The concept of Set Bonuses is awesome. It's nice to have something that is a little different than the normal six or seven stats we normally see on gear. It gives us something different to think about and can even change the way we play our class.
That said, not all set bonuses are created equal. In some cases classes decide to skip a set bonus because it is either weak or useless. Others hold onto a set bonus for a very long time because it is so awesome. Since moonkin have been fairly lucky with set bonuses in the past I've been receiving a lot of questions asking me about the T8 set bonuses and should they drop the T7 bonus. In this post I hope to give you a good idea of what they are worth.
The Model:
I came up with these values using my model and my standard starting stats of a T7 BiS moonkin. Both the Solar and the Lunar model were updated and are being uploaded to File Front (in process). Please review my warnings on using my model found here.
4T7 - Wrath/Starfire Crit:
Your Wrath and Starfire spells gain an additional 5% critical strike chance.
Before week look at the tier 8 set bonuses I think it is important that we understand the value of the 4T7 set bonus. It is an awesome set bonus, but I get the impression that some players believe it to be untouchable.
In Theory: I subtracted 5% crit from both of my models and ran them a thousand times each. My results agree with my valuations of Crit Rating as a stat. For a Lunar rotation the 4T7 set bonus increased my Moonkins DPS by 176.54 DPS or 3.72%. For a Solar rotation the 4T7 set bonus increased my Moonkin's DPS by 213.73 DPS or 4.42%.
In Reality: In terms of DPS I don't know of anything that would alter the theoretical results. If you look at it from a mana perspective though it obviously has additional value due to Mana on Crit.
The Verdict: Anything that increases your DPS by about 4% is good thing so it is no wonder why this set bonus is so well liked. However, as good as a 4% increase is its not so huge that it couldn't be passed by another set bonus.
On a side note, this set bonus is more significant for a Solar rotation because crit is more valuable in a Solar rotation, but it is very good for a Lunar rotation.
2T8 - Eclipse increased by 15%:
Increases the bonus granted by Eclipse for Starfire and Wrath by 15%.
A lot of players are unhappy about this set bonus because it ties even more of Moonkin DPS to Eclipse. I can see their point but on the other hand its not like Eclipse is optional at the moment anyway. This set bonus should just be a supplement to how we are already playing.
In Theory: For a Lunar rotation the 2T8 set bonus increased my Moonkins DPS by 187.98 DPS or 3.96%. For a Solar rotation the 2T8 set bonus increased my Moonkin's DPS by 193.9 DPS or 4.01%.
In Reality: My theoretical numbers are probably a little high for this set bonus. My model assumes a stand still fight with a perfect rotation. In reality part of our Eclipse procs are going to be wasted due to movement or other game mechanics. So, lets assume a 70% usage of the Eclipse procs. For Lunar this would drop the numbers to 131.57 DPS or 2.77%. For Solar the numbers would go down to 135.73 DPS or 2.81 %.
The Verdict: Theoretically the 4T7 and 2T8 set bonuses are about equal in terms of DPS. In reality the 2T8 set bonus is a little bit behind, but some the difference is made up by tier 8's superior stats (yes, T8 does have superior stats). While it might be slightly worth it to stick with 4T7 instead of pickup up 2T8, the difference is very small. It is my opinion that you should break your 4T7 set bonus for the 2T8.
4T8 - Instant Starfire with IS:
Each time your Insect Swarm deals damage, it has a chance to make your next Starfire cast within 10 sec instant.
As you know there was a lot of drama surrounding this set bonus on the forums last week. The good news is that Blizzard will fix the bug and decrease the proc rate to 8% in the next minor patch. It should happen soon since blizzard has already released the patch notes.
In Theory: For a Lunar rotation the 4T8 set bonus increased my Moonkins DPS by 163.38 DPS or 3.31%. For a Solar rotation the 4T8 set bonus increased my Moonkin's DPS by 121.72 DPS or 2.42%.
Some of you may be surprised by this. I've seen many posters and bloggers assume that 4T8 would be better for a Solar rotation. However, the opposite seems true. After I did a little checking it looks like an instant SF is a bigger DPS increase over a normal SF then it is over a normal Wrath. This may even out a little bit when lag is added into the equation.
