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Unidentifiable Organ - paging Theck?

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Unidentifiable Organ - paging Theck?

Postby knaughty » Fri Nov 20, 2009 7:35 pm

Unidentifiable Organ

Unidentifiable Organ
Heroic
Binds when picked up
Unique
Trinket
2128 Armor
Requires Level 80
Item Level 264
Equip: Each time you are struck by a melee attack, you have a 60% chance to gain 27 stamina for the next 10 sec, stacking up to 10 times.

Assumptions:
Boss attack speed 2.0 debuffed to 2.4

Dodge reduced 20%.

I currently have 60.04% avoidance, and pretty decent gear (mix of 245 & 258). This is in my "stack stamina" set.

OK... assume mega-geared-tank can get to 65%. Goes to 45%. 55% of attacks hit.

Four attacks every 10 seconds.

About a 4% chance that four attacks in a row miss. With my gear (60% base avoid), chance for stack to fall off is about 2.5% over 10 seconds.

Time to stack to 10 is pretty long - on my gear, about 40 seconds to stack to full, assuming it never falls off.

That's about the limit of what I can work out.

Page math gods:

For a 6 minute "stand and tank" fight, given my assumptions:

• What's the chance the buff doesn't fall off?
• 10 minutes?
• Full 264 gear, assuming same itemisation proportions as T-9?
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Re: Unidentifiable Organ - paging Theck?

Postby Meloree » Fri Nov 20, 2009 7:48 pm

With 2100 armor, I'd think about that for any fight without significant interruptions in time on target, even with the risk of falling off.

EDIT: Missed the part about only having a 60% chance to stack on hits. Going to go ahead and call this "an interesting but not overly useful" trinket, at best.
Last edited by Meloree on Sat Nov 21, 2009 1:14 pm, edited 1 time in total.
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Re: Unidentifiable Organ - paging Theck?

Postby theckhd » Sat Nov 21, 2009 1:02 pm

knaughty wrote:For a 6 minute "stand and tank" fight, given my assumptions:

• What's the chance the buff doesn't fall off?
• 10 minutes?
• Full 264 gear, assuming same itemisation proportions as T-9?


Well, the basics are pretty easy:
For 45% avoidance, you have 55% chance to be hit and a 60% chance that those hits proc the trinket. Thus, the probability of a proc is
q = 0.55*0.6 = 0.33

The probability of not proccing is p=1-q, or
p = 0.67

Yes I know I'm using p and q in an odd fashion here, we'll see later why.

The probability of r attacks in a row not proccing the trinket is p^r. For this, we're interested in r=4, because following a successful proc there are 4 chances for it to be refreshed before it expires. Thus, the probability of 4 non-proc attacks in a row is
p^4 = 0.67^4 = 0.2015

Note that this is also the downtime of the proc, because this is (chance of no proc)^(number of chances to refresh). The uptime is then simply
uptime = 1 - downtime = 1 - p^4 = 0.7985

In other words, we only expect about 80% uptime on the proc, making it good, but probably not reliable enough to count as effective health. Also note that this is only 80% uptime of the buff, it says nothing of how many stacks of the buff, which means that it's average worth isn't simply 0.8*10*27. More on that later.

Calculating the chance for the buff to fall off is... a pain in the ass basically. While calculating uptime and non-overlapping proc bonuses (like ICD trinkets) are easy, calculating the probability that you have at least one string of k consecutive successes or failures (aka a "run") out of N trials is particularly difficult. There's a brief description of the topic here:

Dr. Math wrote:We must be careful in defining our terms here. If we want a success
run of length r at the nth trial, then a further success at the
(n+1)th trial could undo the run completed at the nth trial. Equally,
if we stipulate AT LEAST r successes, then any run can be extended
indefinitely and a run does not reestablish the initial situation.
Either of the above definitions makes analysis very messy.


