Thrill of the Spreadsheet: Mongoose Bite Charges

I haven't had too much content to dissect lately, so I haven't had much chance to write any Thrill of the Spreadsheet posts.  Fortunately (or not, depending on whether you like these or not), with three new hunter specs, there's a lot to get ready for legion.

At this point, I doubt there are more than a handful of us who are keeping DPS spreadsheets these days. But even if you're not putting together a full blown dps-spreadsheet, there are some small calculations that might be helpful, just while you're thinking about how you might approach a brand new spec. This morning I was looking at the charges of Mongoose Bite with Jademcian, and decided I wanted to make a little calculator for Mongoose Bite charges in the Survival Rotation.

If you haven't read the Legion Hunter Preview yet, Survival's new Mastery, Hunting Companion, increases how often you get charges of Mongoose Bite.  Every time your pet attacks, you have a percent chance (whatever percent your mastery is) to get an additional charge of Mongoose Bite.  In addition to the mastery, you also get 1 charge every 10 seconds, baseline.

So, for anyone who's interested, here's what I threw together.

Mastery Needs

Haste	5%	10%	15%	20%
Chances/sec	1.025	1.05	1.075	1.1
Mastery needed	22.76%	22.22%	21.71%	21.21%

This one is just a basic calculator for how much mastery you need in order to have an expected value of 1 charge every 3 seconds, at fixed values of haste.  The first row, obviously, is just some various haste percentages.

The second row represents how many hits per second your pet should average. This is based on having Claw, Smack or Bite once every 3 seconds, Flanking Strike once every 6 seconds, and your pet's auto-attack once every 2 seconds (which is the only ability affected by haste). To calculate these, I took how many times they occur every six seconds (I only used six because it's the longest CD and that's how I like to think, that number is arbitrary though, you could start by taking how often they occur every 1 second, or every 15, whatever): Flanking Strike once, Bite/Smack/Claw twice. For the auto-attack, you use 6/(2/(1+h)) where h is your haste percentage, 2 is the base occurrence rate. Take the sum and divide by 6 to get your average hits per second, which happens to also be how many "chances" or "rolls" you get per second based on your mastery percent to see if you get a charge of Mongoose Bite.

The third row, then, takes how many chances per second you average, and uses that to calculate the mastery percentage you need to have an expected value of 1 Mongoose Bite charge every 3 seconds (which is roughly what you need to keep the CMB buff up 100% of the time).  To do this, we first want to know how many we need from Hunting Companion, since we already get one charge every 10 seconds baseline.  1 charge per 10 seconds happens to average .3 charges every 3 seconds (showing off my made dividing skills here), so we need to average .7 charges per 3 seconds from Hunting Companion in order to make our goal of 1 charge per 3 seconds. From there we take our .7 (charges we need to average) and divide it by the solution from row two multiplied by 3 (that is, how many chances per second we had, multiplied by 3 seconds).  And that gives us our mastery needed to average 1 charge returned every 3 seconds.

If you'd like to recreate the calculator on your own, you can use this guide:

B2 - "Haste"
B3 - "Chances/sec"
B4 - "Mastery needed"
C2 - [insert the percent haste you want to test]
C3 - "=(3+(6/(2/(1+C1))))/6"
C4 - "=0.7/(C3*3)

Drawing Conclusions

**Disclaimer** The value of this calculator is not in determining how your rotation should look, or what stat percentages you should have. The point is just to get a feel for how each stat will be affecting our rotation.

In this case we see haste has very little effect on how many Mongoose Bite charges we get, though this will help add a little bit of value to the stat, which would otherwise only affect, as far as we know, the damage from Polearm auto-attacks and pet auto-attacks.

It's also worth noting that the numbers this calculator gives you is based on averages, on the expected value of a statistical chance.  As with anything based on pseudo-random number generators, there are no guarantees.  As such, once we get more information about the spec, how much damage everything does and what the talents are, we may determine we need Mongoose Bite Charges much more often in order to be reliable.  Even if you have enough Mastery and Haste to average a charge every 3 seconds, that doesn't mean you'll necessarily get it.  You might get 6 procs in 6 seconds, and then none for 20 seconds.

Again, the goal of this is simply to start getting a feel for how these particular stats will affect this one aspect of our rotation.

Flipping It Around: Calculating Expected Value

If instead of looking at what stats we'll need to achieve a specific Expected Value, we instead want to reverse the calculator, and see what the expected value for MB Charges will be based on whatever Mastery and Haste we already have.  That might look something like this:

Mastery	18.00%
Haste	5.00%
Chances/sec	1.025
Sec/Charge	3.514938

In this calculator you can just put in  your haste and mastery, then it'll tell you how many times, on average, your pet will attack per second, and then how often you can expect to get a new Mongoose Bite Charge.  

The chances/sec row is the same as it is in the mastery calculator.  The fourth row, however, we're looking out from a little bit different angle.  All you need is your chances/sec multiplied by your mastery (which gives you the expected value of charges you'll get per second from Hunting Companion) and add the number of charges you get per second from the baseline ability (0.1).  I then inverted that number, because it seems more useful, to me, to think about how often I'll get a proc (in the example above, about every 3.5 seconds on average) rather than how many procs per second I'll get (which in the example above would have been 0.2845 charges per second).

If you'd like to recreate this so you can put in whatever mastery and haste you'd like to play with, you can use this:

B2 - "Mastery"
B3 - "Haste"
B4 - "Chances/Sec"
B5 - "Sec/Charge"
C2 - [Input mastery]

C3 - [Input haste]

C4 - "=(3+(6/(2/(1+C3))))/6"

C5 - "=C2*C4+0.1"

Anyhow, if it's something you're interested in, have fun playing with the numbers!