Ah well, you're right about Crusader there. I just know that a friend of mine who tested DW crusader on the PTR reported a PPM of around 1 with full WF&SS, that's why I assumed they reduced the PPM chance in the same amount as the strength (something like 0.6 ppm or stuff without everything).

@Pater: I would take the 36000s simulation, it's value range was around 1% of the calculated DPS. If i remember the rule of thumb correctly, 68% of all values will be in the median value +/- std. dev range. 95% will be in the median value +/- 2*std.dev range and finally 99.7% is in median value +/- 3*std.dev

So your std. deviation is 2.56, according to your excel sheet, so 36000s should be mighty fine.

Disquette, I am a little confused about the results in the spreadsheet in your post 808. If am reading the results correctly, it says that 1% crit provides 140% of the bonus of 1% hit. However, your empirical results indicate that 1 crit rating provides 140% of the bonus of 1 hit rating. This would mean that the two are significantly inconsistent, since 1 hit rating gives more hit % than 1 crit rating gives crit %. Am I missing something?

nah, you're not missing anything, I just missed that part of it. Mine is showing Crit Rating to be more valuable, to a higher degree, than the spreadsheet. Good catch.

This definitely merits some more thought then. If the simulation is correct, crit is 50% better than hit. If the theory is right, they are essentially identical. There are some differences in assumption between your simulation and the theory. In particular the simulation assumes parrys and blocks happen while the theory does not. Also, the weapon speeds used are different. I haven't yet thought through what effect this has on the answers however.

I think I found a bug in the model that would account for the difference, the model appears to be overestimating the effect of hit on windfury:

float mhyellowdps = 1 / 100f * ((hitwhite / 100f * hityellow / 100f) * 100f + crit - dodge) * wfproc * 1.4f * (wdps1 + wfap / 14);

We can break this down as:

mhwfswings = (hitwhite - dodge) * wfproc / 100 //how many expected windfury swings do I get
mhwfhitequivalent = mhwfswings * (100 + crit - dodge) / 100 //windfury can crit or be dodged
mhyellowdps = mhwfhitequivalent * 1.4 * (wdps1 + wfap /14) // how much dps this does

Note that I think this breakdown points out a small bug in the code since both the initial swing and the windfury swing can be dodged.

Suppose you increase hitwhite by 1 (i.e. add 1% more hit). This calcuation indicates that you will get wfproc / 100 more windfury swings for an increase of (100 / (hitwhite - dodge))%. Thus according to this model you should get more than 1% more windfury swings. However, Disquette's simulation shows that you actually get more like a .4% increase (if I read the chart from post 331 correctly). Thus this calculation is giving windfury 2.5 or 3x the benefit from +hit it actually receives.

Why is it closer to .4% than 1%? Since windfury has a 36% proc chance outside the cooldown and we are giving it a 18% proc chance with the cooldown, 50% of hits (and thus close to 50% of swings) fall in the cooldown. Furthermore, the additional windfury procs that do get generated my prevent a future windfury proc that would have happened (because it now falls in the cooldown). Of course there may have been other procs that the cooldown we removed suppressed. You can do inclusion/exclusion to calculate this effect precisely if you want, but the important point is that it is a net decrease in procs. So given that about half the additional hits were in the cooldown, and we lost some more procs due to other swings being in the cooldown, .4% seems pretty reasonable. So we are back to the moral that the bogus implementation of windfury screws over +hit.

I'm not 100% sure I understand your reasoning Universal, I can't follow the breakdown of the formula.

float mhyellowdps = 1 / 100f * ((hitwhite / 100f * hityellow / 100f) * 100f + crit - dodge) * wfproc * 1.4f * (wdps1 + wfap / 14);

Let's break it down:
1. (hitwhite / 100f * hityellow / 100f), WF can only proc if a previously white swing hits, in like every case this can be reduced to to hitwhite/100f, since hityellow is 100% anyway.
2. we add crit chance, wf can crit just fine
3. we substract dodge (the whole model assumes we have no blocks or parries, just dodges), should be correct, since dodge can not be mitigated as far as i know.

temp result would be something like 95f+30-5.6 = 129.4 = 1.294 for the factor

4. wfproc is our wf proc chance * 2 swings, for simplicity I assume 0.4 in this example
5. elemental weapons gets multiplied with our wfproc (1.4f)
6. (wdps1 + wfap / 14), we take our weapon dps and add up the increased dps gained from wf.

temp result would be for a 90dps weapon and 2400 ap something like:
0.56*(90+2875/14) = 165 dps*1.294

The 214dps are pre weapon expertise, pre stormstrike bonus and pre flurry bonus, but already includes misses, crits and dodges.


