If you talk about "consistancy", which deals damage more consistantly? The answer is Marked Scourge, because chances are, you have a better than 50% chance of hitting.
Also, its worth noting thus:
Let's say I miss twice, hit once and miss once, and hit twice. In the first scenario, the 18 damage is unlikely to matter, because I missed twice so the monster hasn't taken all that much damage. If I hit once and miss once, which one I'm using doesn't matter. If I hit twice, though, then marked scourge is better because A) it matters and B) I'm more likely to kill it with the added damage at this point.
I'm having trouble following your argument. Are you now arguing that the reason Marked Scourge is better is because it has a greater effect on DPR, because you hit more often than you miss?
In cases where it has a greater effect on DPR, we would all agree that it's a better feat.
If the DPR is the same however (and neither build tends to dramatic overkill), the number of rounds it will take you, on average, to kill one opponent of unknown hit points within a range of certain specifications seems to be the same.
I've been considering the 50-50 chance, equal damage from MS/HR scenario for a couple of reasons - first, you suggested it; and second, the arithmetic is much easier. Here, let me try a couple of sample damage outputs with equal DPR.
Case one: 75% chance to hit, 14 damage on a hit Case two: 50% chance to hit, 6 damage on a miss, 15 damage on a hit Case three: 75% chance to hit, 3 damage on a miss, 13 damage on a hit
All of these cases have identical DPRs of 10.5. I'm going to assert that if these three guys fight one monster with 42 hit points, then one with 43, then one with 44...and so on, until they're fighting one monster with, say, 55 hit points, that the average number of rounds it will take each of them to kill each of the monsters in succession will be incredibly close, but that whichever one of them has the highest 'overkill' total (probably case one, but I'm not sure) will be very slightly behind.
I'm not going to work it out, however, because it would be sort of hard, because I'm actually convinced, and because you probably wouldn't trust my numbers anyway. It's certainly true for the 50-50 hit possibilities that I examined. If someone else feels like taking the time to work something like that out, and finds that I'm wrong, I'd be happy to re-examine my assumptions.
Mostly, you're more likely to hit than you are to miss, so "high variance" isn't really an issue, because in fact something which adds to your hit damage is added more often than soemthing which is added to your miss damage.
Again, we all agree that something that increases your DPR more than something else is indeed better. However, if you hit 90% of the time, and average 20 damage a hit, I would argue that hitting 90% of the time and averaging 19 damage a hit and 9 damage on a miss is going to be (very slightly) better for killing opponents of unknown hit points.
Secondly, if you make your hits more significant when they do occur, and given monsters have a very large number of hit points relative to miss damage, then adding to hits is better because it is more likely to result in you killing the monster with your hit, because the hit adds in so much more damage.
Not so; assuming, again, that the DPR is in fact the same.
No. It proves the math shown is wrong. It makes no general statement about the desirability of hitting or missing. I could have just as easily chosen a case where you deal 300 damage on a 15+, 200 damage on a 14, and 0 damage on any other roll, and compared it to the case wherein you deal 50 damage every turn.
Well, here's the thing - there are an infinite number of examples that are possible. It would seem to follow, then, that there are infinite examples that demonstrate the absolute superiority of each type of damage in that particular case. In order to assert that a thing is really better, it's going to be necessary to compare the examples over a large range of potential hit points. The more 'granular' the damages are, the larger the range will be that's necessary to compare them over, because massive overkill DOES affect this. Since I don't feel like coping with the numbers for your first example (counting all the possibilities up to 2 million or so hit points seems a bit arduous), let's look at the second, more reasonable, one.
This character has a less than 16% chance of not killing a 300 hp monster by round 6; 76% of the time this character kills faster than the 50 damage per turn character.
Well, of course he does. He has TWICE THE DPR. Your original sample character did 100 damage a round, but here you've dropped it to 50. Unsurprisingly, people with much higher DPR tend to kill a lot faster.
The true chance that you will kill it before the (original) sample character is less than 50% - on the same round, about 16%. The average round on which you will kill it is very slightly worse than the 3rd. And, may I note in passing, if the monster kills you on the 4th round (or the 5th, or the sixth...), the knowledge that you had a good chance to kill it earlier than the other guy and were just unlucky isn't going to be much consolation?
