Mitigation Comparisons – 4 tanks

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Postby Sëryph » Thu Oct 09, 2008 9:10 pm

Well I decided to try the opposite approach and build a model since we know exactly how it works heres the links

Bone Shield Test 1.17-1.75

Bone Shield Test 1.76-3.4

I had to do two different models because of the interaction between the CD and weapon swing frequency.

You can reset the model by reopening the file or adjusting the hit%/Charges/Attack Speed


My formula seems to be very accurate for 1.17-1.75 range but for the 1.76-3.4 range it seems instead of

Code: Select all
IF Attack Speed<1.76 Then
    Return 2
Else
    Return 1.5
End If,


I should have

Code: Select all
IF Attack Speed<1.76 Then
    Return 2
Else
    Return 1.5
End If,


I have no idea why though.
Last edited by Sëryph on Thu Oct 09, 2008 9:52 pm, edited 1 time in total.
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Aablaine 70 Druid
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Postby Deathwing » Thu Oct 09, 2008 9:49 pm

Your models are about 1 percentage lower than what I got, which probably verifies them since I expected them to be a bit high. If you don't want to use a separate XLSM with 10 sub sheets, the model I posted would be alot more compact, just subtract 1 from it. The formula would need some editing for the faster speeds where 2 attacks could fall in the CD.

BTW, are you sure the CD is 3.5s? I thought it was proposed, never saw it confirmed. Also, do AE's(spell or physical) and direct damage spells deplete charges?
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Postby Sëryph » Thu Oct 09, 2008 10:04 pm

Deathwing wrote:Your models are about 1 percentage lower than what I got, which probably verifies them since I expected them to be a bit high. If you don't want to use a separate XLSM with 10 sub sheets, the model I posted would be alot more compact, just subtract 1 from it. The formula would need some editing for the faster speeds where 2 attacks could fall in the CD.

Honestly I still not sure I understand what your trying to say if you could run through some math with say 25% chance the mob hits you at 2.4 speed then I'll have a way to relate it.

Deathwing wrote:BTW, are you sure the CD is 3.5s? I thought it was proposed, never saw it confirmed. Also, do AE's(spell or physical) and direct damage spells deplete charges?


I'm sure GC said that it is going to be we never got a confirmation it was in game. My guess from what has been said on the forums is it may not be "fixed" yet.

As far as I'm aware DD's do take off charges I do not believe ae effects do nor dots.
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Postby ziggyunderslashone » Fri Oct 10, 2008 1:32 am

Deathwing wrote:Ziggy,

I'm not following you. How would the average chance to hit approach 1?

Deathwing wrote:5/p*(attack speed) = t

That's your average BS uptime, as long as p is accurate. The only problem is that the player can't take advantage of values above 60s, so the average is on the high side. Not sure by how much.

Heh, that actually, but I had (attack_speed)/p*5 = t.
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Postby Deathwing » Fri Oct 10, 2008 5:42 am

Sëryph wrote:
Deathwing wrote:Your models are about 1 percentage lower than what I got, which probably verifies them since I expected them to be a bit high. If you don't want to use a separate XLSM with 10 sub sheets, the model I posted would be alot more compact, just subtract 1 from it. The formula would need some editing for the faster speeds where 2 attacks could fall in the CD.

Honestly I still not sure I understand what your trying to say if you could run through some math with say 25% chance the mob hits you at 2.4 speed then I'll have a way to relate it.


Ok, I'll give this another try. You maybe getting hung on definite numbers. The point of this is calculate the chance for any attack at any time to deplete a charge. Again, this is for speeds where only 1 hit is within the cooldown.

So, anytime the boss hits you, that deplete a charge. However, if the mob had hit you with the directly previous attack, the present one is in the cooldown and has no affect. These are all the different scenarios you care about:

hit
hit hit
hit hit hit
hit hit hit hit
hit hit hit hit hit

Keep going on and on. You'll see 5 hits in a row, the 1st hit does have an effect on the 5th one(the present one). That's how "chance for an attack to deplete a charge" formula is derived. Take all those scenarios(I usually go out to ten attacks), find their chance to occur and add or subtract them together, depending on whether that scenario causes the last hit to be in the cooldown or not.

