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House rule: Extra Attacks for martials at 5,11,17
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<blockquote data-quote="EzekielRaiden" data-source="post: 9142783" data-attributes="member: 6790260"><p>It does affect DPR though--specifically when you factor in critical hits, not just base damage Assume <em>fire bolt</em>, so 1d10 damage, assume 65% chance to hit.</p><p></p><p>Single-hit cantrip without crit: 0.35×0 + 0.65×22 = 14.3 DPR</p><p>Multi-hit cantrip: 0.015×0 + 0.1115×5.5 + 0.3105×11 + 0.3845×16.5 + 0.1785×22 = 14.3 DPR.</p><p></p><p>Those parts are certainly the same. Now, separately from the above, we can calculate the bonus from crits. For the single-hit, that's simple; 0.05*22 = 1.1.</p><p></p><p>It gets a lot more complicated with the multi-hit, but we can break it into cases of conditional probability.</p><p></p><p>0.1115×0.05×5.5 + 0.3105×(0.05^2×11+0.975×5.5) + 0.3845×(0.05^3×16.5+0.0071×11+0.1354×5.5) + 0.1785×0.05^4×22+0.00048125×16.5+0.0135×11+0.1715×5.5) = 2.21. I'll round that down to 2.1, simply because I didn't put in the extra effort of subtracting out the various lower probabilities (e.g. it should be 0.975-0.05^2 otherwise you're double-counting)--the probabilities are so small that it hardly matters for the end result. (Edit: Just checked. Actual result is ~2.18295, so call it 2.18, a hair under double the damage added by crits as-is.)</p><p></p><p>Changing the chance to hit obviously throws these numbers off--e.g. the easier it is to hit the target, the better multi-hit cantrips are, and conversely, the closer you get to needing a nat 20 to hit in the first place, the closer together the two will be. Now, you might say ~1 point of extra DPR isn't much, but that's around an 8% increase in damage output for classes that really don't need to be getting a damage boost --except Warlocks, who will fall into the same "now they suck relative to other similar classes because they've lost a key differentiator." There's a reason grabbing a couple levels of Warlock to get EB+AB is so tempting for Bards, Sorcerers, and Paladins, and AB is only half of the equation (a very very very nice half, but still half.)</p></blockquote><p></p>
[QUOTE="EzekielRaiden, post: 9142783, member: 6790260"] It does affect DPR though--specifically when you factor in critical hits, not just base damage Assume [I]fire bolt[/I], so 1d10 damage, assume 65% chance to hit. Single-hit cantrip without crit: 0.35×0 + 0.65×22 = 14.3 DPR Multi-hit cantrip: 0.015×0 + 0.1115×5.5 + 0.3105×11 + 0.3845×16.5 + 0.1785×22 = 14.3 DPR. Those parts are certainly the same. Now, separately from the above, we can calculate the bonus from crits. For the single-hit, that's simple; 0.05*22 = 1.1. It gets a lot more complicated with the multi-hit, but we can break it into cases of conditional probability. 0.1115×0.05×5.5 + 0.3105×(0.05^2×11+0.975×5.5) + 0.3845×(0.05^3×16.5+0.0071×11+0.1354×5.5) + 0.1785×0.05^4×22+0.00048125×16.5+0.0135×11+0.1715×5.5) = 2.21. I'll round that down to 2.1, simply because I didn't put in the extra effort of subtracting out the various lower probabilities (e.g. it should be 0.975-0.05^2 otherwise you're double-counting)--the probabilities are so small that it hardly matters for the end result. (Edit: Just checked. Actual result is ~2.18295, so call it 2.18, a hair under double the damage added by crits as-is.) Changing the chance to hit obviously throws these numbers off--e.g. the easier it is to hit the target, the better multi-hit cantrips are, and conversely, the closer you get to needing a nat 20 to hit in the first place, the closer together the two will be. Now, you might say ~1 point of extra DPR isn't much, but that's around an 8% increase in damage output for classes that really don't need to be getting a damage boost --except Warlocks, who will fall into the same "now they suck relative to other similar classes because they've lost a key differentiator." There's a reason grabbing a couple levels of Warlock to get EB+AB is so tempting for Bards, Sorcerers, and Paladins, and AB is only half of the equation (a very very very nice half, but still half.) [/QUOTE]
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House rule: Extra Attacks for martials at 5,11,17
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