Calculating the avoidance value of expertise

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Re: Calculating the avoidance value of expertise

Postby majiben » Fri Sep 04, 2009 7:36 am

theckhd wrote:The threat gain of using a 2.6 speed weapon wouldn't offset the massive threat loss of turning off auto-attacks though. You gain about 200 TPS by switching to a slower weapon of equal ilvl, but our auto-attacks are a significant portion of our threat, upwards of 1000 TPS. I doubt that it's worth the trade-off, especially given that we have so much expertise on our current gear to help reduce parry-haste damage intake already.
The weapon speed was selected to best offset the threat loss. Also there is merit to considering conditions other than what highly progressed guilds find themselves in. There is no guarantee that our expertise levels will remain so high, especially as ice crown is released and paladin's inherently high expertise comes under scrutiny when these calculations become better known.

Say a tank at 26 expertise skill decides to stop their auto attacks and keep up SoV with HotR. Their chance of having their attack parried in a given time period is the same as a tank that had 25.2 more expertise skill or 206.64 rating. That is a huge change. Enough to make one wonder about the losses of using the str libram with AA off over the dodge with AA on for low levels of expertise.

Semi related but http://www.wowhead.com/?item=46097 should be looked into in your weapons speed:threat comparisons since it comes in a little slower at 2.7

Also AA off does have the slight advantage of never having a double parry in one boss swing.
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Re: Calculating the avoidance value of expertise

Postby theckhd » Fri Sep 04, 2009 7:45 am

Candiru wrote:After reading that thread I am pretty sure we don't know fully how the parry mechanic is implemented. There are some strange "ultra-fast" swings when a parry happens very close to the start of a swing time which were never explained.

Yes, but outside those inexplicable "crit parries," the last post fleshes out the model of the parry mechanic quite well. I would not be surprised if those turned out to be double-parry events due to a parry-able attack that wasn't being considered because it wasn't known about at the time (for example, our HV applications) or was assumed to not cause parry haste (HotR deflections). If I find some time to pore over the spreadsheet, I will, but it's probably not worth bothering with.
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Re: Calculating the avoidance value of expertise

Postby theckhd » Fri Sep 04, 2009 8:06 am

Majiben wrote:The weapon speed was selected to best offset the threat loss. Also there is merit to considering conditions other than what highly progressed guilds find themselves in.

I didn't mean to imply that there wasn't. I meant that I doubt it's worth the tradeoff for anyone, and doubly so for tanks with high expertise levels (at any level, really - Ulduar gear could be pretty expertise heavy as well, given the right gear set). I suppose if you're swimming in threat it might be worth considering, but you still increase the chances of Holy Vengeance falling off.
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Re: Calculating the avoidance value of expertise

Postby Awyndel » Fri Sep 04, 2009 9:39 am

I am considering gemming for the hard cap and using a fast tanking weapon, might be the safest way to go, if the threat lost and avoidance lost is not too big. With current gear that would prolly only take 2-3 gems. Put agility in the rest.

Still if a slow weapon makes expertise drop from 80% to 40% ( forgive me if it's the wrong numbers ) wouldn't a slow weapon make it twice as safe. I know you prolly can't see it like that but wouldn't the influence by quite big.

Or would a slow weapon make back to back haste more likely?

Sorry I can't help much with the testing, I just wanna say there is a lot of ppl out here who really appriciate what you guys do.
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Re: Calculating the avoidance value of expertise

Postby theckhd » Fri Sep 04, 2009 10:05 am

Awyndel wrote:I am considering gemming for the hard cap and using a fast tanking weapon, might be the safest way to go, if the threat lost and avoidance lost is not too big. With current gear that would prolly only take 2-3 gems. Put agility in the rest.

Still if a slow weapon makes expertise drop from 80% to 40% ( forgive me if it's the wrong numbers ) wouldn't a slow weapon make it twice as safe. I know you prolly can't see it like that but wouldn't the influence by quite big.

Or would a slow weapon make back to back haste more likely?