So if you add one +hit, in the example above from let's say 95% to 96%, you get 130.4 vs. 129.4 previously, this is an increase of roughly 0.77%, if we already have 100% yellowhit, the same value is gained if you increase 1% crit. 1% crit is a bit more useful since it influences flurry for example

The only real way to change this balance between crit and hit is, if you reconsider the closed form expression of the attack table. But given my initial attack table of (miss,dodge,glance,crit,hit) is correct, this closed-form expression is mathematically sound.

Let's see if I had the attack table correct:
Blizzard once said "The way WoW calculates crit rate is over ALL attacks. Crit rate is not based on hits only. In other words, if you have a 5% crit rate, that 5% chance includes misses."

I take the example from the last page:
If we consider the table: 10% miss, 5% dodge, 25% glancing (with 25% reduction), 25% crit, 35% normal:
average hit is 100 dmg:

for 100 hits it looks:
10 misses, 5 dodges, 25 hits with 75 dmg, 25 hits with 200 dmg, 35 hits with 100 dmg
summed up this adds up to: 10375 dmg in 100 hits = 103.75 dmg/hit

As long as the 25% crit are really the 25% from gear and talents, the AT should be correct
0.9 - 0.05 + 0.25 - 0.25*0.25 = 1.0375
I don't see any way to compute this correctly in a fashion using something like hit*crit or similar. (e.g. hit affecting all the base values, like crit, without modification).

I'm currently running with http://www.wowhead.com/?item=23544 and http://www.wowhead.com/?item=27980 as an offhand. I've just got enough Thrallmar rep together to buy http://www.wowhead.com/?item=29165 is there any point in buying this or is it just too quick to use as an OHer?

If I do end up getting it with the way WF is working at the moment would using it as my mainhand make more sense than OHing it as it has only slightly less DPS than Runic but is far quicker?

I'm grinding Heroics pretty constantly at the moment trying to get one of the slower OHable weapons like bogspine knuckles to drop. Is it likely that OHing one of these slower blues will be a superior combination that any involving Warbringer from thrallmar rep. Is this something I'm simply going to have to test myself?

Great thread.

[edited for wrong link]

I"m assuming you meant to link this - http://www.wowhead.com/?item=29165
And yah that's too fast for an offhand and you definitely do not want to use that as a mainhand. The slowest off hand from a heroic instance available is the axe that drops off Exarch Malledar in Heroic Crypts. http://www.wowhead.com/?item=27872

Remember that WF and SS are not normalized for speed, so having a heavy hitting slow MH is important to maximize their damage, and now the 3 second cooldown demands an OH as close in speed to the MH as possible to minimize WF interference.

Also don't forget http://www.wowhead.com/?item=27747 that drops for Hungarfen, 1st boss from Underbog in heroic.

Those two and http://www.wowhead.com/?item=27490 seem to be the only viable options beyond buying a slow OH from AH. Finding these mechanics truly irritating.

My minor complaint was that I believe dodge should be subtracted from hitwhite before it is multiplied by hityellow because if the initial attack is dodged, windfury cannot proc. Actually, now that I look at it, I think that crit and dodge need to be multiplied by this number too because if the white swing misses or is dodged, nether a crit nor a dodge can happen. This means it would look like:

1 / 100f * (hitwhite - dodge) / 100f * (hityellow + crit - dodge)

My major complaint is that you are using a wfproc is independent of +hit. The model assumes that the expected number of windfury swings you get is per white swing is wfproc * (hitwhite / 100), although as I said above, this should really be wfproc * (hitwhite - dodge) /100. This number is just coming from change of white swing not missing or being dodged multiplied by the probability of a proc, multiplied by 2 for swings from the proc (already implicit in wfproc). This means that adding 1% more hit should increase the number of windfury swings by more than 1% (1 / (hitwhite - dodge) / 100). This should be more than a 1% increase in dps, not the .77% you calculated. I believe the difference is the bug above since as written the formula says that increasing +hit gives you no more windfury crits.

