Feel free to use incorrect numbers in your math if you want. Everyone else will feel free to ignore it.
If you want to use math to make an argument, you need to do the math correctly. Rounding mid-calculation is a no-no. Rounding the final result is fine, but you skew your math by rounding the intermediate numbers. Ever hear the term "rounding error"? That's where it comes from. When you round mid-calculation, you cause errors.
What you consider accurate math only applies to a perfect environment, where lag and error don't exist. The reality is there there is lag, error, and combat windows that don't span vast amounts of minutes where the actual numbers may vary so much more from practical numbers.
Theorycraft is like a waterfall. Blizzard knows how much water goes over the top, but I only care about how much is going downstream. The theorycraft simply tries to simulate the waterfall. If my rounded numbers represent error, then consider it worst-case scenario, where my numbers represent the negative side of percentage error. This only means that average or best-case scenario will have slightly better values to represent.
It dropped off after 30 seconds, I used the in game stopwatch to time it. What's odd is it stacked and refreshed a lot faster than the cooldown suggests. Sometimes it would refresh multiple times in the space of a second or two.
It dropped off after 30 seconds, I used the in game stopwatch to time it. What's odd is it stacked and refreshed a lot faster than the cooldown suggests. Sometimes it would refresh multiple times in the space of a second or two.
Well, during Rabid _any_ successful attack has a 50% chance to increase the stack. That means both melee hits and specials. Pets roughly fire one of either every 0,8 secs. It should, on average, take 2 hits for each point, but that's pure statistics. Get lucky and you could have a 5-stack in 4 seconds.
What you consider accurate math only applies to a perfect environment, where lag and error don't exist. The reality is there there is lag, error, and combat windows that don't span vast amounts of minutes where the actual numbers may vary so much more from practical numbers.
Theorycraft is like a waterfall. Blizzard knows how much water goes over the top, but I only care about how much is going downstream. The theorycraft simply tries to simulate the waterfall. If my rounded numbers represent error, then consider it worst-case scenario, where my numbers represent the negative side of percentage error. This only means that average or best-case scenario will have slightly better values to represent.
No. Dealing with counter-intuitive issues such as averages expressed as a non-integer number of discrete events does not depend on a "perfect environment". Conversely, rounding intermediate numbers to suit perceptions about how averages work does not produce valid lower bound (or "worst-case scenario" data). Understanding why "6.66 Serpent Stings" is physically impossible but mathematically viable for modeling over the long term is at the heart of the statistics needed for theorycraft. Yes, over short periods of time, all values deviate from their expected averages: crit rate, proc rates, even raw damage rolls. But, no, this does not make models based on those averages less correct. Thor'idal's printed damage range is 355-524; with its speed of 2.7, it would be a 131.5 dps weapon given minimum rolls and a 194.1 dps weapon given those rolls' maxima. There will certainly be strings in some WWS somewhere that prove this true. But Thor'idal, over the long term, is neither of these things. It is a 162.8 dps weapon. This is the same type of averaging that is at work in our discussions over Lock and Load, and has been at work in every discussion of every mechanic everywhere at Elitist Jerks. You are welcome, of course, to do something entirely different, to model the complexities of WoW combat in whatever method you prefer, but discounting the mathematics of averages means that your numbers are apples to other posters' oranges and not that you are reflecting "the negative side of percentage error" in some way.
Why all the fuss over rounding numbers in napkin math?
Whichever way you spin it, L&L doesn't seem to be an overwhelmingly worthwhile investment.
It's called Bloodlust, not Heroism. What kind of pansy name is Heroism, anyway?
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12/13 [25] Heroic - Recruiting exceptional players.
What you consider accurate math only applies to a perfect environment, where lag and error don't exist. The reality is there there is lag, error, and combat windows that don't span vast amounts of minutes where the actual numbers may vary so much more from practical numbers.
Theorycraft is like a waterfall. Blizzard knows how much water goes over the top, but I only care about how much is going downstream. The theorycraft simply tries to simulate the waterfall. If my rounded numbers represent error, then consider it worst-case scenario, where my numbers represent the negative side of percentage error. This only means that average or best-case scenario will have slightly better values to represent.
No, YOU are applying it to a worst-case enviroment, we are applying to it the AVERAGE enviroment. You're doing all your math based on a 7 minute fight... but what about the fights that last 6 minutes and 45 seconds? Yours is completely screwed for those. Our math applies to any duration fight, not specific timeframes.
Well, during Rabid _any_ successful attack has a 50% chance to increase the stack. That means both melee hits and specials. Pets roughly fire one of either every 0,8 secs. It should, on average, take 2 hits for each point, but that's pure statistics. Get lucky and you could have a 5-stack in 4 seconds.