Sorry I can't help much with the testing, I just wanna say there is a lot of ppl out here who really appriciate what you guys do.

The two are intertwined. The reason a slow weapon makes expertise less effective is because you have fewer parries per second, thus fewer parry-hasted attacks. In other words, it's because a slow weapon makes you safer that expertise gets less useful in that scenario.
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Re: Calculating the avoidance value of expertise

Postby lythac » Fri Sep 04, 2009 10:46 am

theckhd wrote:In other words, it's because a slow weapon makes you safer that expertise gets less useful in that scenario.


Do we have an avoidance value per 0.1 Weapon Speed?

In practical terms can a 2.6 DPS weapon provide more avoidance (and threat) than a 1.6 Tanking Weapon? If it doesn't quite reach that point, is the reduced chance of burst damage worth considering?

Given expertises reduced effectiveness at slower speeds a slower weapon would have more benefit at lower expertise levels. If we ever lose the SoV glyph sod the rogues and steal their weapons \o/
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Re: Calculating the avoidance value of expertise

Postby Mithos » Fri Sep 04, 2009 4:05 pm

This may be a redundant or silly question, but is it confirmed that big nasty bosses like Algalon, Steelbreaker, Crusher tentacles etc actually have parry haste on? I remember blizz saying they didn't like it but then the discusion kinda just trailed off.
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Re: Calculating the avoidance value of expertise

Postby tlitp » Sat Sep 05, 2009 6:06 am

Lythac wrote:Do we have an avoidance value per 0.1 Weapon Speed?

while the question is as simple as it gets, the answer to it is anything but trivial; the parametric functions are not continuous (nchoosek(N,k) accepts only integers), so this calls for a refinement of the model itself

firstly, let's define some terms :
SPE - single parry event (AA OR HV/SoC) OR (RECK OR HV/SoC) OR (HotR OR HV/SoC) OR SoC_J
DPE - double parry event (AA OR HV/SoC) AND (RECK OR HV/SoC)
DDPE - double distinct parry events ((AA OR HV/SoC) AND (HotR OR HV/SoC)) OR ((AA OR HV/SoC) AND SoC_J) OR ((RECK OR HV/SoC) AND (HotR OR HV/SoC)) OR ((RECK OR HV/SoC) AND SoC_J)
cycle - the interval between two sequential swings of the boss
nota bene : HotR and J, as triggers, cannot generate DDPEs, just like two sequential AAs

now, some input variables :
pbss - player base swing speed
extra_pbss - additive modifier of pbss
pss - player swing speed, after raid buffs
bbss - boss base swing speed
reck - uptime of reckoning, relative to pss

binary toggles for handling the seals :
SoV_flag
SoR_flag
SoC_flag

the number of parry opportunities :
SoV_SPE - bbss/pss *2 in each cycle, plus bbss/pss *2 every 1/reck cycles, plus 2 every 6/bbss cycles
SoV_DPE - bbss/pss *4 every 1/reck cycles
SoV_DDPE - bbss/pss *2+2 every 6/bbss cycles, plus 2+bbss/pss *2 every (1/reck)*(6/bbss) cycles

SoR_SPE - bbss/pss in each cycle, plus bbss/pss every 1/reck cycles, plus 1 every 6/bbss cycles
SoR_DPE - bbss/pss *2 every 1/reck cycles
SoR_DDPE - bbss/pss +1 every 6/bbss cycles, (bbss/pss)+(1/reck) every (1/reck)*(6/bbss) cycles