In any case, the data from Disquette's simulations indicate this is significantly more than it should. Look at the WFOverall column of:

http://www.discofiend.com/wow/Shaman...st_raiding.htm

The data is somewhat noisy, but as hit increases from 18 to 26, the WF proc rate falls from 19 to 18. Another view of the same data is in the graph in post 331. On average over all the data points, 1% hit is giving a little more than 100 extra windfury procs. This is on top of the 25000ish that are already happening. This means we are getting .4% more windfury procs, not 1% or even .77%. The key point is that +hit increases the number of white swings, but because of the way the cooldown works this decreases the percentage that proc windfury. The model holds this percentage constant, so it is overvaluing +hit.

Yeah, that's why I'm so insistent at this point on doing field tests. Your sheet looks compelling and the math seems right. Pater and my simulations seem compelling and the cycles seem right.

But only one of them can be if they produce diff results (yours shows hit rating = crit rating. sims show crit rating > hit rating).

So, I have some tests in mind that I'll be doing sometime in the next couple days. If the sim is wrong, I want to know it. If your closed form analysis is wrong, I want to know it.

We're spinning our wheels atm because there is no clear "this is the way it is" at the moment.

You can also try heroic Hillsbrad for the http://www.wowhead.com/?item=28210

Yes, having three rare heroic drops and the arena 2.6 as the only viable offhand weapons is quite annoying.

Tornhoof, I think we are talking past each other a little bit here. I am going to try and break things down to try and figure out where we disagree.

1) How does +hit effect windfury dps?

Forgetting the exact formula for the moment, where does 1% hit provide more windfury dps? Since we are all hit-capped for yellow attacks, adding hit does not change the damage done by windfury procs at all. By this I mean that, once a proc has happened, +hit has no effect on how much damage that proc will do. So +hit effects windfury dps solely by increasing the number of procs. Furthermore, this means that the percent increase in dps from 1% hit is exactly the percent increase in the number of procs.

2) How many extra procs does +hit generate according to the model underlying Tornhoof's calculations?

In order for a windfury proc to occur, the white swing must hit, crit or glance, we must be outside the cooldown, and windfury must then roll a proc. As I understand it, the model combines the last two considerations into wfnerf. The probability of a white swing hitting, critting, or glancing is (hitwhite - dodge) / 100. This means that the probability of a single swing proccing windfury is wfnerf * (hitwhite - dodge) /100. Increasing hitwhite by 1 means we have increased the proc chance by (wfnerf * (hitwhite + 1 - dodge) /100) - (wfnerf * (hitwhite - dodge) /100) = wfnerf / 100. This is a (wfnerf / 100) / (wfnerf * (hitwhite - dodge) /100) = 1 / (hitwhite - dodge) > 1/100 = 1% increase in the number of procs.

If I am wrong about 1 or 2, please show me how your calculations differ from mine.

Assuming I am correct about 1 and 2, we can draw several conclusions. First, the underlying model says that 1% hit should generate a more than 1% improvement in windfury dps. Tornhoof's calculations show a .77% increase in windfury dps. So if the model is correct, then there is a bug in the calculation. I think my argument above gives that bug. I want to make sure my understanding of the model is correct before I try to explain it again. I will just note that if you plug my formula into the spreadsheet Disquette made of these calculations in place of the current one, you do indeed get an increase in windfury dps of just more than 1% from 1% hit.

Finally, whether the model Tornhoof uses should give .77% or more than 1%, the key observation that I want to make is that Disquettes simulations peg it at .4%. In other words the calculation says +hit has at least twice the effect on windfury dps as the simulation. I believe this difference is large enough to account for pretty much all the difference in +hit valuation between the two. Thus this issue is where any empirical testing should be done to determine which is right.

