1. Edit: trinket list deleted as out of date.

2. Talisman seems way too low :O Don't know about your gear but Renatakis/Talisman at least show up in SC all the time as the best trinkets after a certain haste breakpoint (15-20 %)

3. So, here are my uptimes for comparison at 23% haste (only showing RPPM trinkets since non-RPPM trinkets are trivial):

Talisman of Bloodlust: An oddity due to the stacking nature (inaccurate maths suggests 69.5%), I'm still working on a better mathematical solution, currently modelling it based on Simulationcraft results which yeilds 62.17% but even then, I'm not interested in total uptime but the uptime of each buff
Renataki's Soul Charm: 22.4%

So, how am I getting these results? Well, going from the work done by Conjor here:http://plg.uwaterloo.ca/~rwking/Anal...0Mechanics.pdf both RSC and Bad Juju can be modelled accurately, Talisman stacking causes discrepancies.

As an example, let us take Bad Juju:

Uptime =~ duration/((2-(5/exp(3/2)))/((RPPM*(1+haste))/60))
=~duration/(0.8844/0.0113)
=~20/78.27
=~0.256
25.6% - rounding error causing the additional 0.1%.

4. Here's the formula I've been using for uptime of RPPM trinkets without an ICD:

Your bad juju uptimes seems better than mine going by Simulationcraft uptimes. Conversely my talisman of bloodlust uptime seems better (as compared to Simulationcraft again). Both our maths seems to be off on RSC.

These are the Simulationcraft uptimes I'm seeing:

Renataki ~ 27%
Talisman of Bloodlust ~ 57%

*For now assuming Simulationcraft uptimes are accurate. If anyone has long logs that contradict these uptimes, please share (i'm after 30min+ logs against a dummy using regular rotation, not interested on 'oh look, my trinket had x uptime on this fight', for what I hope will be obvious reasons.

Edited: removed wrong statement (hopefully before anyone saw it). Also added a bunch of extra info

5. @ Ryme and wimp

Do your models include talisman's stacking increasing other trinkets/LMG or are they modelled independantly? Talisman while maybe not as strong as the others on wimp's list can surely be seen as a "supportive" trinket increasing it's value.

6. Originally Posted by theherecy
@ Ryme and wimp

Do your models include talisman's stacking increasing other trinkets/LMG or are they modelled independantly? Talisman while maybe not as strong as the others on wimp's list can surely be seen as a "supportive" trinket increasing it's value.
It's a good point, I'm modelling it independently, but certainly it's worth taking into consideration.

7. Originally Posted by Ryme
It's a good point, I'm modelling it independently, but certainly it's worth taking into consideration.
Absolutely, I'm rolling with TF talisman and HC RSC. If you wish to study some logs they can be found here: http://www.worldoflogs.com/guilds/207244/

8. I have included talisman stacking affecting talisman's chance to proc (though this effect is only 1% higher chance to proc per stack, which, at the moment, is a smaller effect than the differences in maths we're talking about, so I'd say this effect is smaller than the error in the data).

I haven't included talisman's procs' effect on other trinkets, as that would make the list longer (I'd need to include each RPPM trinket twice, once on its own and once if used together with talisman - I could provide this list when I'm a bit more comfortable we have the maths right).

What I was hoping for here (and this might be a bit optimistic) is that the value SC gives would include these beneficial effects of haste (chance of epic meta gem to proc, chance of all RPPM trinkets to drop). If that's the case, then talisman's value should be accurate, as it procs haste, and the EP of that haste is taking into account the fact that it can make other trinkets procs (though in my list that's not the case since I'm not using any RPPM trinkets at the moment - but the maths would be fine).

9. I fear shadowcraft is still over-estimating Talisman slightly (their value on haste is much higher than I expect), but it's probably the best trinket of the bunch once you're using a second RPPM trinket and legendary meta

10. Here is a trinket list, with the same caveats as before (and, I note again, based on my EP weights, and I'm currently not using any RPPM trinkets, so haste is a bit less valuable for me than it will be eventually). But this time I'm using Simulationcraft's uptime percentages instead of the ones derived from our maths. Only as a temporary solution while we perfect the modelling to fit the world (or, failing that, until we bribe someone at blizzard to make trinket behaviour fit our mathematical models...)

pre-comparative chart snip

---------- Post added 2013-04-18 at 01:44 PM ----------

Originally Posted by Ryme
I fear shadowcraft is still over-estimating Talisman slightly (their value on haste is much higher than I expect), but it's probably the best trinket of the bunch once you're using a second RPPM trinket and legendary meta
I have the same fear even when accepting Shadowcraft's value of haste... I think it's over-estimating either the proc chance or the average number of stacks (or both).

11. I'm currently running with TOB normal and it's uptime is around 62% for me at 28% haste. I don't think there will be a better trinket if you're using the meta and double rppm trinks for the synergy effect they have. Real haste also effects Dancing Steel uptime as well, doesn't it now? So there is always that too.