SoC_SPE - bbss/pss *2 in each cycle, plus bbss/pss *2 every 1/reck cycles, plus 2 every 6/bbss cycles, plus 1 every 9/bss cycles
SoC_DPE - bbss/pss *4 every 1/reck cycles
SoC_DDPE - bbss/pss *2+2 every 6/bbss cycles, plus 2+bbss/pss *2 every (1/reck)*(6/bbss) cycles, plus 1+bbss/pss *2 every (1/reck)*(9/bbss) cycles
nota bene : reck=0 will effectively nullify any terms that account for reckoning procs

rearranging to integers :
N=bbss/pss in 1 cycle can be decomposed to floor(bbss/pss) in u cycles and floor(bbss/pss)+1 in v cycles, obtaining a system of linear equations (N=bbss*scalar/pss falls, obviously, in the same category)
floor(bbss/pss)*u+(floor(bbss/pss)+1)*v=bbss/pss
u+v=1
nota bene - u,v should be >= 0 in order to have physical meaning
Code: Select all
[u v]=[bbss/pss 1]/[floor(bbss/pss) 1;(floor(bbss/pss)+1) 1];


from here on the problem becomes trivial, and one can compute the average PH relatively (sic !) easy; either Theck, either his pocket rogue will update the code and post some numerical results... soon


PS. to give a direct answer to the question : one can make an analogy between the model of PH and the model of defense, as in both one encounters non-continuous functions; for a numerical example, 3 additional defense rating can lead to an additional 0 or 1 defense skill, whereas 0.1 additional player (base) swing speed can lead to two distinct average PH values (Theck, feel free to explain it better to normal people :p)
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Re: Calculating the avoidance value of expertise

Postby cordelia » Sat Sep 05, 2009 1:01 pm

Theck,

You've done some great work here, but I think the spike-damage analysis needs to be expanded. Exclusively looking at the parryhaste mechanics involved in only consecutive melee swings overstates the spike damage reduction value of expertise with respect to avoidance by a large factor.

Almost all tanks, and especially paladin tanks, can survive two consecutive melee swings, if fully topped off. Spike damage deaths occur because the tank isn't topped off, either from a prior melee swing, or from a boss special attack. Many bosses use melee special attacks that can be avoided. In order to flesh out the role of avoidance vs. expertise in spike damage, I think the following instagib-risk scenarios occur most frequently:

(1) 2 consecutive successful melee swings with additional non-avoidable incoming damage during the window.

(2) 2 consecutive successful melee swings with an avoidable boss special during the window that lands.

(3) 3 consecutive successful melee swings.

(4) 3 out of 4 consecutive successful melee swings.

I am having some trouble deciding how parry haste interacts with the above scenarios. I believe parry haste decreases the size of the window involved in all four cases.

For cases (1) and (2), parryhaste reduces the time window only when the additional incoming damage falls in the reduced parryhasted window. Parryhaste would always affect the time windows of cases (3) and (4).

Traditional avoidance, however, decreases the likelihood of cases (2)-(4) occurring.

If I get a chance later, I'll start punching these into your model of DTPS.
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Re: Calculating the avoidance value of expertise

Postby Fridmarr » Mon Sep 07, 2009 10:38 pm

theckhd wrote:
Candiru wrote:After reading that thread I am pretty sure we don't know fully how the parry mechanic is implemented. There are some strange "ultra-fast" swings when a parry happens very close to the start of a swing time which were never explained.

Yes, but outside those inexplicable "crit parries," the last post fleshes out the model of the parry mechanic quite well. I would not be surprised if those turned out to be double-parry events due to a parry-able attack that wasn't being considered because it wasn't known about at the time (for example, our HV applications) or was assumed to not cause parry haste (HotR deflections). If I find some time to pore over the spreadsheet, I will, but it's probably not worth bothering with.

Honestly, there's a reasonable chance we aren't quite on with our numbers about parry haste. Most of the research I've seen on them is combat log based, which I don't think is accurate enough. Not only are the timings incorrect, but the order of events are off too, which is common with asynchronous processes and it means that the timings are affected by more than just latency. I used to have logs from back in TBC that showed me getting holy shield procs when, according to the log, holy shield had expired more than a second ago and had not been put back up. How many times did people post log snippets here of them getting hit with a crushing blow that, according to the log, was impossible because of holy shield coverage? When we are looking for effects that happen in close timing and in a specific order like we do with parry haste, the log is going to have some questionable entries.