I won't go through the details of the math (and neither does he really). But he does provide an approximation we can use:
Dr. Math wrote:With the above definitions and a lot of hand-waving explanation, the
probability of no run of length r in n trials is approximately

Code: Select all
             (1 - px)      1
     q(n) = --------- . -------
            (r+1-rx)q   x^(n+1)



where x = 1 + q.p^r + (r+1)(q.p^r)^2 + ....

Note that in our caes, "no run of length r" means no cases where we have r attacks in a row that don't proc the trinket. It's now clear why I chose p and q as I did - we can plug them directly into this formula, and q(n) will represent the chance of having the buff up the full time. Conversely, 1-q(n) is the probability that the buff will fall off at some point during a fight of length n.

For p=0.67, q=0.33, and r=4, we get:
x = 1.0886 (out to two terms)

for a N minute fight, n=floor(N*60/2.4).
30 seconds -> n=12
1 minute -> n=25
3 minutes -> n=75
6 minutes -> n=150
10 minutes -> n=250

q(12) = 0.3895
q(25) = 0.1150
q(75) = 0.0011
q(150) = 9.2E-7
q(250) = 7.7E-9

In other words, it's almost guaranteed that the buff will drop off for a fight of any appreciable length. For anything past 3 minutes, we have a 99% chance that the buff will drop off at some point during the fight.

It's likely to be worse than that as well - this is for the best case scenario where you're being attacked full-time. In most encounters, there are periods where the tank isn't being directly attacked (tank swaps, phase changes, submerge phases, etc) which guarantee the proc will drop and need to be refreshed. Since it will take at best 24 seconds (for a 2.4 swing boss) to build up the stack from nothing, that will count for a lot of downtime.

In fact, since each attack is an independent event, they follow binomial statistics and we can easily calculate ramp-up time. The binomial probability distribution function
Code: Select all
binopdf(k,n,p) = nchoosek(n,k) * p^k * (1-p)^(n-k)

tells us the probability of getting k successes in n attempts with probability of success p. Reversing our old notation a bit, the probability of a success in this case is a trinket proc, which has probability p=0.33. If we calculate binopdf(10,n,0.33), this gives us the probability distribution for the number of attacks n we need to take to get 10 procs. The mean of this is simply
sum(n.*binopdf(10,n,0.33))/sum(binopdf(10,n,0.33))

Evaluating this for n=0:100 gives me a mean of 32.33. That means it takes on average 32.33 attacks to build the 10-stack, which is 32.33*2.4=77.6 seconds for the slow-swinging boss.

So the trinket takes over a minute to charge up to full strength, and has a 20% chance of falling off, forcing you to rebuild the stack from scratch (taking another minute). In other words, this trinket is crap.

Calculating the effective value of this trinket would also be a bit of a pain to do analytically. It's just complicated enough that it's easier for me to write a quick script to simulate it. I'm starting work on that now, once I have some results I'll post them.
Last edited by theckhd on Tue Jan 05, 2010 1:22 pm, edited 1 time in total.
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Re: Unidentifiable Organ - paging Theck?

Postby theckhd » Sat Nov 21, 2009 3:13 pm

First draft of the code is done:
Code: Select all
%this is a simple script to calculate the uptime on proc-based buffs

%time step - default is 0.1 seconds
dt=0.1;

%proc chance
p=0.55*0.6;
q=1-p;

%buff duration in seconds
D=10;

%buff max stack size
S=10;

%time between events - i.e. for a buff that procs on boss attacks, this is the
%incoming boss attack timer.  For a buff that procs on a melee swing, this
%is the net swing speed. 
T=2.4;

%number of chances to refresh the buff before it expires
N=D./T;



%% simulation code - simulate a large number of events

%number of iterations
M=1e7;
% rolls=rand(M,1);
% procs=rolls<p;
% procs=zeros(M,1);   %log of proc events
s=zeros(M,1);       %stack size
d=zeros(M,1);       %remaining duration of buff
tte=zeros(M,1);
t=[0:(M-1)];


%first iteration is the first event (at time t=0)
m=1;
h=waitbar(0,'0%');

%process an event, start the "time till event" counter
tte(m)=T;