Heh that will teach me to read the tooltip, anyhow I did the test with all pet specials disabled due to the high focus cost of Rabid on the current beta, so it should stack up faster in practice. I just hope Rabid is one of the free focus abilities in the next beta build.
Why all the fuss over rounding numbers in napkin math?
Whichever way you spin it, L&L doesn't seem to be an overwhelmingly worthwhile investment.
Because when you make arguments based on incorrect math, your arguments have no worth. If L&L is lackluster, arguing that based on incorrect math won't convince the people that matter to improve it. Also, there's no "spin" to the correct math. Only when you intentionally skew your results like Trogdor was doing is there any spin.
Then someone step up and use the initial values I set and calculate everything out to the "correct, average" math. Then we can compare my rounded results to those results and see how much difference there is. If it's a huge difference, then maybe I should have gone with grid-paper math instead of just paper math, but I'm going to guess that the difference lies only in decimal places.
Concerning L&L, Eurytos came up with 15 DPS and 45 MP5 (in his reply to mine), whereas my numbers came to 20DPS and 40MP5. I'm not so concerned about that difference of 5 DPS or 5 MP5, because I get the general picture. It's just like looking at your actual crit percentage from your statistical crit percentage. There is going to be that slight variation, but most people are content knowing they're within 1-2% of what they're supposed to be.
Besides, the last time I checked all the damage in my combat log were non-decimal numbers. Does the game round up/down, or does it just drop the decimals? Either way, someone can go through and add up all the losses and come up with a figure.. one that doesn't matter in the end because Blizzard doesn't use decimals in the final value of damage. Everyone else wants to get bogged down in all the decimals, trying to model a system that's inherently based on dice. Blizzard doesn't care about the exact model because they have the real numbers. Do you want to know the result of 1D7? Roll it.
If the math discussed here is correct, you're replacing 2 steadies per proc.
If you use only Serpent Sting to proc it, that's 2* 130 mana over ~100 secs per proc, or 2,6*5 = 13 Mp5
If you use both Scorpid+Serpent to proc it, that's 2* 130 mana over ~57,4 secs per proc or 4,5*5 = 22,6 Mp5
Full raid-buffed with a target with all debuffs, Explosive does about 3.9k damage (+38% from target debuffs); probably quite a bit more with level 80 raid gear.
Unbuffed it does about 2.5k.
That's quite a big difference as Eurytos already said, when it comes to being either a very small increase in dps per talent point or a sizeable one.
Besides, the last time I checked all the damage in my combat log were non-decimal numbers. Does the game round up/down, or does it just drop the decimals? Either way, someone can go through and add up all the losses and come up with a figure.. one that doesn't matter in the end because Blizzard doesn't use decimals in the final value of damage. Everyone else wants to get bogged down in all the decimals, trying to model a system that's inherently based on dice. Blizzard doesn't care about the exact model because they have the real numbers. Do you want to know the result of 1D7? Roll it.
Incorrect. They do, in actuality, use floating point numbers for damage and hit points. I've survived fights more than once at 0 hit points - which should mean I was dead, except that I actually had 0.xyz hit points and thus wasn't dead. Also, take a look at fixed-damage abilities that don't deal integer damage (ie, their damage is listed as "from X to X+1 damage" on the tooltip). You'll see that they follow an exact pattern with their Xs and X+1s. For example, an ability that did 50.5 damage would alternate 50, 51, 50, 51, whereas an ability that did 50.25 damage will alternate 50, 50, 50, 51, 50, 50, 50, 51, etc. It's not random, it will always follow the same pattern. This is because it's rounding the displayed health and damage numbers to integers. The actual math used by the game is floating point for higher precision with stacking mutlipliers.
If the math discussed here is correct, you're replacing 2 steadies per proc.
If you use only Serpent Sting to proc it, that's 2* 130 mana over ~100 secs per proc, or 2,6*5 = 13 Mp5
If you use both Scorpid+Serpent to proc it, that's 2* 130 mana over ~57,4 secs per proc or 4,5*5 = 22,6 Mp5
Full raid-buffed with a target with all debuffs, Explosive does about 3.9k damage (+38% from target debuffs); probably quite a bit more with level 80 raid gear.
Unbuffed it does about 2.5k.
That's quite a big difference as Eurytos already said, when it comes to being either a very small increase in dps per talent point or a sizeable one.
Maybe I'm just being an idiot, but how do you use Serpent + Scorpid to proc it? Did they change something so you can keep both stings up at the same time?