EDIT: I was thinking on this some more, let me revise this. Basically, it's your chance to hit - your chance you'll be within the cooldown. Now I'm thinking it might be H - H^2 - H^4 - H^6....

Any thoughts on this?
Last edited by Deathwing on Fri Oct 10, 2008 9:02 am, edited 1 time in total.
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Postby steadypal » Fri Oct 10, 2008 9:00 am

3-4 days before patch hits live still no sign of 3% DR on templar, GG blizz..
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Postby ziggyunderslashone » Fri Oct 10, 2008 10:33 am

steadypal wrote:3-4 days before patch hits live still no sign of 3% DR on templar, GG blizz..

Realistically, it's only an issue if it's not in before WotLK. We'd prefer it earlier obviously, but if 3.0 goes live without it, we'll survive.
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Postby Sëryph » Fri Oct 10, 2008 10:44 am

Deathwing wrote:
EDIT: I was thinking on this some more, let me revise this. Basically, it's your chance to hit - your chance you'll be within the cooldown. Now I'm thinking it might be H - H^2 - H^4 - H^6....

Any thoughts on this?


First my fast attack speed simulation has a small mistake so I corrected it.

I finally figured out what you were trying to do with your calculation and I tested my calculation and yours vs. the model. One thing I noticed is my model needed to be bigger to test below around 10% hit.

I found that your formula was consistently wrong but by a fairly consistent percent except when your near 90+%.

My old model went between right on, to quite a bit off, depending on the hit%, Also my formula was consistently more accurate when the hit was above 90%

What this told me is I had to switch from a step function to a log and I also noticed some anomalies with the charge portion of the equation so I modified that as well.

I came up with a formula that is very accurate except a very slight, but noticeable, deviation at above 95%. The formula is quite accurate in the rest of the range.

I also put in your second formula in the slow attack speed model, you can compare them in the links below.

Fast Attack Model

Slow Attack Model

DK Tank Simulator V2.04
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Postby steadypal » Fri Oct 10, 2008 10:55 am

ziggyunderslashone wrote:
steadypal wrote:3-4 days before patch hits live still no sign of 3% DR on templar, GG blizz..

Realistically, it's only an issue if it's not in before WotLK. We'd prefer it earlier obviously, but if 3.0 goes live without it, we'll survive.



well i only see it useful really for those still going to tank before xpac hits... for lvling i'd go without it to pickup diff talents or allocate those 3 points elsewhere.. wait for 75 to get shield slam etc....



trade hotr for lvl 75 shield slam PST
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Postby ziggyunderslashone » Fri Oct 10, 2008 10:57 am

Oh ya, it'd be useful, but is anyone expecting balance till 80? which is the issue its required to resolve.
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Postby Deathwing » Fri Oct 10, 2008 11:48 am

Sëryph wrote:
Deathwing wrote:
EDIT: I was thinking on this some more, let me revise this. Basically, it's your chance to hit - your chance you'll be within the cooldown. Now I'm thinking it might be H - H^2 - H^4 - H^6....

Any thoughts on this?


First my fast attack speed simulation has a small mistake so I corrected it.

I finally figured out what you were trying to do with your calculation and I tested my calculation and yours vs. the model. One thing I noticed is my model needed to be bigger to test below around 10% hit.

I found that your formula was consistently wrong but by a fairly consistent percent except when your near 90+%.

My old model went between right on, to quite a bit off, depending on the hit%, Also my formula was consistently more accurate when the hit was above 90%

What this told me is I had to switch from a step function to a log and I also noticed some anomalies with the charge portion of the equation so I modified that as well.

I came up with a formula that is very accurate except a very slight, but noticeable, deviation at above 95%. The formula is quite accurate in the rest of the range.

I also put in your second formula in the slow attack speed model, you can compare them in the links below.

Fast Attack Model

Slow Attack Model

DK Tank Simulator V2.04


Can't look at your spreadsheets right now, don't have Excel 2007 at work.

But yeah, I expect my model to be on the high side, especially when uptime approaches 100%. The reason is that I'm using an average from a binomial distribuation, but the "trials" in which BS will last longer than 60s obviously can't be counted because the player will just refresh it.

