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<blockquote data-quote="JoeNotCharles" data-source="post: 4811025" data-attributes="member: 79945"><p>I wouldn't say it's NOT a factor, you just have to take hit rate into account as well as damage.</p><p></p><p>Let's say you have a 50% chance to hit a monster, and you do 1d10 damage with a +10 static mod. (Numbers pulled out of my ass, I'm just demonstrating how to do the math.) Don't forget that a 20 is a crit, so you have a 45% chance to hit for average damage (5.5 per die), a 5% chance to crit for max damage (10 per die), and a 50% chance to miss for 0 damage.</p><p></p><p>So for each attack of Rain of Blows, your expected damage is 0.45 * (5.5 + 10) + 0.05 * (10 + 10) + 0.50 * 0 = 7.975. Total expected damage is 4*7.975 = 31.9. </p><p></p><p>Meanwhile No Mercy has a single attack, with expected damage 0.45 * (7*5.5 + 10) + 0.05 * (7*10 + 10) + 0.50 * 0 = 25.825</p><p></p><p>That's not the whole story, though, because it's quite unlikely you'll actually do 25.825 damage - most of the time you'll do either 0, or much more than that. Let's break it down to cases where you do some damage and cases where you miss totally:</p><p></p><p>For each attack of Rain of Blows, your expected damage IF YOU HIT is (45/50)*(5.5+10) + (5/50)*(10+10). (Since there are 45 cases out of 100 where you hit for average damage, which means 45 cases out of the 50 where you do damage; and 5 cases out of 100 where you crit, meaning 5 cases out of the 50 where you do damage; and 50 cases out of 100 where you miss, which aren't included in this sample.) This works out to expected damage 15.95 for each attack THAT HITS.</p><p></p><p>Now, there's only 1 possibility where all 4 attacks hit, and it has probability 0.5^4=0.0625. There are 4 possibilities where 3 of 4 attacks hit, each with the same probability (total is 4*0.0625=0.25). There are 6 possibilities where 2 of 4 attacks hit (1 and 2 hit, 1 and 3 hit, 1 and 4 hit, 2 and 3 hit, 2 and 4 hit, 3 and 4 hit), again with the same probability (total is 6*0.0625=0.375). And 4 possibilities with 1 of 4 attacks hit (probability 0.25). And 1 possibility where no attacks hit (probability 0.0625). Doublecheck: 0.0625 + 0.25 + 0.375 + 0.25 + 0.0625 = 1.0, so the probabilities seem to work out.</p><p></p><p>Ok, so when 4 attacks hit, the expected damage is 15.95*4=63.8. Expected damage when 3 attacks hit is 15.95*3=47.85. Expected damage when 2 attacks hit is 15.95*2=31.9. And expected damage when 1 attack hits is 15.95. So the total expected damage when any attacks hit is 0.0625*63.8 + 0.25*47.85 + 0.375*31.9 + 0.25*15.95 = 31.9.</p><p></p><p>No Mercy is easier - the formula if the single attack hits is the same as above, (45/50)*(7*5.5+10) + (5/50)*(7*10+10) = 51.65.</p><p></p><p>So: No Mercy has a 50% chance of doing about 51.65 damage, and a 50% chance of doing none at all. (Or you could break this down further and say it has a 5% chance of doing 80 damage, a 45% chance of doing about 48.5 damage, and a 50% chance of doing none.)</p><p></p><p>Meanwhile, Rain of Blows has a 93.75% chance of doing about 31.9 damage, and a 6.25% chance of doing none. (Or you could break it down further and say it has a 6.25% chance of doing about 63.8 damage, a 25% chance of doing about 47.85 damage, a 37.5% chance of doing about 31.9 damage, a 25% chance of doing 15.95 damage, and only a 6.25% chance of doing none.)</p><p></p><p>So with a 50% chance of hitting and a +10 to damage, the two powers seem comparable: No Mercy will either do a large amount of damage or none, once a day, but you can keep trying until you hit (which of course uses up more actions, so it's still a pain). Rain of Blows most often does a smaller but respectable amount of damage, but has a 25% chance of doing just as much, a 25% chance of doing a disappointingly low amount, and only a small chance of missing entirely. It acts more like a "half damage on miss" power, but with a smaller chance of missing. And of course its once an encounter instead of once a day.</p><p></p><p>Of course, this is using numbers I pulled out of my ass. If you can get your hit percent about 50%, Rain of Blows will do more average damage and it will do its top damage more often, while No Mercy's damage stays the same but you can pull it off more often. If you can get your static bonus higher, Rain of Blows' average damage will grow quickly and No Mercy's will only bump up a bit.</p><p></p><p>FAKE EDIT: I just realized I screwed this all up, because 2 of the Rain of Blows attacks depend on the first attacks hitting, and I treated it as 4 independent attacks. So the numbers are all wrong. But I spent so much time on it, I'm damned if I'm deleting it all now.</p></blockquote><p></p>
