Rune of Re-Origination bugged
I had 15.02% haste for that test. I have the 522 Rune of Re-Origination, which has a nominal RPPM proc rate of 0.92 [base value] * 1.15^((528-522)/15) [scaling for item level] * 1.1 [10% buff a month ago] = 0.957 . So the haste-scaled proc rate should be 1.101 procs/minute.
First check: mean proc interval.
The mean proc interval in the above log was 64.95 seconds with standard deviation (of the mean) 2.59 seconds.
Without the bad luck streak prevention mechanic, the mean proc interval should be 22 seconds [icd] - 10 seconds [10 seconds of the icd count toward the proc chance of the first attack thereafter] + 60 sec/min * 1 proc/ (1.101 procs/minute) [the haste-scaled proc rate above] = 66.51 seconds.
With the bad luck streak prevention mechanic, the mean proc interval should be scaled by about 88.44%. This is a result of my math at <http://us.battle.net/wow/en/forum/topic/8197741003?page=4#79>; I and others have also verified by simulations that it is approximately correct. This means the mean proc interval would be 66.51 seconds * 0.8844 = 58.82 seconds.
In summary, the mean proc interval -
Measured: 64.95±2.59 seconds
Prediction assuming no luck streak prevention: 66.51 seconds (matches the measured value)
Prediction assuming luck streak prevention: 58.82 seconds (discrepant with the measured value by 2.4 standard deviations)
Second check: largest interval
Without luck streak prevention, the cumulative distribution for proc interval t is
with k = 1/AverageProcInterval = 1/(66.51 sec), i.e. an exponential distribution.
However, with luck streak prevention, the cumulative distribution function looks like
for k*t > 1.5 .
The largest proc interval in that sample was t = 312 seconds. Assuming no luck streak prevention, that has associated probability exp(-312/66.51) = 0.00918. That's a one-in-109 chance -- not particularly unlikely.
However, with luck streak prevention, the associated probability changes to exp(-312/66.51*(1+(312/66.51/2-1.5)*3)-3.375) = 2.13*10^-9. That's one in 468 million -- far more unlikely.
Final check: the distribution of proc intervals
I made a quick histogram of the the above data. It resides here:
(Error bars are approximate)
Superposed on the data are two prediction lines: one (blue) without luck streak prevention and the other (red) with that mechanic. These are just the probability density functions
f(t) = k*exp(-k*t)
for no luck streak prevention and
g(t) = k*exp(-k*t) , if k*t <= 1.5
g(t) = k*(1+(k*t-1.5)*3)*exp(-k*t*(1+(k*t/2-1.5)*3)-3.375) , if k*t > 1.5
with luck streak prevention.
Without doing any further numerical analysis, it's pretty evident that that the data is following the standard exponential distribution of the "no luck streak prevention" prediction line, rather than the distribution with luck streak prevention.
Bad juju also appears to be bugged and not procing enough. Not proccing on pull very often (even when out of combat for awhile), and procced less on every single fight this week compared to the one before. Proced twice during a 5:30 Dumuru kill and 3 times during a 7:33 Consorts. Really bad luck or is anyone else having this problem?
Yeah. I'm seeing the same problem as well.
I have a couple of the Agi trinkets and I don't have any problems with their proc rates except for Bad Juju and Rune of Re-Origination.
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