A logarithmic function might work in the sense of replicating that diminishing returns as you approach 100%, but I'm not sure if that's the correct way to do it. I've forgotten way too much from my probability class in college.
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Postby ziggyunderslashone » Mon Oct 13, 2008 1:51 am

I’ve been playing around with both models you guys have been working with here, really cool stuff. However, any way I look at it, I can’t find a way to fit bone shield into the comparison sheet.

See, as much as it attempts to show how a very specific and defined boss encounter would be dealt with, it also, by virtue of not relying on external elements, shows how the white melee of an encounter would be handled in isolation.

Seconds till death is a misnomer, really it should read “full health pools worth of damage” which aren’t the same thing when healing is applied, but is a less visceral term.

This is why AD doesn’t work in terms of the sheet. It relies on knowing the exact point of health, which over the arbitrary period my sheet deals with doesn’t exist. Bone shield is much the same. It relies not only on the exact number of hits over a set and not arbitrary period, but also any external damage taken. Adds, specials, aoe etc.

The only thing currently in the sheet that acts in this way is holy shield, but this unlike bone shield is specifically designed to hold up permanently in a boss fight.

I’m not awfully keen on conceding, but I think I have to admit that bone shield, due to its charges mechanic, and the need to determine external data, can’t be modelled within the confines of the comparison sheet.

Brilliantly, we have Sëryph’s sheet for comparison between the two death knight specs, but I have learnt that unholy is not only competitive, but under certain circumstances, more powerful. I’ll refer to the modeled dk as frost from now on.
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Postby ziggyunderslashone » Mon Oct 13, 2008 8:12 am

Rather than working forwards in gear with the a theoretical scale, I've tried working backwards with known available gear.
Image
Image

I suspect in actuality, people will have some 10 man gear before a full set of heroic, but the principle is to see the effect of gear levels.

Bears are bouncing about a lot there. Itemisation is very wierd, whether dps leather has high stamina seems to be more accident than design, and the BoE frost resist set has so much stamina, it'll be standard tanking gear (even outperforming valorous) for some time. Assuming of course threat remains the non issue we're being told it currently is.

There seems to be a dearth of normal tanking drops generally, perhaps this is across all class, its hard to check as much of the beta data isn't linked on any of the resource sites I've been trauling.
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Postby Deathwing » Mon Oct 13, 2008 8:41 am

I agree with your thoughts on BS in a spreadsheet. In fact, I'm guessing that's also the reason most DK's favor frost as the best tank spec. As you said, just changes from boss to boss could wildly affect BS uptime, and tanks hate variance.

If you do happen to model BS in your spreadsheet, Seryph's is pretty good. There's been some discussion over at EJ on this topic as well. I've realized my model is a bit convoluted(still), so let me revise it(thanks Banda):

chance to deplete charge = npc's hit rate

5/(hit rate)*(attack speed) = uptime

If one attack is caught in the cooldown:

5/(hit rate)*(attack speed) + 4*(attack speed) = uptime

If 2 attacks are caught in the cooldown:

5/(hit rate)*(attack speed) + 8*(attack speed) = uptime


It's a really simple equation, dumb of me for not picking up on it previously(the cooldown part). As before, that's technically an average, so it's going to be higher than what would really happen, especially as you approach 90%, because you have to discount cases where BS would last over 60s.

I think Seryph said he was going to put this in his sheet.


If i read your graphs right, druids are only in trouble, scaling wise, once past naxx 25 man?
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Postby ziggyunderslashone » Mon Oct 13, 2008 8:49 am

Deathwing wrote:If i read your graphs right, druids are only in trouble, scaling wise, once past naxx 25 man?

Yeah, its all due to having a single avoidance stat. They don't even have much +miss due to defence. They can cap armour pretty fast, so they're left with hp and dodge. Once diminishing returns kick in, it hurts.

Realistically I can't see a point in wotlk where they'll struggle to tank. Quite the opposite in fact, early in gear progression they're by far the best tank. It'll be a good few ilevels before theres parity (by which time dks will be imbalanced).

As I see it there are two ways round the issue. Totally rework the class or implement a series of nerfs throughout content. Guess which they'll choose, sadly.
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