Thrill of the Spreadsheet: Understanding Multistrike

I've seen a few explanations of how multistrike affects your damage, and each time I was left a bit unsatisfied.  So, as perhaps can be expected at this point, I decided to try to give it a shot, and really spell it out as clear as I can.

Multistrike - gives most abilities up to two separate chances to hit their original target an additional time for 30% of the original amount in PvE. 

Just as a little side note here, to make things a little bit clearer, from this point forward, I'm going to refer to one of the 30% damage shots following your main shot as a "multistrike", and i'm going to refer to the stat as "MS" ("MS%" or "MS Rating").

The trouble in understanding that, is it doesn't really explain how much of a damage increase each % of multistrike gives you.  However, with a little bit of algebra, we can convert this to a bit simpler to understand function.  

To start off, the number of multistrikes you average per shot will be a simple function of the MS%.  If you have, for example, 20% MS, then you have have a 36% chance of getting at least 1 multistrike for any individual ability you use; that is to say, if you fire 100 arcane shots (which do 5000 dam each, we'll get to that later though), you'll get (on average) 36 of those to proc at least one multistrike.  In addition to that, you have a 4% chance of getting 2 multistrikes off of any individual ability.  So of those 36 multistrikes (proc'ed off of a hundred abilities), 4 of them will will have partners, bringing our total up to 40 multistrikes out of every 100 abilities. Of course, that's the same thing as saying you'll average .4 multistrikes per shot, if you have 20% MS.  

Then, because each of those multistrikes do 30% as much damage as the original shot, in our little example here we can go ahead and multiply that in there. If we have 100 arcanes doing 5000 damage each (500,000 damage total), and then we'll have 40 multistrikes which will do .3*5000 damage, that brings us 560,000 damage, a 12% increase in damage.   And that's the number we're really interested in.  For 20% MS, we get a 12% increase in damage.  

The function which explains that for any given MS% or ability's damage is:

Total Damage = (MS% * 2 * .3 * base damage)

Or  we can divide that all by the base damage if we're interesting in just the percent increase in damage:

Increase in damage = (MS% * 2 * .3 * base damage) / base damage

which can be simplified to a much easier:

Increase in damage = MS% * 3/5

In increments of 5% MS, that ends up looking like this:

MS %	Dam. Incr.
20%	12%
25%	15%
30%	18%
35%	21%
40%	24%
45%	27%
50%	30%
55%	33%
60%	36%
65%	39%
70%	42%
75%	45%
80%	48%
85%	51%
90%	54%
95%	57%
100%	60%

For those who don't like to think in algebraic, the easiest way to understand that, I think, is looking at that last entry, with 100% MS.  It makes sense that 100% MS would give you 60% extra damage, since it will guarantee you 2, 30% extra damage shots. The point of all of this is, 1% MS gives you 3/5 % increase in damage.  

There is then, just one more number we need to look at when thinking about the stat: the amount of the stats on gear that it takes to make up 1%MS. As it's tuned currently on the beta (which seems likely to make it onto live, at this point), it takes 66 MS rating.  That means for every 66 MS you get a 3/5% increase to your damage.  For a 1% increase in damage, then, you'll need 110 MS rating, which is a somewhat interesting number, and not because it's the smallest number that's the product of two different substrings (just look it up), but because it's the exact same rating you need to get 1% crit (which much more conveniently, 1% crit happens to equal a 1% damage increase).

So basically, we have two stats which do the exact same thing.  This doesn't mean they'll be of equal worth.  Currently there are a few more mechanics which add benefits to crit; perhaps the biggest for hunters right now is the MM Aimed Shot, which returns 20 focus to you when it crits.  Another major effect on the value of the stats is the newly introduced Stat Attunements, which provide 5% more of the respective stats from gear.  There's also specs like Survival which has a basic, flat increases to Multistrike damage (for those interested, you get more stats from your gear, and you get 20% more damage per multistrike, so in the end you get 1% of MS from less stats, and instead of getting 3/5% damage increase per 1% MS, that extra 20% damage per multistrike gives you a total of .72% damage increase per 1% MS). *Edit* Thanks to dues payer and WHU member Jacques for pointing out that the 20% is not applied to the damage of the original shot, but to the damage of the multistrike.

The last thing I'd like to bring up (which I've already mentioned on this site, but I feel like it's worth reiterating) is that that Multi-strike is multiplicative with with the other secondary stats (except for perhaps haste).  What I mean by that, is if your arcane shot does 5k base damage, and you have 25% crit, and 25% multistrike,  your arcane shot will not average 7500 damage (which would be 5k + 5k*.25+5k*.25), instead, it's going to average 7812.5 (which is 5k*1.25*1.25).   This is because Multistrikes can Crit.  So Critical nets you more damage when paired with Mulistrikes, and vice versa.  This is also true of Versatility, and for hunter specs, Mastery (on applicable abilities).  

Anyhow, after writing this, I'm not sure if I've actually managed to make the subject any simpler, or if perhaps I've made it seem even more confusing.  Hopefully something in here will help someone, though.