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Mitigation Comparisons – 4 tanks

All things related to the expansion

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Postby ziggyunderslashone » Thu Oct 09, 2008 10:21 am

Sëryph wrote:Yes absolutely worst case the BS charges could be striped away. but because of the 3.5 second cd for loosing a charge, its actually highly unlikely. The math favors in almost every case the charges not being used up except at a very steady reliable rate.

I'm not really talking about a common or even likely scenario. At high avoidance levels it's massively unlikely that you'd take 5 or 6 full attacks in a row as any class, but thats what effective health assumes.

I'll have a better look through tomorrow, but either way I feel anything that relies on a key event defeats the purpose of the "raw" field.

To be realistic though, this is entirely my definition.
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Postby Sëryph » Thu Oct 09, 2008 10:24 am

ziggyunderslashone wrote:
Sëryph wrote:Yes absolutely worst case the BS charges could be striped away. but because of the 3.5 second cd for loosing a charge, its actually highly unlikely. The math favors in almost every case the charges not being used up except at a very steady reliable rate.

I'm not really talking about a common or even likely scenario. At high avoidance levels it's massively unlikely that you'd take 5 or 6 full attacks in a row as any class, but thats what effective health assumes.

I'll have a better look through tomorrow, but either way I feel anything that relies on a key event defeats the purpose of the "raw" field.


I'll just agree to disagree. You want that field to mean something on your sheet, I wanted it to mean some thing else on my sheet. Since We both made Spread Sheets I think we're entitled to our separate opinions. ;p
Last edited by Sëryph on Thu Oct 09, 2008 10:30 am, edited 2 times in total.
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Postby Fridmarr » Thu Oct 09, 2008 10:27 am

Sëryph wrote:
Fridmarr wrote:
You will see those types of attack speeds if the boss parries or dual wields. I believe enemy attack speed is exposed via the API now, so we may have a good way to determine it.


I guess I wasn't clear enough.

I'm not talking about near approximations or every once in awhile, I mean they would have to consistently be very close to those speeds because if they're faster than those speeds they will get no chance the first swing(second on the 1.75) to remove a charge, meaning they double the time it takes for them to remove a BS charge. They can be a little bit faster but few mobs are in those attack ranges either (needs to be a constant value).

Most mob attack speeds are 2.4 after speed reductions, meaning the fastest they can remove charges is every other attack. Meaning with absolutely no avoidance your looking at 24 second uptime with BS in that case, I think we can agree that with a DK theres no worse case scenario where they will not at least increase that a a few seconds through avoidance.

You can see how stable these up times are by reducing the avoidance levels and this too acts like a step function(not surprisingly) where some times a 1% reduction in avoidance will drop the BS up time dramatically but then you would need to drop many more points in avoidance to effect it again. This shows that the variability in avoidance does not effect BS uptime to a great extent.


I'm not debating your conclusion, just your comment on certain attack speeds not happening.
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Postby Deathwing » Thu Oct 09, 2008 11:54 am

Seryph, I think you implementation of BS uptime is a bit clunky, and actually underestimating at some gear levels.

Consider this:

chance for an swing to consume a charge = H - H^2 + H^3 - H^4 + H^5...

Continue that out to at least the 10th power, that's where it stops affecting the thousandth place. H = chance to hit. And this is assuming boss attack speed is greater than charge CD/2 and less than charge CD.

From that, you should be able construct:

1 - <chance to consume X charges>....- <chance to consume 5 charges>

where X is max amount of attacks per 60s.

That's your average chance Bone Shield will last 60s, i.e. average uptime. I'm having a really boneheaded moment and can't get that last part to work, it's scaling opposite as I would expect. Anyone help me out there?

EDIT: dur, binomial mass distribution.

Ok, I'm getting really low number though, can anyone help me debug this:

Uptime = BINOMDIST(4,60/R5,R4,1)

Where 4 is max number of successes, 60/R5 is number of enemy swings in 60s, R4 is chance for a swing to consume a charge, and 1 is setting for cumulative.

I think my time window(60s) is wrong, but I'm not sure how to get to the right setting.
Last edited by Deathwing on Thu Oct 09, 2008 2:15 pm, edited 1 time in total.
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Postby Sëryph » Thu Oct 09, 2008 2:14 pm

Deathwing wrote:Seryph, I think you implementation of BS uptime is a bit clunky, and actually underestimating at some gear levels.

Consider this:

chance for an swing to consume a charge = H - H^2 + H^3 - H^4 + H^5...

Continue that out to at least the 10th power, that's where it stops affecting the thousandth place. H = chance to hit. And this is assuming boss attack speed is greater than charge CD/2 and less than charge CD.

