. So, for each of these cases, we look for when your average damage = average to hit (including criticals). Full Round Attack: AC 22 is the break even point where one point of Power Attack helps. AC 22 = 95% hit + 75% hit + 50% hit or 220% chance to hit = 220% damage or 2.2 * (18.5) * 1.2 = 48.84. If you add one for Power Attack here, you would get: AC 22 = 95% hit + 70% hit + 45% hit or 210% chance to hit = 210% damage or 2.1 * (19.5) * 1.2 = 49.140. But, if you add two for Power Attack here, you would get: AC 22 = 90% hit + 65% hit + 40% hit or 195% chance to hit = 195% damage or 1.95 * (20.5) * 1.2 = 47.97. So, adding one point at AC 22 helps, adding 2 points hurts (ever so slightly). Anything AC 23 or higher can only be hurt by Power Attack. AC 23 = 95% hit + 70% hit + 45% hit or 210% chance to hit = 210% damage or 2.1 * (18.5) * 1.2 = 46.62. If you add one for Power Attack here, you would get: AC 23 = 90% hit + 65% hit + 40% hit or 195% chance to hit = 195% damage or 1.95 * (19.5) * 1.2 = 45.63. Basically, once you decrease all 3 chances to hit by 5% (in this case), you are doing more harm than adding slightly less than a 5% increase to 3 sets of damage. Now, the other side of the coin here is to figure out how much Power Attack to add to ACs lower than 22. The answer for this case is real simple. Every 2 points of AC below 22 should have one more added to Power Attack since you are increasing the overall to hit by 20% while increasing the damage by almost 15% (5% times 3 attacks, at least for the higher ACs). So, a nice rule of thumb for this character is: (23 - AC) / 2 round up = points to add to Power Attack OR (24 - AC) / 2 round down, depending on your preference To illustrate this, let’s take an AC of 10. AC 10 = 95% hit + 95% hit + 95% hit or 285% chance to hit = 285% damage or 2.85 * (18.5) * 1.2 = 63.27. If you add 7 for Power Attack here (as per the rule of thumb), you would get: AC 10 = 95% hit + 95% hit + 75% hit or 265% chance to hit = 265% damage or 2.65 * (25.5) * 1.2 = 81.09. If you add 6 for Power Attack here, you would get: AC 10 = 95% hit + 95% hit + 80% hit or 270% chance to hit = 270% damage or 2.7 * (24.5) * 1.2 = 79.38. If you add 8 for Power Attack here, you would get: AC 10 = 95% hit + 90% hit + 70% hit or 255% chance to hit = 255% damage or 2.55 * (26.5) * 1.2 = 81.09. So, this is one of those weird cases where adding 7 to power attack is the same as adding 8 to power attack. Adding 9 to power attack will, yet again, decrease the average damage. In any case, for the ACs that your character will encounter, the full round rule of thumb above is accurate enough to give you really good information as to what to add once you figure out your opponents AC. Whew!!! :) Single Attack: AC 23 is also the point at which it does not help to add for a single attack. AC 23 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09. If you add one for Power Attack here, you would get: AC 23 = 90% chance to hit = 90% damage or 0.90 * (19.5) * 1.2 = 21.06. The equation is similar to full round attack: 23 - AC = points to add to Power Attack AC 22 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09. If you add one for Power Attack here, you would get: AC 22 = 95% chance to hit = 95% damage or 0.95 * (19.5) * 1.2 = 22.23. If you add two for Power Attack here, you would get: AC 22 = 90% chance to hit = 90% damage or 0.90 * (20.5) * 1.2 = 22.14. Taking an AC 12 example since 11 is the most you can add to Power Attack: AC 12 = 95% chance to hit = 95% damage or 0.95 * (18.5) * 1.2 = 21.09. If you add 11 for Power Attack here (the maximum), you would get: AC 12 = 95% chance to hit = 95% damage or 0.95 * (29.5) * 1.2 = 33.63. If you add 10 for Power Attack here, you would get: AC 12 = 95% chance to hit = 95% damage or 0.95 * (28.5) * 1.2 = 32.49. If you add 12 for Power Attack here (if it were allowed), you would get: AC 12 = 90% chance to hit = 90% damage or 0.9 * (30.5) * 1.2 = 32.94. So, the answer for this specific character is: Full Round Attack: (23 - AC) / 2 round up = points to add to Power Attack OR (24 - AC) / 2 round down, depending on your preference Single Attack: 23 - AC = points to add to Power Attack One other note on this: Criticals are totally irrelevant to the conversation. As you can see above, it does not matter what percentage a critical increases your average damage. Power Attack does not change that percentage. What matters is the "to hit" to "damage" ratio and getting those two numbers as close as possible. A square 4x4 has 16 square units. A square 3x5 has 15 square units. The closer you get a rectangle to a square (by adding a unit to the smaller side and subtracting it from the larger side), the more square units you get. Ditto for this. It's the same type of math. [/QUOTE]
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