We know from blizzard that parry haste exists, it's likely significant because on bosses that hit hard they ususally turn it off, so obviously reducing their frequency even on the bosses where it is left on is a good thing. We can only work with what we have, unless a blue decides to spell it out for us, so it's quite possible that our understanding of the mechanic and the numbers are a bit off, but there are patterns in the logs and that is about as good as we are going to get and they are probably reasonable enough as a basis for mathing it all out.
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Re: Calculating the avoidance value of expertise

Postby Solitatis » Tue Sep 08, 2009 1:41 am

theckhd awesome work, even thou as sociology major I only understand about half of it, your bullet point summaries are extremely nice.

My question: You said that you would get back to the overlay between 70%+ avoidance? in regards to expertise, when does the overlay happen? when is expertise "worth more" than dodge.

Raid buffed I am very close to 70%
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Re: Calculating the avoidance value of expertise

Postby Candiru » Tue Sep 08, 2009 2:35 am

The trouble with expertise as an avoidance stat, is that is completely worthless on REALLY hard hitting bosses (EG patchwerk) as its turned off.

On bosses where the main threat is the Special Attack, its also of reduced value (as long as the special can be avoided, on Gormok both expertise and avoidance fail at impale.)

On adds with no special attacks, eg the adds on Anub'arak heroic expertise is worth this much when you are tanking one of them, but when you are tanking more it is again worth less.

Its still very useful to have an upper limit on the value of expertise as avoidance though, as that allows you to make a more informed decision. Its true value will vary between 0 and this 70% of dodge rating depending on the fight mechanics! (Which makes me rather hesitant about stacking it)
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Re: Calculating the avoidance value of expertise

Postby Solitatis » Tue Sep 08, 2009 3:12 am

Currently i am only worried about three bosses in game: Anub hard, Twins hard, and Algalon. I do not tank adds, have an OT for that :) Hence the question. I guess it is: When is 70% of dodge worth more than pure dodge because of DR? (while still maintaining 1.88 dodge/parry ratio)
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Re: Calculating the avoidance value of expertise

Postby Jerey-Darkspear » Tue Sep 08, 2009 4:47 am

Something I noticed after 15 attempts on Northrend Beasts is that no amount of expertise is going to save you from poorly positioned DPS :(
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Re: Calculating the avoidance value of expertise

Postby theckhd » Tue Sep 08, 2009 7:04 am

tlitp wrote:
Lythac wrote:Do we have an avoidance value per 0.1 Weapon Speed?

while the question is as simple as it gets, the answer to it is anything but trivial; the parametric functions are not continuous (nchoosek(N,k) accepts only integers), so this calls for a refinement of the model itself

While this is true for the spike damage calculation, the regular version doesn't use nchoosek, making it pretty simple to test out in that model.

Letting player_base_swing_speed vary from 1.3 to 2.7 in calc_expertise_mitigation.m, we can calculate the number of extra boss attacks we receive in a 5-minute fight due to variation in weapon speed:

Image

We can subtract these data points from their nearest neighbors to get the number of attacks per 0.1 weapon speed. To calculate the number of extra hits prevented, we need to account for the fact that we would have avoided 60% of these. Thus, the number of hits prevented should be -diff(num_attacks_taken)*0.4:

Image

Since the m-file is already calculating the number of attacks dodged for a small additional amount of dodge rating, we can use that as a conversion factor to convert this to an effective amount of dodge rating:

Image

And finally, we can perform a cumulative sum to see what the total effective dodge rating gain is by switching from a 1.3-attack speed to something slower (1.3 is roughly the adjusted attack speed of a 1.6 speed weapon after haste buffs - WF and Swift Retribution give a net 23.6% haste, so dividing the base weapon speed by 1.236 gives you your adjusted attack speed):

Image

So going from a 1.6 speed weapon (1.3 on the plot) to a 2.6 speed weapon (2.1 on the plot) is equivalent to gaining about 54 dodge rating.
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