Here is an experiment that will decide which makes more accurate predictions about windfury procs. First, beat on a servant in the blasted lands long enough to get a good estimate of windfury proc rates. Then, reset talents and do not take any of the +hit talents, for a net change of 9% hit with everything else constant. Repeat the experiment on the servant. If the simulator is correct, the proc rate should go up. If the model is correct, it should be unchanged.

Yeh we missed each other for 1.)
It does increase the DPS by allowing more white hits and such increasing the chance to WF and increasing the WF DPS as in the calculation (not the Damage per Hit or something like that, just the DPS).

As for 2.). Lemme see

Yes, wfnerf * (hitwhite - dodge) /100 is the probality for a WF proc. Should be correct?
We have a wfnerf chance to proc as soon as we hit the mob successfully, let's say we hit the mob in 95% and it can still dodge for 5%, so it should be something like 0.4*0.9 = 0.36

Now if we add 1% hit, we add 1% of white hits on the mob.
Let's say as above we previously hit the mob with 95% probability and 5% dodge, so 90% of our swings should land successfully.
From 1000 swings this should be 900 swings, if we have 91% hit chance (including dodges) it should now be 910 swings which land on the target.

Of these 900 swings, given 100% yellow hits and 20% proc chance we should see 180 WF procs, 360 wf hits at all.
Now increase hit by 1%, 910 swings in the same time, so according to your WF logic it should still be 180 WF procs, 360 WF hits. Correct?

My model assumes that you should get 182 WF procs, 364 WF hits.

I think you can reason both and I think both are wrong:

The question just is do we really lose WF procs if we hit more often?
Yes as soon as we reach an expected WF proc time of around 3s, aka we expect to proc WF in 3s atleast once. For slow weapons this is not the case. For fast weapons it is.

The question is just how much do we expect it, yes it certainly can, but what is the probability.

To conclusively answer it, we need a proper discrete probability model of Windfury. That model could answer the question: At what weapon speeds are we >95% sure that we're losing WF procs.
We're 100% sure for two fast daggers (doing 5+ swings in 3s).

My discrete probability knowledge is rusty, so I'll guess we need to try.

Hey guys,

Yesterday after farming scryers rep all day I noticed a few inconsistencies with common knowledge.

It seemed that the Offhand damage for Stormstrike is now halved, and also that Thundering Strikes was now working properly with Stormstrike and Windfury.

I have some screenshots of this behavior which I will do my best to upload as soon as possible, and I'll also try and reconfirm this when I get on to farm again tonight, 10k rep to go yeesh.

Anyway, just putting this out there to see if anyone else has noticed this.

Great work on the simulator guys. I've been following this thread closesly and its been an interesting read so far

-Freyalis

I was pretty sure that Stormstrike did full damage with both hands until 2.1. Or maybe i didnt notice and that was fixed earlier which sounds a tad more likely, my eye has always been on windfury tbh.

I'll post the screenshots i have when i get home from work.

Heya,

thanks for the reports. In the simulator, I already have Stormstrike offhand doing 50% damage, per the offhand weapon penalty, and i also have thundering strikes affecting all attacks, including windfury and stormstrike.

Slant has asked repeatedly for proof that Thundering Strikes is working correctly, but I haven't offered up any proof or solid combat logs yet to confirm this (so far it's just anecdotal recap results). Once I do my tests in the next day or two, I should be able to do so.

I think everyone at this point agrees that Stormstrike's offhand penalty is a "known" reduction of 50%, and in fact, your report is the first time I've heard someone suggest otherwise ;-)

~_~

I'm obviously behind the times with the SS changes then.
In any case, all i have to present on the Thundering Strikes change is, like you said, anecdotal evidence picked up by KombatStats. I'll post them regardless.

White Damage


Stormstrike


Windfury


This data is from 2.1 till yesterdays farming session. Hopefully there is enough hits in there to provide a large enough sample size. My crit rate, as shown on character sheet is 26.26%.

