# Thread: RPPM Analysis + Haste Benefits / 5.2 Trinket Analysis

1. Yeah, I considered that behavior to be most likely.
Last change gave extra buff to ICD trinkets - now you start at 22-sec worth of time after ICD, and you used to start with 10-sec.

2. Originally Posted by Thiron
Yeah, I considered that behavior to be most likely.
Last change gave extra buff to ICD trinkets - now you start at 22-sec worth of time after ICD, and you used to start with 10-sec.
That is a very good observation. That didn't even cross my mind. Makes renataki's even better.

3. Originally Posted by Thiron
You use poisson formula for trinkets with ICD, while it should be actually linear, since they can't overwrite the proc.
The only thing not certain, is if the chance starts calculating from when ICD starts or from when ICD ends.

I used some math from here and here and made this spreadsheet, but I'm still not sure how to input "unlucky protection". It will increase average proc rate, since the chance is modified when it starts working.
Actually you would still use a non-homogenous Poisson distribution for those cases (they are not "linear"). The math for it is in my paper. If you look at the subtitle in there you will see that my analysis applies only to trinkets with no icd.

Give me some time to do the math for the trinkets with icds.

Originally Posted by Thiron
It will increase average proc rate.
You are misinterpreting how independent events are working within the probability distributions (and how they are applied within the RPPM system). The average proc rate is not changed. At all. End of story. The proof for it is in my math.

---------- Post added 2013-03-15 at 09:07 AM ----------

Originally Posted by Thiron
Yeah, I considered that behavior to be most likely.
Last change gave extra buff to ICD trinkets - now you start at 22-sec worth of time after ICD, and you used to start with 10-sec.
That is not how it works. If you do your analysis like that you will end up with crazy skewed results. Once I have published my math behind it you will see why.

As a prefece (assuming my intuition is correct), the value of Renataki's and other trinkets with ICDs will actually go down, not up. It's a pure fact right from the integration of the probability function (as your range of integration gets smaller).

4. The equation is designed to work when you've gone over the expected interval of the proc and thus should only prevent the bad luck streaks, while it may affect up- time/proc rate (to the point where it actually procs instead of not proccing for 8 minutes), theoretically it should be the same expected RPPM.

5. Ok, unfortunately I don't know exact english math terms, and I do admit that statistics are my weak point, so I'll use simple explanations (I know you'd understand complex ones, but I'd make some mistake in formulating them).
I admit that I'm wrong on first point, yes. But on other two you seem to make some mistake. Let's look from the "average time before next proc" point of view.
1.Unlucky protection lowers average time before next proc. Can you really argue with that? On your formula at the end of second page, you substitute p(t), using only t<3/2L and ignoring t>3/2L
2.Integration range gets smaller, but it gets "cut" at the lower part, raising the average.

6. Originally Posted by Thiron
Yeah, I considered that behavior to be most likely.
Last change gave extra buff to ICD trinkets - now you start at 22-sec worth of time after ICD, and you used to start with 10-sec.
Time Since Last Chance to Proc should still be capped at 10s. There wasn't an announced change to the standard Chance to Proc formula. The change introduced a multiplier to that formula such that once you exceed 150% of the Average Proc Interval (60/haste-modified RPPM) without a proc, you begin to see an increase in proc chance. For Rentaki, with 10% haste, you won't see that multiplier until well over 2m with no proc.

7. You have to remember that the "time since last chance to proc" is just that: the time since it last had a CHANCE to proc. If it enters the ICD, clearly it has no chance to proc over that icd. It will begin counting its "time since last chance to proc" at the end of the ICD.

I'm almost done looking at the equations. There are some cases where nothing has changed from the non-icd trinkets.

8. Rune of Reorigination should still be =2*(\$P\$17+\$P\$18) as far as I know.

9. Originally Posted by kindath
Rune of Reorigination should still be =2*(\$P\$17+\$P\$18) as far as I know.
I would like to see some blue post on that. I recall GC saying that it just converts all your haste, mastery, and crit into the highest of them. Nothing about a multiplier. The tooltip doesn't even mention a multiplier.

10. Originally Posted by Conjor
I would like to see some blue post on that. I recall GC saying that it just converts all your haste, mastery, and crit into the highest of them. Nothing about a multiplier. The tooltip doesn't even mention a multiplier.
GC said that it doubles what you gain in a blue post somewhere.