Maybe I'm just being an idiot, but how do you use Serpent + Scorpid to proc it? Did they change something so you can keep both stings up at the same time?
*big sound of frying pan hitting forehead*
You got me there :p For some reason I have been thinking you could while I certainly know you can only keep 1 sting up
Incorrect. They do, in actuality, use floating point numbers for damage and hit points. I've survived fights more than once at 0 hit points - which should mean I was dead, except that I actually had 0.xyz hit points and thus wasn't dead. Also, take a look at fixed-damage abilities that don't deal integer damage (ie, their damage is listed as "from X to X+1 damage" on the tooltip). You'll see that they follow an exact pattern with their Xs and X+1s. For example, an ability that did 50.5 damage would alternate 50, 51, 50, 51, whereas an ability that did 50.25 damage will alternate 50, 50, 50, 51, 50, 50, 50, 51, etc. It's not random, it will always follow the same pattern. This is because it's rounding the displayed health and damage numbers to integers. The actual math used by the game is floating point for higher precision with stacking mutlipliers.
Right. So with L&L, one would expect it to be 6, 6, and then 7 Serpent Sting applications to trigger it. But by choosing to use 7, 7, 7 I've set the number for a 100% guarantee (105% actual), ideally. 6 Serpent Stings @ 15% chance is only 90%. But there is still no decimal for single hits. If the end damage is 1748,48 I'm only going to do 1748 for that hit. Dots fluctuate like that because it's a set amount of damage divided over a period of time, but a single melee attack or autoshoot is going to do one value only, undivided.
When I am buffed at 50% crit rate, one would expect that every other shot will crit, yet I've gone through strings of 4-6 shots with no crits as well as strings of 4-6 all crits. All the numbers are valid because it's all within the range of possibilities, which is essentially the roll of the dice. So when I said that my numbers were a "worst case scenario for L&L", it meant that at most it should take 21 stings to get three procs, but ideally it should happen at 19 stings. We can look at combat blocks of hours put together, or we can look at each individual window and take it for what it's worth. I choose the latter for practicality and simplicity.
The math I have is in the range of possible chances, yet there is argument that it's so "incorrect". I haven't said that any other calculations were wrong; in fact I look at those and compare it to mine and everything else to get the big picture.
Someone correct me if the math is wrong somewhere, but this is only supposed to be paper math (slightly more involved than napkin math, yet not quite grid-paper math). I didn't take in account T&T, Armor Penetration, other raid buffs, etc etc. It simply is what it is; a reference point. Some people want to sting, some don't. I also didn't take into consideration the difference in mana drain, fight longevity (due to mana), or mana regeneration from the difference in potential Hunting Party procs. Though, if mana isn't too much of an issue in a raid environment, it shouldn't be too huge a factor, depending on the differences of mana versus the differences in damage dealt (speculation w/o math to back it, mind you readers).
Oh, and I don't count Wyvern as a "wasted" point, because I actually use it for PvE (soloing, farming, etc) and [casual] PvP.
Are you using a 13% quiver? Wouldn't AS speed be 2.55 with a 15% quiver? Regardless, with Steady Shot being a 2 sec cast now, it'll take more than a quiver to get it down to the GCD. This makes either L&L slightly better since you're replacing 1.7s Steady shots with 1.5s Explosive Shots, or it makes using using SSting even better since you'll need more haste to get down to the GCD on SS.
Right. So with L&L, one would expect it to be 6, 6, and then 7 Serpent Sting applications to trigger it. But by choosing to use 7, 7, 7 I've set the number for a 100% guarantee
No. In actuality, with 7 stings, there is still a 32.057708828125...% chance that you won't get a single proc. There's no such thing as a guarantee when you're dealing with less than a 100% chance. That's the MEANING of a less than 100% chance. You can't do your math and assume that 7 will guarantee a proc - that's the entire reason why we're using the average number of times you have to cast a sting to get a proc. The average is the only valid number we can base the math off of.
There's a mathematical principle called the Law of Large Numbers, which states that, as your sample size increases (you fire more stings), the mean result (number of stings per proc) of a random event (15% chance) will approach the expected/average value (6.6666... stings per proc). This means that, since we're concerned with the overall use of the ability across the entire Hunter class on every server in every country and every use of a sting while talented with L&L, which is a massive sample size, the best and safest assumption is one proc per 6.66666... stings.
Presumed relevant raid buffs/debuffs:
Windfury
Curse of Elements w/ Malediction (or Ebon Plague)
Misery
Improved Scorch
Note: Winter's Chill not included because it can be presumed that Explosive Shot is not a 'fire spell' but instead a ranged attack that deals fire damage.
