5.2 Trinkets Discussion

[Ryme]

So as assassination if i want to have some decent procs from bad juju normal i should sacrfise mastery for haste?

Getting more haste will increase your uptime, in a near linear fashion (for realistic haste values) despite all the exponentials floating around Link to graph.

Looking at Bad Juju, if my maths is right, you hit a 99% uptime once your haste reaches 2412%, 50% uptime at 278% haste, 25% uptime at 57% haste and you should get ~17% uptime with 0 haste.

However, this says nothing about haste's value relative to other stats. The interaction between them is far more complex and something that should be left to simulation in my opinion.

[Mazius]

Looking at Bad Juju, if my maths is right, you hit a 99% uptime once your haste reaches 2412%, 50% uptime at 278% haste, 25% uptime at 57% haste and you should get ~17% uptime with 0 haste.

On Horridon HC (~12 min fight) our enhacnement shaman had bottle uptime at ~40% and Juju uptime at ~30%.
2990 haste (4485 with flurry up - it's 10,5% haste).

[Ryme]

Interesting, could you link me a log at all? It's very possible I'm overlooking something...

Was this uptime on Juju consistently around 30%? This statistical approximation is just that, a statistical approximation. The full range of uptimes from 0 - 100% are still possible.

[Tehstool]

Interesting, could you link me a log at all? It's very possible I'm overlooking something...

Was this uptime on Juju consistently around 30%? This statistical approximation is just that, a statistical approximation. The full range of uptimes from 0 - 100% are still possible.

Quoting my old post now that raid has ended with results that were... fascinating..

Here are the 2 Kill logs I had with the new trinket(reforged Mast -> Crit) and it replaced my DMF Trinket.

Tortos 25NLog
-Bad Juju uptime 31.2%
-Ranked 26th as Survival(25N)

Magaera 25NLog
-Bad Juju uptime 31.4%
-Didn't rank because died at end for ~20 secs

All I can say: OMG.

Estimated "ICD" is ~1 minute from these 2 logs, making it have Agi proc worth of ~2273 Agility by average.
That is just goddamn massive.

Definitely trumps Relic, having higher uptime, less RNG on proc and way more agility per proc.

Some guys logs that was posted in a different thread.

[Ryme]

Some guys logs that was posted in a different thread.

Fantastic I'll sit down and start digesting.

---------- Post added 2013-03-15 at 12:42 PM ----------

On first glance, perhaps Rapid Fire and a decent uptime on time warp aided somewhat to this - but that doesn't account for a lot, something is certainly amiss somewhere, I'll be back!

[fierydemise]

Rapid fire and lust probably account for some of that deviation but another factor that I don't think anyone has a good model for yet is the impact of bad luck protection. Intuitively bad luck protection increases trinket uptimes but I couldn't figure out how to model it mathematically so to sanity check myself I wrote a simple simulation.

Assume a trinket with 1% chance to proc per second for simplicity, the exact RPPM and haste required to get this doesn't really matter. Expected interval would be 100 seconds, simulated over 64K procs I get 100.04 seconds. Simulating with bad luck protection (if someone has a better name for this let me know) I get an average interval of 88.8 seconds.

[theturn]

Rapid fire and lust probably account for some of that deviation but another factor that I don't think anyone has a good model for yet is the impact of bad luck protection. Intuitively bad luck protection increases trinket uptimes but I couldn't figure out how to model it mathematically so to sanity check myself I wrote a simple simulation.

Assume a trinket with 1% chance to proc per second for simplicity, the exact RPPM and haste required to get this doesn't really matter. Expected interval would be 100 seconds, simulated over 64K procs I get 100.04 seconds. Simulating with bad luck protection (if someone has a better name for this let me know) I get an average interval of 88.8 seconds.

So over an 8 min fight that's an uptime of 22-23%? If that math is correct thats pretty close to what I'm seeing in logs. Alot a variability still with these trinks. Sometimes you have 30% uptime then you get 14%. Not really sure what blizz was hoping to accomplish with these trinkets.

[fierydemise]

Those numbers were for a completely arbitrary trinket as a demonstration of an effect, they don't actually correspond to any real trinket. If you are asking about bad juju 22-23% uptime seems reasonably correct depending on haste but I have yet to see a good closed form approximation of uptime that takes into account the effects of bad luck protection on uptime.

[Ryme]

Those numbers were for a completely arbitrary trinket as a demonstration of an effect, they don't actually correspond to any real trinket. If you are asking about bad juju 22-23% uptime seems reasonably correct depending on haste but I have yet to see a good closed form approximation of uptime that takes into account the effects of bad luck protection on uptime.

Because it shouldn't effect it since the bad luck protection will only kick in after you're passed the expected time interval to proc.

[Nitwit]

Because it shouldn't effect it since the bad luck protection will only kick in after you're passed the expected time interval to proc.

?