In Reality: For this set bonus I think my numbers are probably a little low. There are two primary reasons I think this. First, since it gives you an instant SF you can cast it while moving. This a significant bonus. Second, there will be times when you can DoT up multiple targets while moving. If you have IS's ticking on multiple targets then then you will get more procs. More procs means more DPS
The Verdict: I think it is a great set bonus and I will be equipping it once the fix is live. A couple of people have asked me if it is really worth it to equip it instead of hard mode gear. In my opinion, it makes the Tier(25) pieces better then hard mode gear. For hard mode gear to be better you would have to be getting at least 95 additional spell power or its equivalent. While a lot of the hard mode gear is great, its not earth shattering.
Conclusions:
In short, I like the T8 set bonus once the 4T8 set bonus is fixed. The old 4T7 set bonus is awesome for its level, but its not so good that you should continue to use it in Ulduar at the expense of Tier 8 set bonuses.
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On a Side Note: This will sound like a strange request to some of you, but I'm looking for some help with statistics. I did very well in my stats classes in college but that was over 12 years ago and I don't really remember it. So, I'm looking for some one with a good back ground in statistics to answer a couple of questions for me regarding my model.
1. To come up with relevant results I am running my model a thousands of times and taking the average DPS for each test. Is a simple average a relevant measure or am I missing something obvious that would make my results less accurate?
2. When I am running my model a thousand times I notice that the average results change very little after about 300 or 400 trials. How many trials do you think I need to run to get relevant results with a relatively low margin for error?
If you have a good knowledge of Stats and would like to help, please use my email to respond.
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18 comments:
I'm not a stats person (and my stats courses were much longer ago than yours), but what you are seeing with the 300-400 trials seems to be on par with polling type of statistics and is why polling a few hundred people is fairly accurate for a much larger pool of people.
Thanks for the info, is there any chance that you could add the problem the instant SF can cause in a lunar rotation precast?
I mean i'm casting wrath to proc eclipse, i get the insta SF and instead of a lunar rotation i get a solar one.
ust a thought on the 4T8 for a Lunar cycle: What if it pops in the precasting phase? Do you let it expire if you don't get an eclipse? Do you risk popping the wrong eclipse if it crits? I see this as being a logistical problem that decreases the value of 4T8 for a Lunar cycle.
Also, in regards to the 2T8 and breaking 4T7, it allows you the freedom of possibly picking up two or three more Ulduar pieces. I do not value the 2T7 bonus that highly since IS rarely contributes more than 10% of my DPS anyway, amounting to a max of 1% DPS lost. I'd much rather chuck that and pick up some very nice non-set upgrades.
~Relevart
EDIT: I couldn't edit it so I deleted it and brought it here. I added a second thought up there.
Types of descriptive statistics: Minimum, maximum, range, mean (what you call "average"), median, mode.
I tend to just report averages, and/or ranges.
There is a trade-off between "sample size" and accuracy. After a certain point, you'll see very little return for your time (why the 300 trials gives you about the same average as 1000).
If you wanted to run inferential statistics (ie. does solar or lunar have statistically significant differences?), then you may end up needing larger sample sizes to detect smaller differences...
Oh, it's helpful to report both the mean and some type of range term (ie. variance, standard deviation) for people who actually understand statistics (so we know not just what the average is, but also what the spread of your distribution looks like). However, other than people like me who live statistics... mean is probably the most informative thing that the average person knows how to interpret.
Very very interesting article on the T8 that answer a lot of interrogations about it.
For your mathematical question :
The problem of average is only encountered if the difference beetween two values are huge - as the different values for DPS (even crit) are not very "different" the average is quite a good measure (and simple to understand).
So you are probably right in using the average.
Speaking of statistic : the number of figures needed to be "ok" depends of the quality of the input.
Anyway as your figure are mathematical results, with no "wrong figures" you can assume that 400 can be enough.
Eg in poles (like for election) the "representative value" is about 1500. Doing a collect of 60 000 is irrelevant expect on a huge period of time (not the case here).
So if you run 1500 iterations of your calculation it would be far enough to prove your figures.
The other statistic that would be interesting (to a few) is some idea of the variance - range or even better would be the standard deviation / variance. E.g. a coin with 499 & 501 would have the same average ( 500) as a coin with 1 and 999. But the latter would have more spread - ten flips would be 4990-5010 vs 10-9990.
