Legion Beta: Hunter's Mark

**UPDATE**

The RPPM for Hunter's Mark was changed the day after I wrote this.  Once I have enough data, I'll try to update the whole post with current numbers. 

On the Hunting Party Podcast the other day,  I did a fairly horrible job of explaining the effect of Hunter's Mark changing to an RPPM.  As such, I thought I'd go over the basics of it here, and perhaps what we can expect.

Marksmanship Core Mechanics Refresher:

• Hunter's Mark - Your Arcane Shot and Multi-Shot have a chance to apply Hunter's Mark, marking the targets for Marked Shot.
• Marked Shot - 
• Rapidly fires a shot at all targets that are affected by Hunter's Mark, dealing 350% Physical damage. 
• Also exposes Vulnerabilities in the target, snaring them by 15%, and increasing Aimed Shot damage done to the target by 25%. Lasts 30 sec, and stacks up to 3 times.
• Relevant Talents:
• Heightened Vulnerability - Level 75 Tier - Your next Marked Shot applies 3 stacks of Vulnerability to all Marked Targets.
• Patient Sniper - Level 75 Tier - Gain the patience of a veteran sniper, increasing your maximum focus by 30 and causing Marked Shot to apply Deadeye instead of Vulnerable. Deadeye increases your Aimed Shot damage by 150% for 6 sec.
• Sidewinder - Level 100 Tier -  
• Launches Sidewinders that travel toward the target, weaving back and forth, dealing 300% AP as Nature damage to each target that they hit. Cannot hit the same target twice. 
• Generates 60 Focus. 
• Replaces Arcane Shot and Multi-Shot.

These mechanics together create the core rotation (if it can be called that) of Marksmanship Hunters in Legion.  Cast Arcane Shots to proc Hunter's Mark; cast Marked Shot to convert Hunter's Mark into a stack of Vulnerable; repeat to build 3 stacks of Vulnerable, then cast very powerful Aimed Shots, while maintaining your 3 stacks of Vulnerable with Arcane/Marked Shot combos as necessary. There is of course some nuance to how you weave in various talents and other abilities, and this can change substantially depending on if you take any of the 3 talents listed above, but the basic rotation revolves around the interaction of Hunter's Mark, Vulnerable and buffed Aimed Shots.

Proc'ing Hunter's Mark

The way Hunter's Mark has proc'ed has been changing over the last few builds of the Legion Alpha. From a fairly simple flat percent chance to proc when you cast Arcane Shot, to a more complicated RPPM chance to proc, with an added synthetic bad luck protection.

With the previous flat chance to proc Hunter's Mark (in one build it was a 50% chance per Arcane Shot), you run into a sort of oddity, in that the number of Hunter's Mark procs you get is going to be directly related to the number of Arcane Shots you cast.  There's no problem with that inherently, but it feels weird (for lack of a better term) to occasionally want to spam your Focus generating ability despite not needing to generate focus, but because you're trying to get a Hunter's Mark proc.

That aspect of it didn't bother me too much, but what did concern me was how much variation there would then be in our DPS because of this RNG factor.  With a flat 50% chance to proc Hunter's Mark on each Arcane Shot, for every 3 Arcane Shots you cast, you have a 12.5% chance of proc'ing Hunter's Mark on each one of them, and really 1 in 8 isn't at all uncommon.  At the same time, you also have the exact same chance, 12.5%, of not getting any procs at all.  So one out of eight pulls you'll have an amazing, meter-breaking opener, and one out of eight pulls you'll just want to go die and try to wipe the raid, 'cause your on-pull burst will be ruined.

The RPPM Hunter's Mark

My understanding is that the goal of implenenting RPPM in general was twofold: to provide an alternative to the predictability of ICDs, and to create a mechanic for proc'ing something that has a similar chance to proc regardless of your APM (actions per minute, or in this case, actions that could cause a proc per minute).  The way it does this is by increasing the chance to proc by how long it's been since your last chance to proc.  That is, if it's been 2 seconds since your last chance to proc something, then you'll have double the chance from when it had only been 1 second since your last chance to proc.

For the current iteration of Hunter's Mark we have 6 rppm, which is affected by haste. Only Arcane Shot and Multi-shot can proc HM (though i'll only be talking about Arcane Shot today), so we can look specifically at "time since our last Arcane Shot" instead of more generally "time since last chance to proc".  If we call that T, measured in seconds, and use "h" to represent our haste percentage as a floating point decimal, then if P(x) is our chance to proc Hunter's Mark, we have:

P(x) = 6T(1+h)/60

It's worth noting here that T is capped at 10 seconds. This info is based on what Blizzard has told us about how other RPPM mechanics work; while I haven't found any indication that this isn't the case for Hunter's Mark, I still don't have enough data to actually say so definitively, so we're just working on that assumption.

What this means is if we have, for example, 15% haste, we should expect to average one Hunter's Mark proc every 8.696 seconds, regardless of whether we cast Arcane Shot on every single GCD, every other GCD, or every third GCD, etc.  This is because two 11.5% chances gives you the same expected value as one  23% chance.

A fun mathematical oddity: while this remains true for the average over a large enough data set, they do have different ranges. So if we were looking instead for the maximum possible result (as we sometimes do when trying to theorycraft for DPS ranking, instead of progression raiding),  Two 11.5% chances have slightly less chance to get 1 proc than one 23% chance; however, two 11.5% chances have a slight chance (1.3225% of the time) of getting two procs, while that's never possible with one 23% chance. This of course only affects rare occasions, and will in no way affect how you play Marksmanship in normal raiding situations.  

Bad Luck Streak Prevention

Just a couple patches after introducing the RPPM mechanic, Blizzard decided to add in a Bad Luck Streak prevention, since RPPM chances tended to be much lower than the chances on the old ICD method, which meant it was much more common that you'd never get a proc.  The bad luck streak prevention adds in another multiplier that increases your chance to proc something after you're gone more than 1.5 times the average proc interval, without getting a proc.

So if we have 15% haste, then we have a base RPPM of 6*1.15, which means the average proc interval will be 8.7 seconds.  If, then, we've gone more than 13.04 seconds without proc'ing a Hunter's Mark, the proc chance will start to go up.  The commonly used expression for this is:

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

For our calculation above, with 15% haste, if it's been 14 seconds since our last proc, our bad luck prevention multiplier will be:

MAX(1, 1+((14/8.7-1.5)*3) = 1.33

Bad Luck RPPM Integration

We then need to just include the result from the bad luck prevention as a multiplier in with our RPPM calculation.  If we defined MAX(1,1+((TimeSinceLastSuccessfulProc/AverageProcInterval)-1.5)*3) as B, then we have:

P(x) = 6*T*B*(1+h)/60

In most cases, (that is, until we've gone more than 1.5*AvgProcInterval without a proc) B will equal 1, and won't change the likelihood of a proc, but it starts scaling very quickly as soon as we go above 1.5 times the average proc interval.

Effects on the Marksmanship Playstyle

As I briefly mentioned above, the primary effect this will have on our play-style is removing the temptation to spam Arcane Shot when you're building stacks of vulnerable.  There's no reason not to use Aimed Shot or other focus dumping talents in between Arcane Shots, because of how the RPPM mechanic affects proc chance.  

Of course, with Sidewinder, Heightened Vulnerability and Patient Sniper, things will work out a little differently.  I'll be going more in depth into those in Part II.