Auto Shot average damage = (((5500/14+138+73)*2.8)*.55+((5500/14+138+73)*2.8)*2.3*.45)*.7 = 1875.94
Steady Shot average damage = (((138+73)*2.8+0.2*5500+280)*.55+((138+73)*2.8+0.2*5500+280)*2.3*.45)*.7 = 2186.6
Serpent Sting average damage = (5500*0.2+1210)*1.13*1.05 = 2740.82
Explosive Shot average damage = ((5500*0.2+451)*1.5)*.4+((5500*0.2+451)*1.5)*1.8*.6 = 3443.22
Note: The 1.8 here is the crit multiplier for Explosive Shot. It is magical damage so the multiplier starts at 1.5 instead of 2.0. However, it is still a ranged attack so it should be affected by Mortal Shots and should be reported as a bug if it isn't.
Serpent Sting takes up 1.5/15=.1=10% of our GCD's
Explosive Shot takes up 1.5/6=.25=25% of our GCD's
Steady Shot takes up 1-.25-.1=.65=65% of our GCD's
Average GCD damage = .1*2740.82+.25*3443.22+.65*2186.6 = 2556.18
1.5/(2.8/1.15/1.2) = 0.74 Auto shots per GCD
Average DPS = (2556.18+.74*1875.94)*(1/1.5) = 2629.58
Now, to add Lock and Load:
Lock and Load shifts 1.5/100*2=.03=3% of your GCD's out of Steady Shot and into Explosive Shot.
Average GCD damage with Lock and Load = .1*2740.82+.28*3443.22+.62*2186.6 = 2593.88
Average DPS = (2593.88+.74*1875.94)*(1/1.5) = 2654.72
(2654.72/2629.58-1)/3 = 0.00318682 = .32% single target personal damage increase per point of Lock and Load
Are you using a 13% quiver? Wouldn't AS speed be 2.55 with a 15% quiver? Regardless, with Steady Shot being a 2 sec cast now, it'll take more than a quiver to get it down to the GCD. This makes either L&L slightly better since you're replacing 1.7s Steady shots with 1.5s Explosive Shots, or it makes using using SSting even better since you'll need more haste to get down to the GCD on SS.
Attack Speed = 3
Quiver = 1.15
new AS = attack speed / [(multiple of all % haste) * (1 + haste raiting / conversion from raiting to % haste)
3 / 1.15 = 2.608 ~~ 2.61
Presumed relevant raid buffs/debuffs:
Windfury
Curse of Elements w/ Malediction (or Ebon Plague)
Misery
Improved Scorch
Note: Winter's Chill not included because it can be presumed that Explosive Shot is not a 'fire spell' but instead a ranged attack that deals fire damage.
Auto Shot average damage = (((5500/14+138+73)*2.8)*.55+((5500/14+138+73)*2.8)*2.3*.45)*.7 = 1875.94
Steady Shot average damage = (((138+73)*2.8+0.2*5500+280)*.55+((138+73)*2.8+0.2*5500+280)*2.3*.45)*.7 = 2186.6
Serpent Sting average damage = (5500*0.2+1210)*1.13*1.05 = 2740.82
Explosive Shot average damage = ((5500*0.2+451)*1.5)*.4+((5500*0.2+451)*1.5)*1.8*.6 = 3443.22
Note: The 1.8 here is the crit multiplier for Explosive Shot. It is magical damage so the multiplier starts at 1.5 instead of 2.0. However, it is still a ranged attack so it should be affected by Mortal Shots and should be reported as a bug if it isn't.
Serpent Sting takes up 1.5/15=.1=10% of our GCD's
Explosive Shot takes up 1.5/6=.25=25% of our GCD's
Steady Shot takes up 1-.25-.1=.65=65% of our GCD's
Average GCD damage = .1*2740.82+.25*3443.22+.65*2186.6 = 2556.18
1.5/(2.8/1.15/1.2) = 0.74 Auto shots per GCD
Average DPS = (2556.18+.74*1875.94)*(1/1.5) = 2629.58
Now, to add Lock and Load:
Lock and Load changes shifts 1.5/100*2=.03=3% of your GCD's out of Steady Shot and into Explosive Shot.
Average GCD damage with Lock and Load = .1*2740.82+.28*3443.22+.62*2186.6 = 2593.88
Average DPS = (2593.88+.74*1875.94)*(1/1.5) = 2654.72
2654.72/2629.58/3 = 0.318682 = .32% single target personal damage increase per point of Lock and Load
Judging by your numbers it may behoove someone to go ahead and ask a Blue if this intended to operate as both a PvP and PvE talent. Obviously the proc from traps screams "PVP!", however the low proc off of stings pretty much means this talent will be seeing little use.