When the trinket procs (without bad luck mitigation) is normally distributed around the average expected proc interval for a given RPPM value (e.g. 1 minute for a 1 RPPM trinket and 0% haste). Sometimes it'll happen more or less frequently, but the average will be 1 minute. The bad luck mitigation only "attacks" procs on the upper tail end of this distribution, so your overall average has to be reduced by some amount.

It works out to about ~13.07% more procs, because maths.
http://www.mmo-champion.com/threads/...1#post20512410

[Ryme]

?

When the trinket procs (without bad luck mitigation) is normally distributed around the average expected proc interval for a given RPPM value (e.g. 1 minute for a 1 RPPM trinket and 0% haste). Sometimes it'll happen more or less frequently, but the average will be 1 minute. The bad luck mitigation only "attacks" procs on the upper tail end of this distribution, so your overall average has to be reduced by some amount.

It works out to about ~13.07% more procs, because maths.
http://www.mmo-champion.com/threads/...1#post20512410

Well that's just gorgeous

---------- Post added 2013-03-17 at 01:45 PM ----------

Well that's just gorgeous

It also perfectly explains why the trinkets above are at the proc rate real life tests are showing, thank you!

---------- Post added 2013-03-17 at 05:51 PM ----------

So, even the warlock in my guild (a far cleverer man than I has come to the same conclusion) links to his work below:

Okay, let's see. I'll link my work and then try to explain a bit.

Source
us.battle.net/wow/en/forum/topic/8197741003
Trinket functionality change


1st page
oi46.tinypic.com/ei8ub6.jpg

Contains the previous results at start. After that I created the function for the multiplier.
Also, we can easily see the multiplier effect starts at 1.5*expected time between procs, based on the blue post.
After that I just changed the new "chance to not proc in T time from last proc" to the form with e.

2nd page
oi45.tinypic.com/k9gbcp.jpg

Basic change to proc in T for both T>=1.5*E(T) and T<1.5*E(T) , in other words cumulative probability distribution.

Graph to make it easier to understand:
oi47.tinypic.com/28ic1mh.jpg
H=R=1.0
As we can see, at 1.5*E(T) the lines cross, and after that the multiplier kicks in, resulting in the probability approaching 1 much faster than before the change.

After that I have the derivatives for both functions, as well as the real expected value Er(T) for T<1.5*E(T).

3rd page
oi46.tinypic.com/2cqcsax.jpg

This is where the stuff got a bit more nasty as I said. What I did was create an approximation using T= 90/(HR) = 1.5*E(T) for the T before the integral, resulting in a much easier approach.
Using this I got a very easily useable approximation for the total expected value Et(T).

4th page
oi50.tinypic.com/258qmub.jpg

After this I did the real expected value for T>1.5*E(T), which led to error function (erf).
Using this I could make a couple comparisons between the real result (real) and my approximation version (short).

5th page
oi50.tinypic.com/xaxdo6.jpg

Here are the real values of E(T) when T>1.5*E(T) in a nice and tidy format.
After getting this I just summed the E(T) ,T<1.5*E(T) and E(T) ,T>1.5*E(T) to get the real expected total time between proc.
To my surprise this led to a very similar formula to my approximation, the difference in the expression being the error of approximation function.


Now, this does not take into account ICD, which I haven't gotten into yet. However, comparing this to the newest simulationcraft results they seem to be close, the difference being made by the guaranteed proc at the start of the fight as well as the possible effects of ICD.

Combining this the work of Conjor and Surutcra, I think a final model (still in vacuum analysis) is pretty much there, and another list will be posted with all credit given where applicable tomorrow - unless someone fancies doing it already?

[wimp]

I just found this thread: there are way too many threads trying to cover this math. On the plus side, it's good we're all arriving at the same numbers. A very small correction to the assertion that you get 13.07% more procs - that's not quite accurate: 13.07% is the increase to the average proc rate (or the decrease to the average time between procs). This doesn't always quite translate to 13.07% more uptime has was suggested higher up in this thread (close, but not quite).

I'll repost here the math I posted on a bunch of other threads/on EJ:

I think we're getting there with the modelling of bad luck protection and proc overlaps. This is what I'm working with at the moment:

Let the average proc rate, avg_rate = (RPPM*(1+Haste))/60

For trinkets with ICD: proc overlap is obviously not a concern here. The uptime is just [proc duration / average time between procs]. Average time between procs is [1/avg_rate] + ICD

For trinkets without ICD: here we can't just measure proc uptime by [proc duration / average time between procs], because procs can overlap. Instead, we can model the RPPM mechanic as a Poisson distribution, which gives us an uptime = 1-EXP((-avg_rate*Proc_duration))

Bad luck protection:
There are two approaches here. One is to multiply the average proc time by 13.07%. For the mathematical derivation of this assertion, please see this link to work by Jay (@Hamlet EJ): pbs.twimg.com/media/BFRHvJ4CQAANzmS.jpg:large

There is a second approach, which uses mathematica to get a formula which takes into account bad luck protections (and so eliminates the need to multiply by 13.07%, which feels like a bit of a fudge). The approach here is to integrate the equations over the two time periods (the 'regular time' and the 'time after bad luck protection kicks in'). Conjor is working on that at the moment (links to his thread and work above on this thread), but for now multiplying by 13.07% seems more accurate to me.

