Understanding RPPM's "Consistencies"?

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So, I understand the premise of RPPM and how the chance to work for each ability is modified by the execution time of that ability, etc., to roughly average to a certain number of procs per minute, and I know how haste affects this in an unreliable manner. Yet there's one thing I'm uncertain on.

I know that prior to RPPM when you simply had a proc chance and a ICD that everything would go off at the start of the fight simply because the chance was high per ability and then they simply couldn't happen again for a set amount of time.

Now, with RPPM, I'm slightly confused.

During a fight, my procs behave as I'd expect: all over the place but with at least an average that I can handle for things like my Unerring Vision. It's the start of the fight that I'm confused.

Sometimes I'll notice I won't get procs right off the bat, but often I notice that I'll get almost everything to go off within the first 10 seconds of the fight. I don't pay as much attention to Jade Spirit, Acceleration, etc., but I definitely see my Perfect Aim alert from Weak Auras go off sometimes at what seems like the exact same time several pulls in a row.

Is there something that makes them very likely to go off at the beginning of combat?

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Basically if you are out of combat for more than 4-5 minutes you get like a 16.5x coefficent on your procs. So if something had a base proc rate of 10 percent, it would get a 165 percent chance to proc on damage/heal after after that wait on the next pull (yes, I used 10 because I'm way too tired to use something else and 10 makes math easier).

If I remember where the post is, I'd link the RPPM explanation that explains this and bad luck protection and all that.

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