Of course a higher proc chance from stings would make it OP for hunter's who run a mana burn combo. Maybe if it was unhooked from Viper and had the proc increased?
No. In actuality, with 7 stings, there is still a 32.057708828125...% chance that you won't get a single proc. There's no such thing as a guarantee when you're dealing with less than a 100% chance. That's the MEANING of a less than 100% chance. You can't do your math and assume that 7 will guarantee a proc - that's the entire reason why we're using the average number of times you have to cast a sting to get a proc. The average is the only valid number we can base the math off of.
There's a mathematical principle called the Law of Large Numbers, which states that, as your sample size increases (you fire more stings), the mean result (number of stings per proc) of a random event (15% chance) will approach the expected/average value (6.6666... stings per proc). This means that, since we're concerned with the overall use of the ability across the entire Hunter class on every server in every country and every use of a sting while talented with L&L, which is a massive sample size, the best and safest assumption is one proc per 6.66666... stings.
The sample size I count ends with each WWS report. So with that in mind, how about you take a look at two of these Felmyst pulls and apply your principles to explain what the results are.
I'm just pulling this up and throwing it out; these two were very close in my active presence. So compare the auto shot hits versus crits. 55% crit rate on pull two, 44% crit rate on pull three. I didn't change groups. My starting buffs were all the same, totems the same, etc. Both of these pulls are individual combat windows, but with a significant difference in crit rates over the two minutes they each lasted. You can say "longer combat windows..." and whatever, but there is a cap to these combat windows, and you can't argue the results. They're right there. We can keep going and adding in more and more and more reports to get that average and refine it, but it's still not going to change what the actual results are. I am not so concerned with what it's "supposed" to be as much as what it "really is".
So take the 6.66 and calculate out the DPS and MP5 value equivalents for it, and then show me that it's so incredibly off from my model using 7 as the constant value. I want to see what this superior difference is that you're so tenaciously defending, just so I know how it'll impact my end results.
@Eurytos:
I dig those numbers. 3/3 L&L is ~1% PvE application worth of damage.. how does that translate to a DPS value, in that model?
Judging by your numbers it may behoove someone to go ahead and ask a Blue if this intended to operate as both a PvP and PvE talent. Obviously the proc from traps screams "PVP!", however the low proc off of stings pretty much means this talent will be seeing little use.
Of course a higher proc chance from stings would make it OP for hunter's who run a mana burn combo. Maybe if it was unhooked from Viper and had the proc increased?
No, because my numbers only showed the single target dps increase. It did not portray the mana and AoE damage benefits as well as the group/raid mana benefits from increased Hunting Party procs.
Note: The 1.8 here is the crit multiplier for Explosive Shot. It is magical damage so the multiplier starts at 1.5 instead of 2.0. However, it is still a ranged attack so it should be affected by Mortal Shots and should be reported as a bug if it isn't.
Do you have any source on this? I always believed Arcane Shot (our 'other' magical shot) had a base 2.0 crit multiplier. I'd assumed Explosive Shot would work the same.
Do you have any source on this? I always believed Arcane Shot (our 'other' magical shot) had a base 2.0 crit multiplier. I'd assumed Explosive Shot would work the same.
It was said earlier in this thread that that was the case on beta. Arcane is 2.0... so yeah, it could be a bug (it may have already been corrected, I don't know), but if it's not 1.5, it just makes Exposive Shot that much more overpowered.
The sample size I count ends with each WWS report. So with that in mind, how about you take a look at two of these Felmyst pulls and apply your principles to explain what the results are.
We can keep going and adding in more and more and more reports to get that average and refine it, but it's still not going to change what the actual results are.
Easy: tiny sample size. I don't know how you get from "entire hunter community across every instance of the game for the entirety of the game's life post-WotLK release" to "two pulls of Felmyst".
The Law of Large Numbers requires large numbers. 73 auto-shots is an irrelevantly tiny sample size. The actual variance here was 5 more crits from one set, and that set had 3 more shots total.
And, yes, it WILL change what the actual results are. Your first pull was a 55% crit rate against your expected crit rate of, what, 45% or so with raid buffs? The two pulls combined average to a 50.68% crit rate on autoshots. Over the entire run, your autoshot crit rate was 47.79% crit rate. See how, with greater and greater sample sizes, your mean result gravitates towards the expected result?
08/20/08, 3:13 PM
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