I'm still curious about RSC and Bad Juju as a second trinket, SC seems to tell me that HC bad Juju is always worse than HC RSC even if I'm over expertise cap in some scenarios. SC even rates bottle HC DU better than Bad JuJU HC.

12. Originally Posted by orderofmaken
I'm currently running with TOB normal and it's uptime is around 62% for me at 28% haste. I don't think there will be a better trinket if you're using the meta and double rppm trinks for the synergy effect they have. Real haste also effects Dancing Steel uptime as well, doesn't it now? So there is always that too.

I'm still curious about RSC and Bad Juju as a second trinket, SC seems to tell me that HC bad Juju is always worse than HC RSC even if I'm over expertise cap in some scenarios. SC even rates bottle HC DU better than Bad JuJU HC.
I'm in the same boat, almost 9% expertise is horrific but that trinket just seems to have such a high proc rate and the proc rate is very strong, especially when using anticipation to "delay" your moves until when you have ~15k agility. I'm about 400 expertise over with master = expertise, i.e. bad juju has an edge of 480 EP. Looking at some of the tables above, you can see that RSC has a bigger edge then 480.

Though I'm not entirely sure if my maths is correct, this might help you discover that overcapping expertise isn't as bad as it looks.

13. The averaged proc gain from RSC is slightly worse than Juju, but the burst potential on RSC is clearly higher. It comes down to uptime, I'm not sure how everything else is estimating ICD RPPM trinket uptimes, because it's by far the most complex using calculus - the integrand is hideous.

14. As most people just want to see the answer without having to see the maths, I've rewritten and re-ordered this post.

Trinket list:

Interested in EP-values dependent on fight length? Check this post

Assumptions: 16.09% haste, 450 second fight duration, 5% spell haste buff, heroism/bloodlust were used.Sstat EP values for BiS gear as per the EJ Assassination OP (Agility: 2.72; Crit: 1.15; Mastery: 1.17; Haste: 1.39)

1) The 'trinket with talisman' assumes you have a talisman of the same ilvl as the trinket (so, e.g. the '522 renataki with talisman' assumes you have a 522 talisman; the '541 renataki with talisman' assumes you have a 541 talisman.

2) The EP values have been derived from 'in a vacuum' modelling, meaning that assuming the maths is right, these are the results you'd get in an infinitely long fight. Fight lengths skew EP values enough as to change the ranking (e.g. compare a short fight which ends as a VP trinket is about to proc with a fight which ends as the VP trinket proc comes to an end = in the former the VP trinket would be great, in the latter it wouldn't). Further edit of this point: the 'fight length = 450s' has only been used to model the extra uptime of the RPPM trinkets. The EP values of the non RPPM trinkets are those of an infinitely long fight in both cases If you want a time-dependent analysis, check this post which has pretty graphs

3) I have assumed you can reforge out of expertise/hit, so I'm treating both of those as 60% mastery and 40% haste. Read this to mean: the value of these trinkets will be lower if you can't reforge so as not to go over the 7.5% caps.

4) The maths doesn't take into account the changes in EP values as stats change due to trinkets procs. For this reason, I haven't included Rune in this list, since for that trinket the changes in EP values are too large to ignore.

***

More detailed explanations (somewhat outdated now - specially the cocky bits about having it all figured out...):

We now have what I believe is an accurate mathematical model for all trinkets - if you just want to see the trinket list, skip the words and jump down to the picture of tables. This post might be a bit dense, so please bear with me (some of you will be thinking of xkcd.com/365).

Let Lambda = (RPPM*Proc_duration*(1+Haste))/60

RPPM trinkets without an ICD: Uptime is given by =bad_luck_protection*(1-EXP(-Lambda))
RPPM trinkets with an ICD: Uptime = =(bad_luck_protection*Proc_duration)/MPT, where MPT is the mean proc time and is equal to: 60/(RPPM*(1+Haste))+ICD-10

RPPM trinkets with stacking behaviour in which each stacks affects the proc chance... Yes, Talisman of Bloodlust, this means you! This one is the most time consuming one. The uptime for the talisman to have 'at least n stacks' is given by =bad_luck_protection*(1-EXP(-Lambda))^n. To get the uptime for the nth stack, work out the uptime of 'at least n stacks' and substract the uptime for 'at least (n-1) stacks'.

The problem here is that the proc chance changes for each stack number. And, since the size of each stack is different for the four different trinket levels, but the haste rating to haste percentage relationship is constant, the proc chance is different for all stack sizes and for all ilvl trinkets.

All talismans have the same uptime. But as you get higher ilvl talismans, they spend more time at higher stacks (since each stack gives you more haste which makes them proc more often). And so the average number of stacks per proc is different for each of the different ilvl trinkets.