From that, you should be able construct:

1 - <chance to consume X charges>....- <chance to consume 5 charges>

where X is max amount of attacks per 60s.

That's your average chance Bone Shield will last 60s, i.e. average uptime. I'm having a really boneheaded moment and can't get that last part to work, it's scaling opposite as I would expect. Anyone help me out there?


Heres how my formula works.

Basicaly What you need to know is 4 things:

  1. The average amount of attacks before a charge will be used.
  2. The amount of attacks that will happen without a chance for charges to be removed.
  3. The attack speed of the mob.
  4. The amount of Charges



On the first question I need to know how many attacks happen before it results in a 50% or less chance of being struck. This tell me how many attacks give me a better than half chance a charge was expended. This is basically what the first part does.

A = Avoidance, basically your chance to be hit every swing.

Code: Select all
IF A<0.5 Then
   return 1
Else IF (A^2)<0.5 Then
   return 2,
Else IF (A^3)<0.5 Then
   return 3
Else IF (A^4)<0.5 Then
   return 4
Else IF (A^5)<0.5 Then
   return 5
Else
   return 6
End IF


I then add this number to the amount of attacks possible pre CD, I derive it like this:


Code: Select all
IF Attack Speed<1.76 Then
    Return 1
Else
    Return 2
End If,


Basically this determines how many hits are going to fall within the 3.5 second CD.

I then Multiply the sum of the past two numbers by the mobs attack speed since the chance for a charge to be removed is relative to the mob attacking which is then tells us the average duration a charge will last.

Then finally multiply by the number of charges for the final average BS duration.

I honestly do not understand what your trying to say up above maybe by explaining what I did you can tell me where you think I went wrong.
Last edited by Sëryph on Thu Oct 09, 2008 9:33 pm, edited 2 times in total.
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Postby Deathwing » Thu Oct 09, 2008 2:37 pm

What I was trying to explain is how to model it so that you know the chance for any swing to consume a charge. That's what the first equation is. Obviously, the first part is the enemy's chance to hit you. But what if they hit you before and you're still in the cooldown? That's what -H^2 is. But what if they hit you 3 times in a row and now the hit directly before the present one didn't consume a charge? That's what +H^3 is. I kept going back and forth like that until there was very little change to the chance. That equation only works if the npc is clipping one attack per cd.

Now that you have chance per any attack, you can just plug that into a cumulative binomial distribution function. I'm pretty sure my number of total trials(attacks) for the function is off, but I think this is the most accurate way to do it.


I'm having trouble following your method. This sounds a lot like thinking 33% crit should give 100% flurry uptime.
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Postby Sëryph » Thu Oct 09, 2008 3:00 pm

Deathwing wrote:What I was trying to explain is how to model it so that you know the chance for any swing to consume a charge. That's what the first equation is. Obviously, the first part is the enemy's chance to hit you. But what if they hit you before and you're still in the cooldown? That's what -H^2 is. But what if they hit you 3 times in a row and now the hit directly before the present one didn't consume a charge? That's what +H^3 is. I kept going back and forth like that until there was very little change to the chance. That equation only works if the npc is clipping one attack per cd.

Now that you have chance per any attack, you can just plug that into a cumulative binomial distribution function. I'm pretty sure my number of total trials(attacks) for the function is off, but I think this is the most accurate way to do it.


I'm having trouble following your method. This sounds a lot like thinking 33% crit should give 100% flurry uptime.


Instead of trying to model the entire uptime I modeled the average swings before a mob hits you just once.

Then add in the amount of swings that can not take away charges. For example with a 2.4 speed swing 1 attack will have no effect on the remaining BS charges.

Then I multiple the average swings before a charge is consumed by attack speed and charges giving me the average BS uptime.
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Postby Deathwing » Thu Oct 09, 2008 3:50 pm

Yeah, that's why I mentioned crit rate and flurry. You're not doing the same exact thing, but it's similar. Just like you can't say "How many average hits until I get a crit?", you can't do what you are doing for BS.

Basically, you're not counting for hit and miss streaks(in flurry's case, this would be crit streaks, or buff clipping). On the surface, it doesn't sound like it would make a big difference. But with 2 1H weapons and 33% crit rate, a warrior's flurry up time is ~88%. Streaks can have a big impact on BS as well.
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Postby Sëryph » Thu Oct 09, 2008 4:24 pm

Well if you can come up with a better model for it I'll integrate it once I can equate it in excel. As of right now my formulas is not exact but it does give you a reasonable idea of how long BS will last in relation to your gear/buffs


I still do not understand how your model accounts for the cool down however if you could try to explain more fully I would appreciate it.
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Postby ziggyunderslashone » Thu Oct 09, 2008 4:28 pm

Sëryph wrote:Continue that out to at least the 10th power, that's where it stops affecting the thousandth place. H = chance to hit. And this is assuming boss attack speed is greater than charge CD/2 and less than charge CD.