%roll for event
if rand<p
    s(m)=1;
    d(m)=D;
end
   
for m=2:M
    %waitbar to watch progress
    if mod(m,0.05.*M)==0
        waitbar(m/M,h,[int2str(int32(100*m/M)) ' %'])
    end
   
    %update to new time by reducing duration
    d(m)=max([0 d(m-1)-dt]);   
    tte(m)=max([0 tte(m-1)-dt]);
   
    %check to see if stack has fallen off
    if d(m)<=0
        %if so, reset stack count
        s(m)=0;
    else
        %otherwise, set stack count to pevious timestep's value
        s(m)=s(m-1);
    end
   
    %see if it's time for another event yet
    if tte(m)<=0
       
        %if so, reset event timer
        tte(m)=T;
       
        %and roll for an event
        if rand<p
            %success, refresh the duration, add to stack
            d(m)=D;
            s(m)=s(m)+1;
           
        end
    end
   
   
   
   
end

close(h)

%% summary calculations

%downtime/uptime
downtime=sum(s==0)/length(s)*100;
uptime=100-downtime;

%mean number of stacks
meanstacks=mean(s);


[log10(M) p uptime meanstacks]


Running this for 10^7 iterations with 45% avoidance (p=0.55*0.6=0.33), which takes about a minute, gives me 80% uptime and a time-averaged stack count ( mean of the current stack size ) hovering around 4. I also ran it for a few other values of avoidance to see the scaling:
Code: Select all
Avoidance    p    uptime    mean stack size
40        0.36     84.5      5
45        0.33     80        4
50        0.30     77.5      3.2
60        0.24     68        2

Keep in mind that these values are somewhat fungible, since even with 10^7 iterations we see +/- 1% uptime and about 0.1 stack size.

Not surprisingly, getting hit more raises both the uptime and the mean effectiveness of the trinket, and getting hit less reduces its effectiveness. Unfortunately, this is sort of counter-intuitive; as your gear improves and your avoidance increases, the trinket gets progressively worse.

Even in the best case scenario of an average of 5-stacks, this is only an average of 135 stamina, which is quite weak. It could be a good bit stronger for tanking multiple mobs, or for bosses that attack more quickly. For example, using 45% avoidance and a 2.0 boss attack speed boosts the uptime to 86.6% and the mean stack size to 6.4.

We'll have to see what the attack speed of a normal ICC boss is to determine exactly how effective we expect this to be.
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Re: Unidentifiable Organ - paging Theck?

Postby pulexirae » Sun Nov 22, 2009 11:23 am

Just throwing this out there because my guild hasn't done algalon yet, but likely will eventually if we have some down time to waste one week. How does this look on tanking someone like algalon if I'm second tank in a 2stack 3 stack tank rotation? With the time I'm not being hit is it still unreliable or with his fast hitting attacks would it be worthwhile on that fight?
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Re: Unidentifiable Organ - paging Theck?

Postby fuzzygeek » Sun Nov 22, 2009 1:24 pm

pulexirae wrote:Just throwing this out there because my guild hasn't done algalon yet, but likely will eventually if we have some down time to waste one week. How does this look on tanking someone like algalon if I'm second tank in a 2stack 3 stack tank rotation? With the time I'm not being hit is it still unreliable or with his fast hitting attacks would it be worthwhile on that fight?



TBQH if you're wearing ilvl 264 gear, it shouldn't matter too much what you wear to a 239 ilvl boss party.
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Re: Unidentifiable Organ - paging Theck?

Postby Kelaan » Wed Nov 25, 2009 1:15 pm

theckhd wrote:Even in the best case scenario of an average of 5-stacks, this is only an average of 135 stamina, which is quite weak. It could be a good bit stronger for tanking multiple mobs, or for bosses that attack more quickly. For example, using 45% avoidance and a 2.0 boss attack speed boosts the uptime to 86.6% and the mean stack size to 6.4.