Unless you are *really* into theorycrafting you'll be very bored of this line of thought, so as not to make this post even duller, I won't give the average uptimes of all the stack sizes for all the different ilvls of this trinket. If you want to see the numbers, use the formula above, or drop me a pm if you'd like my spreadsheet.

I've checked the results of the maths above against different simcraft simulations, and the model fits the data. Hurray. About time...

I can't take all the credit for this work - barely any in fact. First and foremost, Poisson was quite a dude. More recently, and more directly plagiarised: Hamlet. If you have any issues with the math above, I'd recommend you read his excellent post here: http://iam.yellingontheinternet.com/...advanced-rppm/

I'm now fairly confident about providing a trinket list which I believe is accurate for my current gear (EP values: Agility: 2.743; Crit: 1.025; Mastery: 1.135; Haste: 1.095).

These trinket lists take into account the stacking effect of Talisman on itself, and this is reflected on its EP value. It also takes into account the EP values of the other trinkets when these are used together with Talisman (you will see each RPPM trinkets has two entries - one for when it's not used with talisman, and and one for when it's used with talisman).

The 'bad luck protection' which was introduced for RPPM trinkets has the effect that waiting 'enough time' before a fight, so that a trinket procs on the pull, increases the trinket's overall uptime (and so EP value) in fights of a finite length.

In a finite fight, we'll see an additional uptime = (Probability of not having this extra proc) * (additional uptime due to the guaranteed proc at the start).

The 'additional uptime due to the guaranteed proc at the start' is easy enough = proc_duration/fight_length.

The probability of not having a proc at the start is a bit harder. I'm using the Poisson answer to 'probability of not having a proc in a time equal to the proc duration', which is EXP(-Lambda'*proc_duration). Where Lambda' is the average number of procs per second, which is = (RPPM*(1+Haste))/60.

Since we're modelling this, we should also answer the question 'How long do we have to wait?' The answer to that is easier, in order to guarantee a proc on the pull, we have to wait =(MPT*(MPT+35))/30, where MPT is the mean proc time. The answer varies for the different RPPM trinkets, with the wait time decreasing as the square of the RPPM. Want a quick and dirty answer? For bad juju and renataki's, roughly 6 minutes for a proc on the pull, 5 minutes to be pretty certain of something which will feel like a proc on the pull.

The trinket list below assumes 16% haste. There are two columns of uptimes: ones which shows results for an infinitely long fight, and one where the RPPM trinkets have the higher uptimes which you'd get if they are guaranteed to proc on pull. The 'waiting columns) assume a fight length of 450 seconds (as the fight length increases, the increase in uptime due to waiting before the pull decreases).

15. Going to go back and minimize some of the out-of-date charts you've got back there so we don't confuse people - nevermind, beat me to it O.o. Thank you for all the work you've been doing on this; I do think it's worth noting, given your second caveat in the end, that all of the RPPM trinkets have a slight lead over apparent value because they will (almost) always proc at the beginning of a pull - on short fights (Jin'rokh), or fights where you lust at the very beginning, this is disproportionately valuable over longer fights (Horridon), and takes away the advantage the VP trinket "tends" to hold by putting it on the same opening-of-the-fight footing. The list should remain pretty well intact.

16. Great work, just some really great work.

I'll spend a short while tomorrow going through a second opinion of this as well; I'd never seen that website before, my maths hormones are tingling ;)

17. I was surprised to see how far off Elitistjerks value of Renataki was so far off from what you got, at least in the Assassination thread, I wonder why though, is it because they modeled ICD RPPM trinkets badly?

18. Originally Posted by Fluorescent0
I was surprised to see how far off Elitistjerks value of Renataki was so far off from what you got, at least in the Assassination thread, I wonder why though, is it because they modeled ICD RPPM trinkets badly?
A) It's based off BIS lists, so I would imagine you would be surpassing the expertise even without RSC
B) There's been a lot of "jiggling" with the rppm trinkets to bring them into line/make them more desireable and therefore simulationcraft needs updating
C) Elitist Jerks *never* up date those pages :P

19. Originally Posted by theherecy
A) It's based off BIS lists, so I would imagine you would be surpassing the expertise even without RSC
B) There's been a lot of "jiggling" with the rppm trinkets to bring them into line/make them more desireable and therefore simulationcraft needs updating
C) Elitist Jerks *never* up date those pages :P
A can be thrown off the table right away, with Renataki you're able to get exactly to the exp cap or close thereof in full BiS gear, just checked.
B should be out of the equation too, Shadowcraft is simulating it just like these results (as in Renataki being slightly over Bad Juju in BiS)
It's probably C, it's some mistake from the early periods where modeling wasn't that clear which just got left there.

20. so the final BiS trinket for Assassination is talisman+renataki?

damn why did i pass that trinket before

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