[QUOTE="JoeNotCharles, post: 4811025, member: 79945"] I wouldn't say it's NOT a factor, you just have to take hit rate into account as well as damage. Let's say you have a 50% chance to hit a monster, and you do 1d10 damage with a +10 static mod. (Numbers pulled out of my ass, I'm just demonstrating how to do the math.) Don't forget that a 20 is a crit, so you have a 45% chance to hit for average damage (5.5 per die), a 5% chance to crit for max damage (10 per die), and a 50% chance to miss for 0 damage. So for each attack of Rain of Blows, your expected damage is 0.45 * (5.5 + 10) + 0.05 * (10 + 10) + 0.50 * 0 = 7.975. Total expected damage is 4*7.975 = 31.9. Meanwhile No Mercy has a single attack, with expected damage 0.45 * (7*5.5 + 10) + 0.05 * (7*10 + 10) + 0.50 * 0 = 25.825 That's not the whole story, though, because it's quite unlikely you'll actually do 25.825 damage - most of the time you'll do either 0, or much more than that. Let's break it down to cases where you do some damage and cases where you miss totally: For each attack of Rain of Blows, your expected damage IF YOU HIT is (45/50)*(5.5+10) + (5/50)*(10+10). (Since there are 45 cases out of 100 where you hit for average damage, which means 45 cases out of the 50 where you do damage; and 5 cases out of 100 where you crit, meaning 5 cases out of the 50 where you do damage; and 50 cases out of 100 where you miss, which aren't included in this sample.) This works out to expected damage 15.95 for each attack THAT HITS. Now, there's only 1 possibility where all 4 attacks hit, and it has probability 0.5^4=0.0625. There are 4 possibilities where 3 of 4 attacks hit, each with the same probability (total is 4*0.0625=0.25). There are 6 possibilities where 2 of 4 attacks hit (1 and 2 hit, 1 and 3 hit, 1 and 4 hit, 2 and 3 hit, 2 and 4 hit, 3 and 4 hit), again with the same probability (total is 6*0.0625=0.375). And 4 possibilities with 1 of 4 attacks hit (probability 0.25). And 1 possibility where no attacks hit (probability 0.0625). Doublecheck: 0.0625 + 0.25 + 0.375 + 0.25 + 0.0625 = 1.0, so the probabilities seem to work out. Ok, so when 4 attacks hit, the expected damage is 15.95*4=63.8. Expected damage when 3 attacks hit is 15.95*3=47.85. Expected damage when 2 attacks hit is 15.95*2=31.9. And expected damage when 1 attack hits is 15.95. So the total expected damage when any attacks hit is 0.0625*63.8 + 0.25*47.85 + 0.375*31.9 + 0.25*15.95 = 31.9. No Mercy is easier - the formula if the single attack hits is the same as above, (45/50)*(7*5.5+10) + (5/50)*(7*10+10) = 51.65. So: No Mercy has a 50% chance of doing about 51.65 damage, and a 50% chance of doing none at all. (Or you could break this down further and say it has a 5% chance of doing 80 damage, a 45% chance of doing about 48.5 damage, and a 50% chance of doing none.) Meanwhile, Rain of Blows has a 93.75% chance of doing about 31.9 damage, and a 6.25% chance of doing none. (Or you could break it down further and say it has a 6.25% chance of doing about 63.8 damage, a 25% chance of doing about 47.85 damage, a 37.5% chance of doing about 31.9 damage, a 25% chance of doing 15.95 damage, and only a 6.25% chance of doing none.) So with a 50% chance of hitting and a +10 to damage, the two powers seem comparable: No Mercy will either do a large amount of damage or none, once a day, but you can keep trying until you hit (which of course uses up more actions, so it's still a pain). Rain of Blows most often does a smaller but respectable amount of damage, but has a 25% chance of doing just as much, a 25% chance of doing a disappointingly low amount, and only a small chance of missing entirely. It acts more like a "half damage on miss" power, but with a smaller chance of missing. And of course its once an encounter instead of once a day. Of course, this is using numbers I pulled out of my ass. If you can get your hit percent about 50%, Rain of Blows will do more average damage and it will do its top damage more often, while No Mercy's damage stays the same but you can pull it off more often. If you can get your static bonus higher, Rain of Blows' average damage will grow quickly and No Mercy's will only bump up a bit. FAKE EDIT: I just realized I screwed this all up, because 2 of the Rain of Blows attacks depend on the first attacks hitting, and I treated it as 4 independent attacks. So the numbers are all wrong. But I spent so much time on it, I'm damned if I'm deleting it all now. [/QUOTE]
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