Proc munching is also an issue sure but I think the bad luck protection is an issue. Before we had our expected interval which was also our average time between procs because proc times were equally distributed about the proc interval. Now our true average is actually less then the expected interval because proc times greater then 3/2 expected interval are less likely.

To check that I wasn't going crazy I wrote a quick simulator to look at a trinket with a proc chance per second of 1%. Simulating 64K procs, with no bad luck protection I got an interval of 100.04 seconds, as expected given the expected interval of 100 seconds. With proc protection added I get an average interval of 88.8 seconds. This suggests that the average proc interval is in fact less then the expected interval and by a large enough value to potentially skew results.

@Wimpyone

Is your AverageProcInterval the same as Expected Proc Interval (i.e. 60/(1+HasteValue*RPPM))? I am trying to math these things out myself, and I want to be certain that I have a clear picture of the math I am playing with. Also, I am assuming that t = time (in seconds), is that an incorrect assertion?

How are people calculating uptime for RPPM trinkets with ICD? I'm trying:

1) Avg_proc_interval + ICD
2) Avg_proc_interval + (Trinket duration - ICD)

The second would make more sense, since I assume the ICD starts when the trinket procs. But I'm worried it might be an over-simplification.

I have a request for someone with a Renataki's Soul charm to do some testing. As Renataki's has an ICD which is similar to the trinket duration, it's the ideal candidate for determining if either of the above models is similar to reality. If anyone could PM me some uptime details that would be great (or post them on this thread if you prefer).

I'd need to know: your base haste in % (or your toon name, so I can look it up on the armory),and trinket uptime % (skada can tell you this, or you can log the fight). Ideally a 30-minute dummy fight doing your usual rotation (hey, it's good practice!)

So, I think we're getting there with the modelling of bad luck protection and proc overlaps. This is what I have 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 average proc time by 13.07%, as mentioned above on this thread. For the mathematical derivation please see this work by Jay (@Hamlet EJ).

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 above on this thread), but for now multiplying by 13.07% seems more accurate to me.

Using the math above, and assuming 23% haste, 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.

Any and all feedback or corrections on the math are very welcome.
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Edited: corrected one incorrect statement (multiplier applies to average proc time, not average uptime as originally stated) and edited sample uptime values accordingly.