Also in regards to the weapon enchants, While i do agree that Mongoose > Crusader > Potency, I feel a lot of people are disregarding Fiery as a viable enchant. I've only done some mental math and quick scribbled equations about it and plan to sit down and hopefully look at it more tonight. However by those quick calculations it beats Potency for increase in DPS and costs less to get enchanted =). And thats before the contributions from Imp Scorch, CoE & Misery.

That's a large enough sample size for me, thanks Frey. Good stuff. My tests awhile ago showed a definitive 5% drop, there's no question they fixed it with your tests.

Interesting question.

Fiery enchant is 6ppm, assuming 30% haste, 20% windfury, 6 stormstrikes per minute, and a 2.6s weapon, it would effectively be 10.92ppm and thus do 7.28dps. Assuming a 14% resist rate on a lvl 73 with that resto talent for +3% to spell hit, 6.26dps.

Potency is 20 str, 40 attack power, so that's 4.29dps on white damage, 1.12dps on stormstrikes (2.6s weapons again), and 2.23dps on windfury attacks for a total of 7.64dps. Assuming 30% armor mitigation, 5.35dps.

Fiery does even better on <lvl73 mobs, where the resist rate drops drastically. But then you can factor in melee crit vs spell crit and weapon mastery and so on and the math gets hinky, which is why we have guys like disquette making complicated simulators instead of just spreadsheets like other classes. It's safe to say that they're pretty damn close.

Ok, so I think we are pretty much converged about those issues, so lets try and tackle some more complicated things.

First, look at your model's predictions about windfury (ignoring for the moment that neither of us thing it is quite right). It says that in your example 1% hit increased the number of procs from 180 to 182. This is a (182 - 180) / 180 * 100 > 1% increase in dps. Any numbers you use for the model will give a result >= 1%. However, in the example earlier, the calculation gave a value of .77%. This means there really is a bug in the calculation. I believe it is the on I pointed out earlier. Basically, the reasoning behind multiplying white * yellow is that the initial attack must hit before the windfury can hit. But is also has to hit before the windfury can crit.

As for figuring out the probabilities for windfury, I agree that modelling it is a total mess. I can get a little ways in, but it rapidly becomes too messy. Suppose you get a new windfury proc as the result of adding more hit. This increases your procs by 1. However, consider the next two swings after that. Both must now be in the 3 second cooldown (since each weapon is < 3.0). Assuming both of these were outside the cooldown before this new proc, with probability greater than .5 one of these swings would have procced windfury (each hit has a .36 chance so this is actually 1 - (1 - .36)^2). Thus your net gain is actually (1 - .36^2). However, this proc that you now supressed may itself have been supressing other procs. If this was the end of the story, you could just sum up the series and be done. However, in reality sometimes a proc will have a cooldown for the next 3 swings and sometimes the next 2 depending on whether it is MH or OH if both happen at the same time. Stormstrike also factors in to make a mess of things. Disquette's simulator may be the best answer here for figuring some reasonable values to hack into the equation (much in the same way wfnerf is really a hack at the moment based on a linear fit of test realm data).

Yup, going by those figures Fiery does appear to outperform Potency.

Some more stuff to consider though.
* Fiery has a static 5% crit chance for 150% damage. This makes the average base hit 41 dmg
* Fiery can receive up to +33% damage from:
CoE: 10%, Malediction: 3%, Imp Scorch: 15%, Misery: 5%
You can reasonable expect 30% as Malediction isn't guaranteed. This boosts average base hit to 53 rounded and would bump projected DPS from 6.26 to 9.70

However

* Potency affects your other weapons attacks as well as the enchanted weapon
* With enough crit to grant sustainable Unleashed Rage, potency effectively grants 44 AP upping DPS from 5.35 to 5.88
* Potency's DPS contribution scales with your melee crit rate.

Good point bringing up the spell hit, as i had forgotten about that for lvl 73 mobs. Also another note about which weapon you should enchant with what. You want your best weapon enchant to go on your offhand item as you will still retain this when disarmed, which really doesn't happen that often to be honest. Otherwise for a shaman you should see the exact same proc rate over time for each weapon given the same enchant =)