Using the math above, and assuming 23% haste (rogue here), I'm getting the following average uptimes:

Bad Juju: 22.5%
Renataki's: 22.7%
Talisman: 53.5%
RoRo: here the uptime increases with ilvl. 16.9% for 541, 16.3% for 535, 15.6% for 528 and 15.1% for for the 522 one.

I'm not providing a ranked trinket list, as that would depend on your EP values. E.g. the rogue ranking would be different to the hunter ranking.

Any and all feedback or corrections on the math are very welcome.

[Tehstool]

Ryme: since you like looking at logs, here's my recent tortos kill with 37.2% uptime on renataki's soul charm

http://www.worldoflogs.com/reports/r...?s=5328&e=5650

17.13% haste with hero/rf/troll racial averaged in.

[Ryme]

Thanks all, whilst I may not always be the most accurate in my calculations here, the combined work of everyone is heartwarming to see.

As to average uptimes, with Talisman, since it has no ICD and gives a substantial amount of haste on proc, is the uptime taking into consideration the proc?

[wimp]

As to average uptimes, with Talisman, since it has no ICD and gives a substantial amount of haste on proc, is the uptime taking into consideration the proc?

My calculations haven't. A few thoughts here:

While haste increases average uptime, I don't think the effect is as drastic as most people think. For instance, at 20% haste, increasing haste by 1% (additive) changes the average uptime of talisman by around .3% (also additive. In fact all percentage changes mentioned in this paragraph are), and those of trinkets with lower uptime by even less).

With regards to the talisman, One permanent stack of the normal talisman would increase the average uptime by 1%, and 5 stacks would increase the uptime by 5%. Due to the possibility for the talisman to stack, the modelling would take quite a bit more than napkin math, but my ballpark guess would be the uptime would be between 1% and 2% higher than I mentioned (additive yet again). More or less. Ish.

The one trinket which would affect uptimes significantly is RoRo if you have more haste than either crit or mastery, since that gives you huge amount of haste. But as the proc only lasts 10 seconds, the trinket has a 22 seconds ICD and has the lowest uptime of any trinket... Once again, this would just be around 2% (additive) increase to the talisman's average uptime. More or less. Ish.

[Ryme]

Whilst small, that percentage is still large enough to make me want to incorporate. For now, It's probably just worth noting that ToB in the following list (as I love my reference lists) is probably being undervalued slightly.

Lists to come once I ensure I've stopped making errors

[Deleted]

Thanks for your list Ryme!
Can we assume that Bad Juju (N) now is better than Bottle (H DU) for T14H equip too?

[Ryme]

Thanks for your list Ryme!
Can we assume that Bad Juju (N) now is better than Bottle (H DU) for T14H equip too?

It really will depend on your haste, I have normal juju overtaking double upgraded bottle at around 10-11% haste.

[fierydemise]

Are you still using the SimCraft assassination profile for stat values? The Simcraft assassination BiS profile doesn't appear to have been updated since the RPPM change reduced the value of haste across the board. I'm not sure the assassination BiS profile was ever that well optimized but quickly generating scale factors on the BiS prfile shows mastery is pretty well ahead (3.45 vs. 3.1). If you are using haste values that high it is inflating the value of the RPPM trinkets, I think 15% -20% haste is a reasonable approximation for haste values at BiS levels not the nearly 30% haste in Simcraft's BiS profile.

It really will depend on your haste, I have normal juju overtaking double upgraded bottle at around 10-11% haste.

Remember that haste doesn't take into account the haste buff so if you are looking at your character sheet look at spell haste to get a haste percentage without the haste buff.

[Ryme]

Are you still using the SimCraft assassination profile for stat values? The Simcraft assassination BiS profile doesn't appear to have been updated since the RPPM change reduced the value of haste across the board. I'm not sure the assassination BiS profile was ever that well optimized but quickly generating scale factors on the BiS prfile shows mastery is pretty well ahead (3.45 vs. 3.1). If you are using haste values that high it is inflating the value of the RPPM trinkets, I think 15% -20% haste is a reasonable approximation for haste values at BiS levels not the nearly 30% haste in Simcraft's BiS profile.

I'm using an assassination scale of

Agility: 6.88
Mastery: 3.23
Haste: 3.04
Crit: 2.82

Used at 15% haste and a combat scale of:

Agility: 6.61
Mastery: 2.96
Crit: 2.63
Haste: 3.62

Used at 25% haste.