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Fixing the 3e Math in a simple and easy way
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<blockquote data-quote="Cheiromancer" data-source="post: 4818553" data-attributes="member: 141"><p>I'm assuming that a 20th level fighter is hitting an opponent with four iterative attacks. Then I'm seeing how well he does with the iterative fix (Wulf's system) and then how it works with your proposal. </p><p></p><p>The percentages are the chance of hitting a particular target with a flurry vs an iterative attack. For example, Wulf admits that his fix is a little off when the fighter misses only on a 1. We see this by considering the odds of a fighter hitting someone with a full attack consisting of 4 iterative attacks: the first one hits 95% of the time, the second 70% of the time and so on. The mean damage is 230% of a single attack, which I've expressed as 2.3. Two attacks at no penalty (95% chance of hitting each time) gives a mean damage of 190%, which I've expressed as 1.9. So at this edge case, Wulf's fix would result in the fighter dealing less damage to an opponent- the equivalent of 1.9 hits rather than 2.3 hits. That's 82.6% of the normal damage.</p><p></p><p>If we were using your proposal for BAB ("Sadrik BAB") then all the percentages are 30% lower (for the -6 virtual penalty). Two attacks at 65% is only 1.3 hits total. With your latest suggestion it could become 4 attacks, with a total expected damage of 2.6. Now it's better than the standard case, which may be OK. (13% more damage than the standard isn't huge).</p><p></p><p>Wulf's system is designed to give similar mean damages when there's about a 70% chance of hitting the opponent on the first attack. I used 75%. The dual flurry gives 1.5 hits (75% twice) and the iterative attack gives 1.55. Very close.</p><p></p><p>The 30% penalty for Sadrik BAB means that the attacks are at 45%. Two would be 0.9, three would be 1.35, and four would be 1.8. The last would be 16% more damage than the standard 1.55, which, again, is probably fine.</p><p></p><p>The place where the 30% virtual penalty causes the most trouble is when the chance to hit (for a standard fighter) is low. Wulf says (I think rightly) that for half-way decently designed monsters they will never happen at upper levels. But just for kicks, let's see what the numbers would be.</p><p></p><p>Suppose there's a 40% chance of hitting the creature. For a dual flurry (Wulf's system) that's 0.8 hits. For a standard iterative attack it's (.4 + .15 + .05 + .05) = 0.65 hits. A 23% discrepancy.</p><p></p><p>But for Sadrik BAB it's 0.4 hits if you flurry four times. Each attack has only 10% chance of hitting. That's only 61.5% as much as the standard. A bigger discrepancy. But hopefully this won't happen too often; monsters shouldn't have that good an AC.</p><p></p><p>Long story short, it seems that adding more iterative attacks helps make up the virtual penalty at higher levels. There might still be the tendency for them to be a "flurry of misses" though. </p><p></p><p>The exact details of the progression is unclear. I'd guess single attack, dual attack at -2, triple attack at -1, and quadruple attack at no penalty.</p><p></p><p>But even then... suppose the fighter has to move and attack? He's got a 45% chance of hitting vs 75%. That's a lot less damage on average. Only 60% of what Wulf's fighter or the PHB fighter would do.</p></blockquote><p></p>
[QUOTE="Cheiromancer, post: 4818553, member: 141"] I'm assuming that a 20th level fighter is hitting an opponent with four iterative attacks. Then I'm seeing how well he does with the iterative fix (Wulf's system) and then how it works with your proposal. The percentages are the chance of hitting a particular target with a flurry vs an iterative attack. For example, Wulf admits that his fix is a little off when the fighter misses only on a 1. We see this by considering the odds of a fighter hitting someone with a full attack consisting of 4 iterative attacks: the first one hits 95% of the time, the second 70% of the time and so on. The mean damage is 230% of a single attack, which I've expressed as 2.3. Two attacks at no penalty (95% chance of hitting each time) gives a mean damage of 190%, which I've expressed as 1.9. So at this edge case, Wulf's fix would result in the fighter dealing less damage to an opponent- the equivalent of 1.9 hits rather than 2.3 hits. That's 82.6% of the normal damage. If we were using your proposal for BAB ("Sadrik BAB") then all the percentages are 30% lower (for the -6 virtual penalty). Two attacks at 65% is only 1.3 hits total. With your latest suggestion it could become 4 attacks, with a total expected damage of 2.6. Now it's better than the standard case, which may be OK. (13% more damage than the standard isn't huge). Wulf's system is designed to give similar mean damages when there's about a 70% chance of hitting the opponent on the first attack. I used 75%. The dual flurry gives 1.5 hits (75% twice) and the iterative attack gives 1.55. Very close. The 30% penalty for Sadrik BAB means that the attacks are at 45%. Two would be 0.9, three would be 1.35, and four would be 1.8. The last would be 16% more damage than the standard 1.55, which, again, is probably fine. The place where the 30% virtual penalty causes the most trouble is when the chance to hit (for a standard fighter) is low. Wulf says (I think rightly) that for half-way decently designed monsters they will never happen at upper levels. But just for kicks, let's see what the numbers would be. Suppose there's a 40% chance of hitting the creature. For a dual flurry (Wulf's system) that's 0.8 hits. For a standard iterative attack it's (.4 + .15 + .05 + .05) = 0.65 hits. A 23% discrepancy. But for Sadrik BAB it's 0.4 hits if you flurry four times. Each attack has only 10% chance of hitting. That's only 61.5% as much as the standard. A bigger discrepancy. But hopefully this won't happen too often; monsters shouldn't have that good an AC. Long story short, it seems that adding more iterative attacks helps make up the virtual penalty at higher levels. There might still be the tendency for them to be a "flurry of misses" though. The exact details of the progression is unclear. I'd guess single attack, dual attack at -2, triple attack at -1, and quadruple attack at no penalty. But even then... suppose the fighter has to move and attack? He's got a 45% chance of hitting vs 75%. That's a lot less damage on average. Only 60% of what Wulf's fighter or the PHB fighter would do. [/QUOTE]
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