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Need the Math Gurus: DR 1 vs AC +1
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<blockquote data-quote="KarinsDad" data-source="post: 2751362" data-attributes="member: 2011"><p>More like level 10.</p><p></p><p>A first level Fighter with a Strength of 18 and a Greatsword does an average of 13 points of damage. By level 10, assuming he bumped up his Strength by 2, he has Weapon Specialization, a +3 Weapon, and a +4 Girdle of Giant Strength, he is doing 23 average points of damage. But, this is a pretty much maxxed out damage Fighter. A two weapon fighter or one with weapon and shield will not be doing this much damage per successful attack.</p><p></p><p>Granted, some monsters could do more damage per hit at a lower CR than this, but not many.</p><p></p><p>+1 DR kicks butt on +1 AC.</p><p></p><p></p><p>However, Thanee's math is not quite correct. The chances of hitting someone is nowhere near 95% until much higher level.</p><p></p><p>Hence, you are not typically dropping 95% down to 90%. Most of the time, you are dropping 40% to 35% or 60% to 55% or some such.</p><p></p><p>So, depending on what your chance to hit is, the amount of damage you would need to do for +1 AC to be equal to +1 DR is:</p><p></p><p>95%: 19</p><p>90%: 18</p><p>85%: 17</p><p>80%: 16</p><p>75%: 15</p><p>70%: 14</p><p>65%: 13</p><p>60%: 12</p><p>55%: 11</p><p>50%: 10</p><p>45%: 9</p><p>40%: 8</p><p>35%: 7</p><p>30%: 6</p><p>25%: 5</p><p>20%: 4</p><p>15%: 3</p><p>10%: 2</p><p>5%: never</p><p></p><p>The equation is chance+5% of (damage-1) = chance% of damage. Or in the case of 95% at 18 damage = 90% chance at 19 damage.</p><p></p><p>In other words, if you have a high chance of hitting, then you have to hit for a lot of damage for that DR 1 to be negligible. If you have a low chance of hitting, then you do not need as much damage to negate it.</p><p></p><p>A first level Fighter with 18 Strength tends to have a +5 to hit (assuming no Weapon Focus or Masterwork weapon) and does about 8 to 11 points of damage depending on weapon. The first level oathsworn you talked about would have an AC of 13, so the Fighter would have a 65% chance of damaging him. He needs to do 13 or more points on average for +1 AC to be worthwhile.</p><p></p><p>A sixth level Fighter with 21 Strength (gauntlets +2) and Weapon Focus and Weapon Specialization and a +1 sword tends to have a +13 to hit and does about 12 to 17 points of damage depending on weapon. The sixth level oathsworn you talked about would have an AC of maybe 18, so the Fighter would have a 80% chance of hitting him. He needs to do 16 or more points on average for +1 AC to be worthwhile.</p><p></p><p>Eventually, the Fighter will get so good that the Oathsworn is screwed no matter which route he takes. But, once the Fighter gets the 95% chance to hit and does more than 19 points of damage, the DR is always the best choice because +25 to hit against AC 23 is the same 95% as +25 to hit against AC 24 (or AC 25 or AC 26).</p><p></p><p>So even if there is a level or so where the AC boost is better, eventually it goes back to the DR boost being better again.</p><p></p><p></p><p>For a different class that can have a very high AC (i.e. 5% to 25% chance of most opponents hitting), +1 to AC is always better since most opponents will be doing more than a few points of damage.</p></blockquote><p></p>
[QUOTE="KarinsDad, post: 2751362, member: 2011"] More like level 10. A first level Fighter with a Strength of 18 and a Greatsword does an average of 13 points of damage. By level 10, assuming he bumped up his Strength by 2, he has Weapon Specialization, a +3 Weapon, and a +4 Girdle of Giant Strength, he is doing 23 average points of damage. But, this is a pretty much maxxed out damage Fighter. A two weapon fighter or one with weapon and shield will not be doing this much damage per successful attack. Granted, some monsters could do more damage per hit at a lower CR than this, but not many. +1 DR kicks butt on +1 AC. However, Thanee's math is not quite correct. The chances of hitting someone is nowhere near 95% until much higher level. Hence, you are not typically dropping 95% down to 90%. Most of the time, you are dropping 40% to 35% or 60% to 55% or some such. So, depending on what your chance to hit is, the amount of damage you would need to do for +1 AC to be equal to +1 DR is: 95%: 19 90%: 18 85%: 17 80%: 16 75%: 15 70%: 14 65%: 13 60%: 12 55%: 11 50%: 10 45%: 9 40%: 8 35%: 7 30%: 6 25%: 5 20%: 4 15%: 3 10%: 2 5%: never The equation is chance+5% of (damage-1) = chance% of damage. Or in the case of 95% at 18 damage = 90% chance at 19 damage. In other words, if you have a high chance of hitting, then you have to hit for a lot of damage for that DR 1 to be negligible. If you have a low chance of hitting, then you do not need as much damage to negate it. A first level Fighter with 18 Strength tends to have a +5 to hit (assuming no Weapon Focus or Masterwork weapon) and does about 8 to 11 points of damage depending on weapon. The first level oathsworn you talked about would have an AC of 13, so the Fighter would have a 65% chance of damaging him. He needs to do 13 or more points on average for +1 AC to be worthwhile. A sixth level Fighter with 21 Strength (gauntlets +2) and Weapon Focus and Weapon Specialization and a +1 sword tends to have a +13 to hit and does about 12 to 17 points of damage depending on weapon. The sixth level oathsworn you talked about would have an AC of maybe 18, so the Fighter would have a 80% chance of hitting him. He needs to do 16 or more points on average for +1 AC to be worthwhile. Eventually, the Fighter will get so good that the Oathsworn is screwed no matter which route he takes. But, once the Fighter gets the 95% chance to hit and does more than 19 points of damage, the DR is always the best choice because +25 to hit against AC 23 is the same 95% as +25 to hit against AC 24 (or AC 25 or AC 26). So even if there is a level or so where the AC boost is better, eventually it goes back to the DR boost being better again. For a different class that can have a very high AC (i.e. 5% to 25% chance of most opponents hitting), +1 to AC is always better since most opponents will be doing more than a few points of damage. [/QUOTE]
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Need the Math Gurus: DR 1 vs AC +1
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