Thrill of the Spreadsheet: Proc'ing Marking Targets

I've been playing with haste values and Marking Targets recently, just making sure I've got a good grasp on what's actually going on. I've had a few misconceptions in my head that I hadn't really thought out before, so I figured I may as well post some of it up here, for anyone's mathy pleasure.

Proc'ing Marking Targets 

As it currently exists, Marking Targets has 5 RPPM (affected by haste).  What makes it different (at least a little bit) from other RPPM abilities is it only procs from our Auto-Shots, which are cast at fixed intervals.  

Before taking Bad Luck Streak Protection into account, each Autoshot has a 25% chance to proc Marking Targets.  The formula for this is: 

5(rppm) * (1+haste) * (3/(1+haste)) / 60 [sec per min] = .25

The haste effects cancel each other out, so the 25% chance to proc per Auto-Shot is regardless of your haste rating, though of course the higher your haste, the more often you Auto-Shot. 

Bad Luck Streak Protection gives you an increased chance to proc Marking Targets when you've gone more than 1.5 times the normal expected interval.  With 0% haste, 5 RPPM is once every 12 seconds.  So at 18 seconds, you start getting an increased chance to proc.  This creates a coefficient that looks like:

MAX(1, 1+((TimeSinceLastSuccessfulProc/AverageProcInterval)-1.5)*3)

Because hast affects Marking Target's procs per minute at the same rate it affects how often we cast Auto-Shot, we'll always have the same number of Autoshots before Bad Luck Streak Prevention (which I'm now going to call BLSP because I'm tired of typing it out) kicks in.  That is to say, if we have 0% haste, Marking Targets has 5 RPPM, meaning 12 seconds is the "AverageProcInterval", meaning BLSP kicks in at 18 seconds while Auto-Shots cast ever 3 seconds, meaning the first 6 aren't affected by BLSP, but the 7th or beyond, assuming marking targets hasn't proc'ed, will be; similarly, if you have 20% haste, Marking Targets has 6 RPPM (5*1.2=6), meaning the "AverageProcInterval" is 10 seconds and BLSP kicks in at 15 seconds, while Auto-Shots cast every 2.5 seconds (3/1.2=2.5), so just like before, the first six Auto-Shots after a successful proc won't benefit from BLSP, but the seventh and beyond will.  

The chances to proc then look like this:

Auto Shot	Successfully proc's Marking Targets
Auto Shot	25% chance to proc' Marking Targets
Auto Shot	25% chance to proc' Marking Targets
Auto Shot	25% chance to proc' Marking Targets
Auto Shot	25% chance to proc' Marking Targets
Auto Shot	25% chance to proc' Marking Targets
Auto Shot	25% chance to proc' Marking Targets
Auto Shot	43.75% chance to proc' Marking Targets
Auto Shot	62.5% chance to proc' Marking Targets
Auto Shot	81.25% chance to proc' Marking Targets
Auto Shot	100% chance to proc' Marking Targets

The only thing that changes is when those Auto-Shots happen.  With a few haste options, those look like:

10% haste	15% haste	20% haste	25% haste
0.00 sec	0.00 sec	0.00 sec	0.00 sec	0th Auto Shot	Successfully proc's Marking Targets
2.73 sec	2.61 sec	2.50 sec	2.40 sec	1st Auto Shot	25% chance to proc' Marking Targets
5.45 sec	5.22 sec	5.00 sec	4.80 sec	2nd Auto Shot	25% chance to proc' Marking Targets
8.18 sec	7.83 sec	7.50 sec	7.20 sec	3rd Auto Shot	25% chance to proc' Marking Targets
10.91 sec	10.43 sec	10.00 sec	9.60 sec	4th Auto Shot	25% chance to proc' Marking Targets
13.64 sec	13.04 sec	12.50 sec	12.00 sec	5th Auto Shot	25% chance to proc' Marking Targets
16.36 sec	15.65 sec	15.00 sec	14.40 sec	6th Auto Shot	25% chance to proc' Marking Targets
19.09 sec	18.26 sec	17.50 sec	16.80 sec	7th Auto Shot	43.75% chance to proc' Marking Targets
21.82 sec	20.87 sec	20.00 sec	19.20 sec	8th Auto Shot	62.5% chance to proc' Marking Targets
24.55 sec	23.48 sec	22.50 sec	21.60 sec	9th Auto Shot	81.25% chance to proc' Marking Targets
27.27 sec	26.09 sec	25.00 sec	24.00 sec	10th Auto Shot	100% chance to proc' Marking Targets

Anyhow, the 10th Auto-shot after successfully proc'ing Marking Targets will always guarantee a new Marking Targets proc; though, if you make it all the way to 10 Auto-Shots without getting a proc, your DPS on that pull is going to be in really bad shape regardless.

My friend Mal made me a custom weakaura that shows roughly (there's a slight issue in that A. your auto-shots don't actually happen at exact intervals; and B. combatlog records when an autoshot hits, but Marking Targets is applied when you "cast" your auto-shot) what percent chance your next Auto-Shot has to proc Marking Targets.  Most of the time, this won't be useful at all, but on some occasions, you might be on an unlucky streak, and want to hold off on casting Sidewinders naked if your percent is getting high.