As we're using an arbitrary time period from an infinite period (for example you aren't ever going to be hit for 3k on a single swing, but on average swings do that much damage), can you not simply work out the point at which the average chance to hit equals 1? (swing/(1-avoidance))

It's late and I'm fuzzy so thats possibly nonsense.
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Postby Sëryph » Thu Oct 09, 2008 4:35 pm

Deathwing wrote:Basically, you're not counting for hit and miss streaks(in flurry's case, this would be crit streaks, or buff clipping). On the surface, it doesn't sound like it would make a big difference. But with 2 1H weapons and 33% crit rate, a warrior's flurry up time is ~88%. Streaks can have a big impact on BS as well.


One thing to mention is hit & miss streaks aren't quite the same with BS as with flurry the one reason for this is once you get hit a charge is taken off and now they can hit you another time but it won't matter because of the cooldown.

I'll look more into modeling BS uptime but Ideas on where to look would be appreciated
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Postby Deathwing » Thu Oct 09, 2008 4:56 pm

Sëryph wrote:Well if you can come up with a better model for it I'll integrate it once I can equate it in excel. As of right now my formulas is not exact but it does give you a reasonable idea of how long BS will last in relation to your gear/buffs


I still do not understand how your model accounts for the cool down however if you could try to explain more fully I would appreciate it.


Ok, at first glance, chance to deplete a charge is the mob's hit rate

y = H

Now, to account for most cases of the CD, you have to look at the attack before the preset one. Did it miss? We don't care then. Did it hit? We care about that. So, in the case of the boss hitting twice in a row, the second hit(the present hit, the one we're examining) doesn't deplete a charge

y = H - H^2

How else could even further back attacks affect the present one? If the boss hits 3 times in a row, the present hit can now deplete a charge because the second one was within the CD

y = H - H^2 + H^3

You see how this can keep going back and forth forever? Actually, 1 minute worth of attacks would be the limit, and it reaches steep diminishing returns well before then anyway.


Anyway, if you don't like that method, you could just take the base hit rate and stick that in a binomial mass distribution function. Wonder if there's a way to get the excel function to disclude certain cases(hits next to each other).

Hit streaks still matter, as I showed with 3 hits in a row.


Ziggy,

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


EDIT: Ok, I was getting hung up on how to use a binomial distribution(which is still cool), totally forgot you just use the average distribution value:

average = n * p

Where n equal number of trials(hits) and p = probability of depleting a charge(from above).

60/(attack speed)*p = x

Yeah, I'm "durring" over that too. Couldn't see the forest for the trees. That will give you average amount of charges spent in 60 seconds. Flip it around to solve for time instead

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.
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Postby steadypal » Thu Oct 09, 2008 8:12 pm

closer and closer we get to next tuesday and i dont see the 3% DR added to that templar talent, the less and less i see it actually happening, so hmm how far back were we before when u tested us not having that? i see ppl just taking it for granted that it will actually get added into our talents, hmmm
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Postby majiben » Thu Oct 09, 2008 8:20 pm

steadypal wrote:closer and closer we get to next tuesday and i dont see the 3% DR added to that templar talent, the less and less i see it actually happening, so hmm how far back were we before when u tested us not having that? i see ppl just taking it for granted that it will actually get added into our talents, hmmm
Not putting it in for wotlk is a really bad PR move. Can you imagine the uproar if a promised change wasn't implemeted? There was already a lot of talk before the announced change that we weren't going to measure up to warriors in mitigation.
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Postby steadypal » Thu Oct 09, 2008 8:26 pm

Majiben wrote:
steadypal wrote:closer and closer we get to next tuesday and i dont see the 3% DR added to that templar talent, the less and less i see it actually happening, so hmm how far back were we before when u tested us not having that? i see ppl just taking it for granted that it will actually get added into our talents, hmmm
Not putting it in for wotlk is a really bad PR move. Can you imagine the uproar if a promised change wasn't implemeted? There was already a lot of talk before the announced change that we weren't going to measure up to warriors in mitigation.



shoot uproar if its not out in next weeks patch..... when xpac comes out we wont need that talent for solo grinding quests as much as ppl needing it to still raid before xpac comes out...
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