Once again, characters win, I'd guess, at least 90% of all fights (probably more like 99%). Guarding against ill-fortune seems to me to be obviously better than exploiting good fortune, assuming the net effect is the same - and, in this case, the net effect does seem to be the same.
And therefore the statement false, because if a countercase can be found, you prove that it is not true across the whole range.
You seem to be misunderstanding the statement. It's not against any given hit point value.
It's against an entire range of possible hit point values.
Indeed, it isn't even true in general, as demonstrated by people running the two vs a given hp value.
Against any given HP value it won't be the same. Usually, one way of doing damage will be better. Against a range of similar hit point values, the average round where you kill stuff will tend to be the same, assuming your initial conditions don't lend themselves to massive overkill. Where there IS high variance in the DPR conditions (as in your 2000 on a critical scenario), the high variance is always the worse choice across the range.
That said, all the models presented are flawed in that they do not represent the variation in actual hit damage. Let's say that I deal 50 damage on average with a hit, via something like 4d6 + 36 damage. However, a little less than half the time, if I hit four times I'd fail to kill them with four hits. Now, if I change that damage to 4d6 + 45 damage per hit, suddenly my odds of failing to kill them drop dramatically if I hit them X many times, and it'd make a large difference in my odds of killing, say, a monster with 220 hp in four hits.
I don't think that makes a difference, to be honest; I think it just complicates the arithmetic. Once again, it's necessary to compare it against a range of possible monster hit points; any single monster hit point total will favour one solution, but that's not necessarily a sign that that solution is generally better.
Case one: 75% chance to hit, 14 damage on a hit Case two: 50% chance to hit, 6 damage on a miss, 15 damage on a hit Case three: 75% chance to hit, 3 damage on a miss, 13 damage on a hit
The average number of rounds to kill monsters from between 42 and 55 hit points are: Case one: 5.238 Case two: 5.164 Case three: 5.152 Expected from DPR: 4.619
[INDENT][/INDENT]Ok, I figured out a relatively easy way to describe the formula:
RtK(N): [INDENT]N<=0 : 0 N>0 : 1/PH + Sum( PD(i)*RtK(N-i) )[/INDENT]Where: [INDENT]RtK(N) is the number of rounds to kill a creature with "N" hit points PH is the probability of doing damage at all (e.g. .75 for 75%) PD(i) is the probability of doing "i" points of damage when you do damage[/INDENT]Note: [INDENT]Sum( PD(i) ) should be 1[/INDENT]
This formula is recursive, but spreadsheets are good at that. Just use one row for each possible hit point total.
Example 1: You hit 50% of the time, and do 12 damage when you hit: [INDENT]RtK(N) = 1/0.50 + 1.00*RtK(N-12)[/INDENT]
Example 2: You hit 100% of the time, and do 3 damage (50%) or 9 damage (50%): [INDENT]RtK(N) = 1/1.00 + 0.50*RtK(N-3) + 0.50*RtK(N-9)[/INDENT]
Example 3: You hit 65% of the time, and do 1d6+6 damage: [INDENT]RtK(N) = 1/0.65 + 1/6*RtK(N-7) + 1/6*RtK(N-8) + 1/6*RtK(N-9) + 1/6*RtK(N-10) + 1/6*RtK(N-11) + 1/6*RtK(N-12)[/INDENT]
The problem with "high variance is bad" is that it isn't. Its a flawed theory for any number of reasons. Firstly, the odds of your "high variance" matter. Mostly, you're more likely to hit than you are to miss, so "high variance" isn't really an issue, because in fact something which adds to your hit damage is added more often than soemthing which is added to your miss damage. Secondly, if you make your hits more significant when they do occur, and given monsters have a very large number of hit points relative to miss damage, then adding to hits is better because it is more likely to result in you killing the monster with your hit, because the hit adds in so much more damage.
Uhm - no. If the aim is to maximize the probability of reducing monsters to 0 or fewer hitpoints within a given timespan, then it's simply a mathematical conclusion that increased variance counteracts that aim. You talk of "the odds of high variance" - do you understand the concept of variance? Being the expected value of the square of the deviation from the mean? Decreasing the odds of high-variation events decreases the variance - that's kind of the whole point of the measurement. Marked Scouge increases variance, Hammer Rhythm decreases it.