Also I think you may be misreading that. You last had a chance to proc it when the trinket procced, therefore you should have capped at 10 seconds when the trinket wears off.

11. Originally Posted by Conjor
You have to remember that the "time since last chance to proc" is just that: the time since it last had a CHANCE to proc. If it enters the ICD, clearly it has no chance to proc over that icd. It will begin counting its "time since last chance to proc" at the end of the ICD.

I'm almost done looking at the equations. There are some cases where nothing has changed from the non-icd trinkets.
Well, this is one thing devs simply didn't clarify, so I guess we don't know for sure. If it was "time since last chance to proc, but didn't" - then yeah, we surely start from 0 after ICD. But simply "time since last chance to proc" means that we could count since proc time on first hit after icd.

12. Found the quote:

Originally Posted by Blizzard Entertainment
We're going to make some changes to this trinket based on testing and feedback. Our goal was to make it decent if you didn't game it at all but offer some opportunities for enhanced benefits if you did. We're going to try to meet that goal better with these changes:

- 10 sec duration (down from 20 sec) but with double the proc rate.
- Increase your highest secondary stat by 200% of the sum of your two lowest secondary stats. For example: you have 3500 mastery, 5000 crit, 7000 haste. Rune procs, and you get [-3500 mastery, -5000 crit, +17000 haste]. Same logic as before, just double the size of the buff to your highest stat.
http://us.battle.net/wow/en/forum/to...61?page=22#431

13. I did what I think will be my last update to the sheet and the math. It includes ICD stuff.

I'll leave the rest up to you guys :P

14. Wanted to send Conjor a PM, but don't have the post count to have developed that right. Here's what I wrote:

Hi Conjor,

I just wanted to thank you for all your work modelling the RPPM trinket mechanics - great paper and very useful spreadsheet.

When I get a chance I'll be adapting your spreadsheet for rogues and posting it on the rogue elitistjerks mechanics thread - will credit you when I do so. In the meantime, I've put a link to both this thread and your paper, as it answers many of the questions we've been struggling with.

Thanks again for sharing your work!

15. I'd also like to thank Conjor for his hard work on this issue. While I like to think of myself as a decent theorycrafter, reading this post has taught me I have a long way to go. I can't imagine the work that went into this, so I'd like to give you my appreciation and thanks.

16. I've been doing some more work on the spreadsheet. Here are my thoughts so far:

1) The uptime calculations for trinkets with ICD should use (ICD - Proc duration), since the ICD starts at the start of the proc, not at the end. This means proc chances for some trinkets is somewhat higher (small effect for the Rune, large effect on Renataki's, since the ICD is only 2 seconds longer than the proc duration).

2) I'm concerned by the lack of convergence of the two formulas used to calculate trinket up-time (for trinkets with ICD and for trinkets without ICD). I'm still working on this, but my gut feeling is that the equation for trinkets without ICD should coverge with the equation used for trinkets with ICD when you set the value of ICD to be 0.

3) Sharing a note I've added to RoRo for the rogue version I'm working on: modelling for this trinket is not accurate, as the EP values of haste, crit and mastery will change when you drastically change all of them as this trinket does. Also note this trinket will affect the proc chance of other RPPM trinkets (postively if you have more haste than either mastery or crit, negatively otherwise).

17. Originally Posted by wimp
I've been doing some more work on the spreadsheet. Here are my thoughts so far:

1) The uptime calculations for trinkets with ICD should use (ICD - Proc duration), since the ICD starts at the start of the proc, not at the end. This means proc chances for some trinkets is somewhat higher (small effect for the Rune, large effect on Renataki's, since the ICD is only 2 seconds longer than the proc duration).
See my math for why you add the ICD. It all has to do with (nonhomogenous) Poisson distributions.

In laymens terms, you have to think of the ICD as translating the time at which a trinket has to proc. Since the chance to proc starts counting at the ICD, clearly the "next proc" will happen at the ICD + (average time to proc).

Originally Posted by wimp
2) I'm concerned by the lack of convergence of the two formulas used to calculate trinket up-time (for trinkets with ICD and for trinkets without ICD). I'm still working on this, but my gut feeling is that the equation for trinkets without ICD should coverge with the equation used for trinkets with ICD when you set the value of ICD to be 0.
The notes in the sheet explain why this happens. One column uses decaying exponentials to model asymptotic behaviors, the other doesn't. The main difference comes from one taking into account overlapping at the head of the probability distribution and the other doesn't.