Interesting. So, the trinket has 2k armor plus ~100-135 stamina (if we consider averaged proc depth, right?). That sounds pretty good, doesn't it, for physical damage?
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Re: Unidentifiable Organ - paging Theck?

Postby Alixander » Wed Nov 25, 2009 2:20 pm

Hey Theck, just realized (after I spent around 20 minutes putting together a reply >_<) that you seemed to forgot to take into acocunt Chill of the Throne (aka -20% dodge while in ICC raid). As a consequence, at the absolute maximum, people will be at 40-45% avoidance range, with many being under it. Could we get the numbers assuming avoidance in the areas of 25%, 30%, and 35%?

EDIT: I will add that Theck's numbers are completely legit outside of ICC raid and make this trinket not so great there, but it's value inside ICC could be quite awesome. With this in mind I'll paste my copied text from the post I was working on since it will apply to outside ICC raid:

Kelaan wrote:
theckhd wrote:Even in the best case scenario of an average of 5-stacks, this is only an average of 135 stamina, which is quite weak. It could be a good bit stronger for tanking multiple mobs, or for bosses that attack more quickly. For example, using 45% avoidance and a 2.0 boss attack speed boosts the uptime to 86.6% and the mean stack size to 6.4.


Interesting. So, the trinket has 2k armor plus ~100-135 stamina (if we consider averaged proc depth, right?). That sounds pretty good, doesn't it, for physical damage?
That's the best case scenario. I think you misunderstood what Theck meant by "an average of 135 stamina" (either that or I did).

That number is the best case scenario. The important information that I got from Theck's posts are:
theckhd wrote:Running this for 10^7 iterations with 45% avoidance (p=0.55*0.6=0.33), which takes about a minute, gives me 80% uptime and a time-averaged stack count ( mean of the current stack size ) hovering around 4. I also ran it for a few other values of avoidance to see the scaling:

Code: Select all
Avoidance    p    uptime    mean stack size
40        0.36     84.5      5
45        0.33     80        4
50        0.30     77.5      3.2
60        0.24     68        2
Keep in mind that these values are somewhat fungible, since even with 10^7 iterations we see +/- 1% uptime and about 0.1 stack size.


In layman's term (assuming I'm understanding it correctly is) first off, it's value depends on your avoidance. Now taking your avoidance into account, these are the average normal stamina bonuses you get over the course of six minutes.

With 40% avoidance you have the average bonus of 114.075 Stamina (5 stacks * 27 stamina = 135 stamina * 0.845 average uptime)
With 45% avoidance you have the average bonus of 86.4 Stamina (4 * 27 = 108 * 0.8)
With 50% avoidance you have the average bonus of 66.96 Stamina (3.2 * 27 = 86.4 * 0.775)
With 60% avoidance you have the average bonus of 36.72 Stamina (2 * 27 = 54 * 0.68)

So basically, like so many other things which rely on being hit such as Reckoning, it's value is goes down as your avoidance goes up. And with most people's avoidance sitting comfortably over 50% it's average benefit is about half of the best case scenario that Theck mentioned (which would probably happen once in a blue moon anyways).

Now, for melee heavy fights, even with high avoidance, this trinket may still trump everything else due to it's pretty decent amount of armor. Though as shown in Theck's post about "The New EH", the more magic or bleed heavy a fight is, the less valuable armor is (duh, but still now we have values).

PS: Sorry for the sloppy math and I hope I did and understood everything right. I'm not the math wiz that Theck is.
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Re: Unidentifiable Organ - paging Theck?

Postby jathitimus » Wed Nov 25, 2009 7:39 pm

My biggest issue with a trinket that procs off hits or avoids like this one, is the fact it would actually get worse as you geared up, which is something a piece of gear should never do. Its kinda like the issue with our reckoning talent.

I understand that they are trying to make copies of the stacking dps and healing trinkets for tanks, but they need to come up with a way for them to stack, that is not based off avoidance. Having tank trinkets proc off of outgoing damage like dps trinkets would work much better imo.
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Re: Unidentifiable Organ - paging Theck?