It should be fairly clear that consistently and reliably dealing relatively more damage (wrt monster hit points) than the monster deals to you (wrt your hit points) enables you to more reliably kill the monster before it kills you. My previous argument examined this in more (intuitive) detail, including examining "chunkiness" of the damage; but the result is clear: Unpredictability (i.e. high variance) improves the odds of the underdog - which tends not to be the PC.
Increasing the low end damage is better than increasing the high end damage for increasing the kill rate.
For example, if MS does 12 points of damage per hit, and HR does 9 on a hit and 3 on a miss, you hit 50% of the time, and you are fighting an opponent with 100 hit points, MS will take an average of 18.000 rounds to finish him off, while HR will only take an average of 17.375.
In this scenario, on average HR kills the opponent 0.375 rounds faster than MS, although it is still 0.542 rounds slower than DPR would indicate (because of the possibility of wasted damage).
The formulae are relatively easy (with a spreadsheet), so it would be possible to calculate this even if the odds of hitting weren't 50% or to adjust for random damage.
So what you're trying to say is they kill them off in exactly the same amount of time. Statistics are great, but there is no .5 of a round.
And why are all the pro-MS people's examples always with a 50% hit rate? Even before Weapon Expertise blew that wide open people didn't have 50% hit rates.
So what you're trying to say is they kill them off in exactly the same amount of time. Statistics are great, but there is no .5 of a round.
Sure there is. A power that kills the monster 0.5 rounds faster has a 50% chance of taking one less round to kill the monster. If you were facing a dozen of these, you'd take 6 less rounds (on average).
Which is better: - 50% chance of killing the monster in 1 round and 50% chance of killing it in 2 rounds. (1.5 rounds on average) - 100% chance of killing the monster in 2 rounds. (2 rounds on average)
I've removed content from this thread because Trolling is a violation of the Code of Conduct. You can review the Code of Conduct here: http://forums.gleemax.com/community_coc.php
I don't think that makes a difference, to be honest; I think it just complicates the arithmetic. Once again, it's necessary to compare it against a range of possible monster hit points; any single monster hit point total will favour one solution, but that's not necessarily a sign that that solution is generally better.
It makes a very big difference.
The problem is basically that your odds of killing something scale much more with your hit damage than they do with your miss damage. Your miss damage has little effect on how fast you kill something; if you miss something three times in a row, chances are you need just as many hits to kill it as you would have needed had you dealt no damage on a miss. On the other hand, because your damage is variable, adding damage to your hit damage means you're more likely to kill something you "should have" killed, and because your kill rate scales much more directly with your hit rate, chances are you won't miss many kills due to missing repeatedly.
More or less, while it allows for a longer tail, it creates a bigger hump up in front. You're much more likely to take > 3N rounds to kill the monster (where N is the number of hits necessary to kill the monster), but you're also more likely to kill the monster in < 2N turns.
It would seem to follow, then, that there are infinite examples that demonstrate the absolute superiority of each type of damage in that particular case.
And therefore asserting either is correct in general over the other is false, as it is situational.
That being said, this is a subcase, where hit >> miss, which makes a big difference. If you assume only hit > miss, then its a lot more complicated, but with hit >> miss, miss damage isn't singificant enough.
The average number of rounds to kill monsters from between 42 and 55 hit points are: Case one: 5.238 Case two: 5.164 Case three: 5.152 Expected from DPR: 4.619
The problem is average number of rounds isn't the correct measure here. Median and mode are both more significant, as is the probability of killing the monster in less than some number of rounds.
Uhm - no. If the aim is to maximize the probability of reducing monsters to 0 or fewer hitpoints within a given timespan, then it's simply a mathematical conclusion that increased variance counteracts that aim. You talk of "the odds of high variance" - do you understand the concept of variance? Being the expected value of the square of the deviation from the mean? Decreasing the odds of high-variation events decreases the variance - that's kind of the whole point of the measurement. Marked Scouge increases variance, Hammer Rhythm decreases it.
This is just plain old wrong.
Say I deal 50 damage per hit normally, and can either deal 60 per hit or 50 per hit and 10 per miss, on average. Assume that the 50 per hit guy kills a monster in two hits 50% of the time, and for every +10 damage on your average, you add +20% to your odds of killing them in two hits.
The odds of killing the monster in two rounds for the guy who deals 60 per hit is 0.225, whereas the guy who deals 50 per hit has only a 0.125 chance of killing by that point. That is to say, the guy who deals 60 damage per hit is 80% more likely to kill on the second round.