You'll notice that the ones based on confidence converge because they both use the same method to determine "average" times between procs.

Regarding my 2nd point:
Originally Posted by Conjor
The notes in the sheet explain why this happens. One column uses decaying exponentials to model asymptotic behaviors, the other doesn't. The main difference comes from one taking into account overlapping at the head of the probability distribution and the other doesn't.

You'll notice that the ones based on confidence converge because they both use the same method to determine "average" times between procs.
My mistake, of course you're right there - no convergence as one overlaps and the other one doesn't. Goes to show maths > gut feeling.

Regarding my 1st point:
Originally Posted by Conjor
See my math for why you add the ICD. It all has to do with (nonhomogenous) Poisson distributions.

In laymens terms, you have to think of the ICD as translating the time at which a trinket has to proc. Since the chance to proc starts counting at the ICD, clearly the "next proc" will happen at the ICD + (average time to proc).

The notes in the sheet explain why this happens. One column uses decaying exponentials to model asymptotic behaviors, the other doesn't. The main difference comes from one taking into account overlapping at the head of the probability distribution and the other doesn't.

You'll notice that the ones based on confidence converge because they both use the same method to determine "average" times between procs.
Once again I agree with your maths, but I'm afraid here only up to a point.

I'm seeing data showing Renataki having an uptime of 23.5% (a 30-minute dummy test - log from a rogue with a haste value of aprox 5,000, and a number of other shorter logs with similar uptimes). The data doesn't fit the theory in this case.

I think the problem here is that we're ignoring the case when t> (3/(2*Lambda))-Ticd - i.e. we are ignoring the 'bad luck protection'.

In your math, you give the uptime formula for when t is smaller than that, but not for when t is larger than that figure, as you argue that:

Originally Posted by Conjor
As you go longer and longer without a proc, whether it is with an ICD or not, you slowly increase the instantaneous rate of procs (the "protection" they added). However, that increase does not affect the previous procs, nor does it increase the "average" proc rate across the board, nor does it affect the proc rate of future procs
I agree with the first statement: the bad luck protection doesn't affect the previous procs.
I agree with the last statement: the bad luck protection doesn't affect the proc rate of future procs.

But the 'average' proc rate across the board does go up, as it must do as a result of the higher proc rate on the cases when t> (3/(2*Lambda))-Ticd, since this higher proc rate isn't countered by a lower proc rate elsewhere.

This graph shows what that distribution looks like, which might help some people visualise the maths. The mean of this distribution is roughly 0.8844*AverageProcInterval, corresponding to a 13.07% increase in average proc rate (borrowed from Midwinter's Stenhaldi):

i.imgur.com/OvSqAi8.png (please put the http stuff before it to make it a link, i don't have enough post count to be able to post links).

19. I tried gemming/reforging Agi > Haste > Crit > Mastery for raid tonight and this happened: http://www.worldoflogs.com/reports/99j99032he1ey8pt/

The highest WoL rank i've ever gotten without playing something stupid (like MM in T14 Hmodes) and my gear isn't that great (http://us.battle.net/wow/en/characte...pbeep/advanced) compared to most the people doing top10 ranks.

Not sure but since the gap between Crit, Haste and Mastery used to be so low, with RPPM maybe it's worth going Haste over Crit. I still don't have T15 Set Bonus or a 2nd RPPM trinket so Haste will become more powerful as I get them.

Thoughts?

20. Originally Posted by Glurp
I tried gemming/reforging Agi > Haste > Crit > Mastery for raid tonight and this happened: http://www.worldoflogs.com/reports/99j99032he1ey8pt/

The highest WoL rank i've ever gotten without playing something stupid (like MM in T14 Hmodes) and my gear isn't that great (http://us.battle.net/wow/en/characte...pbeep/advanced) compared to most the people doing top10 ranks.

Not sure but since the gap between Crit, Haste and Mastery used to be so low, with RPPM maybe it's worth going Haste over Crit. I still don't have T15 Set Bonus or a 2nd RPPM trinket so Haste will become more powerful as I get them.

Thoughts?
My first thought was that your Rentakiki's had a kinda low uptime considering how high your haste is (unless I'm reading the log wrong).

But looks good..!
I think it also depends on what your 'duties' are on the encounter etc.

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