Postby theckhd » Wed Nov 25, 2009 8:55 pm

Alixander wrote:Hey Theck, just realized (after I spent around 20 minutes putting together a reply >_<) that you seemed to forgot to take into acocunt Chill of the Throne (aka -20% dodge while in ICC raid). As a consequence, at the absolute maximum, people will be at 40-45% avoidance range, with many being under it. Could we get the numbers assuming avoidance in the areas of 25%, 30%, and 35%?

Even the weakest-geared tank going into ICC should have 60% avoidance before Icewell Radiance, which is why I only went down to 40% on the chart. However, it would be trivial to run it again for 25, 30, and 35, so I'll try and remember to come back to this tomorrow.

Alixander wrote:In layman's term (assuming I'm understanding it correctly is) first off, it's value depends on your avoidance. Now taking your avoidance into account, these are the average normal stamina bonuses you get over the course of six minutes.

With 40% avoidance you have the average bonus of 114.075 Stamina (5 stacks * 27 stamina = 135 stamina * 0.845 average uptime)
With 45% avoidance you have the average bonus of 86.4 Stamina (4 * 27 = 108 * 0.8)
With 50% avoidance you have the average bonus of 66.96 Stamina (3.2 * 27 = 86.4 * 0.775)
With 60% avoidance you have the average bonus of 36.72 Stamina (2 * 27 = 54 * 0.68)

Actually you don't need to multiply by uptime, the "mean stack size" calculation already accounts for that (the stack size is 0 when it's not up, and that gets averaged too). So 40% avoidance is 135 stamina, 45% is 108, and so forth.
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Re: Unidentifiable Organ - paging Theck?

Postby theckhd » Wed Nov 25, 2009 8:57 pm

jathitimus wrote:I understand that they are trying to make copies of the stacking dps and healing trinkets for tanks, but they need to come up with a way for them to stack, that is not based off avoidance. Having tank trinkets proc off of outgoing damage like dps trinkets would work much better imo.

Even better, make them proc off of avoids rather than hits. That also has the side benefit of making avoidance a more desirable stat.
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Re: Unidentifiable Organ - paging Theck?

Postby Flex » Thu Nov 26, 2009 12:37 am

theckhd wrote:Even better, make them proc off of avoids rather than hits. That also has the side benefit of making avoidance a more desirable stat.


Unfairly punishes druids for being druids.
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Re: Unidentifiable Organ - paging Theck?

Postby theckhd » Thu Nov 26, 2009 2:31 pm

Flex wrote:Unfairly punishes druids for being druids.

How so? Do they actually have significantly lower total avoidance than we do? I was under the impression that while we might have 65% dodge+parry+miss, they're likely to have roughly 65% of dodge+miss, because their dodge is much higher.
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Re: Unidentifiable Organ - paging Theck?

Postby Meloree » Thu Nov 26, 2009 3:01 pm

theckhd wrote:
Flex wrote:Unfairly punishes druids for being druids.

How so? Do they actually have significantly lower total avoidance than we do? I was under the impression that while we might have 65% dodge+parry+miss, they're likely to have roughly 65% of dodge+miss, because their dodge is much higher.


Druids have 10-20% lower total avoidance than plate tanks, while having significantly higher armor and health, assuming they're stacking EH.

For reference, Naiad (Edge's Feral Tank) has roughly 67k hp/37k armor (raidbuffed), in his EH gear, but only very slightly over 50% total avoidance. He has me beat by ~4k armor, and ~8k hp, but gives up 15% avoidance. We're at basically similar gear levels. He might be slightly better off, overall. Luck of the drops.
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Re: Unidentifiable Organ - paging Theck?

Postby Awyndel » Fri Nov 27, 2009 7:45 am

Makes one wonder why not everybody uses druid tanks for all hard modes. AD and block cap still don't bring us even close to those numbers in EH.

Anyway more on topic, I had a feeling the proc on this trinket was gonna be crap. Although combined with the already high armor on it it might still be very good for hard hitting bosses.
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