The old way would be use Excel; but now the Cool Kids post an online Googel Doc spreadsheet. :-)
Thx for a great article. I don't think people realize just how much the price of level200+ items can bounce around; you can save a lot of gold by planning ahead.
Rather than run a single simulation with randomly generated numbers, it might be better to do N independent simulations with different sets of random numbers. That way you could do a true ensemble average.
In statistical language, you're currently equating "time average" with "ensemble average", which is often true for quantities like mean DPS, but may not hold for higher order moments like the variance and won't let you get a reliable sense of the parameter sensitivity. Particularly if certain nonlinear effects like details of the eclipse mechanics are dominating the results.
Maestro: I'm guessing that will be dependent on gear, but it should be easy to figure out if the difference in damage done during a solar eclipse instead of a lunar is greater than your average damage on a starfire. I doubt it is though. Solar has really gotten boosted.
Anyway from tests on a dummy, and test on real circonstances (ulduar 10/25) :
warth to proc eclipse as an average DPS (on a 10min fight) of 3100 -
starfire to proc eclipse average 3050.
So we can say both are very very close now.
Your estimate get's closer to the true average at a speed of the square root of the number of samples you are running.
So incresing your sample size by a factor of 100 would improve the accuracy of the number by a factor of 10. If you think your already pretty close after 300-400 samples (and the number varying little after that is a useful way of saying that your pretty close) then increaseing to thousands will help a little but not a lot, so it's just a question of how long the extra samples takes you.
Volatility of the dps is good a decent measure to look at. Probably quote it in terms of 10% of the time your dps will be above X and 10% below Y (You might t do this via running more stamples and looking at the percentiles). This is easier for most people to understand I think.
I think an understanding of this could help in interpreting dps numbers and someone having a bad or great day could just be RNG. But on a full raid it feels to me like this averages out a lot across 15 or so dps each randomly having "good" or "bad" days.
Feel free to mail me if you want more details or have any questions.
Thx,
Centorious
kininebdfATgmailDOTcom
great writeup. i am doing a few gear lists myself based on your weights limited to what reckon i have a chance of getting anytime soon (no hard modes basically). i just wonder about tier-bonus weights. is "95 additional spell power or its equivalent" as you mention here for 2p and 4p combined or 4p only? if so, what is the weight of 2p, and if both combined, what are the respective weights? thanks in advance.
Thanks for all the responses to my Statistics question. It has given me a lot to think about and I my have to ask a few more questions in the future, but here are some of the fun things I've found since then. Most of my trials have a variance of around 50 DPS and Standard Diviation of about 7 or 8. Given that the mean is around 5k this seems very small to me so I am more confident in my numbers. Thanks for the help.
@Anon1
My model assumend that you wouldn't risk procing the wrong eclipse so, if the buff falls of the buff falls of. However, I will say though that on average you will proc eclipse within ten seconds. So, wasted procs should be few and far between.
@Maestro aka Relevart
As I said to anon my numbers assume that you don't risk proccing the wrong eclipse. I also agree that holding on to the 2T7 set bonus isn't a big deal. My napkin math says it worth about a 0.8% increase to DPS.
@Hamlet
Each of my numbers is independant of the other number. My 4T8 valuation assumes you have 2T8, but the valuation is the increase in DPS over the 2T8 set bonus. So each section is just for that set bonus.
Regarding the 95 Spell Power figure, Several people asked was it worth going for 4T8 or should the skip it and go for hard mode gear. The 95 Spell Power figure was the minimum and was for a solar rotation.
I don't have my spreadsheet available to me right now, but the Lunar rotation was around 130. The 2T8 set bonuses would be even higher then that. Probably around 150 or so.
thank you for the reply. so if i understand you correctly, assuming a lunar rotation, equipping 4+ t8 pieces gives a weight increase of the equivalence of ~(130 + 150) = 280 spellpower. that is pretty massive :). i guess it's a simplification of the matter but having some "hard numbers" brings the math down to my level...
Email me I had to stats for my psych degree
- Neren
A wasted proc is on average for me 14k damage (it would have to crit for it to be wasted in the first place). I doubt the difference between a solar and a lunar eclipse is that big. Have you done any modeling that suggests this is worth giving up?
@nin
I'm actually looking into this right now and will probably have something written up on it by tomorrow. I think the difference might come down to the idol bonus, but we shall see.
Small question - is it worth to change T7.25 to T8.10?
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