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So, I've been on a kick lately figuring out the DPR for a lot of our characters, and one class has stumped me: the magus. It's all fun and games until spellstrike enters the mix.

I could make my life easier and just use a non-spellstrike spell, but everyone knows that's not how to achieve maximum theoretical DPR. That needs Intensified shocking grasps and a nice high-threat weapon.

I've been using the expanded damage formula taken from the DPR Summer Olympics thread, which can be found here.

Spoiler:
h(d+s)+ft(cd+cb+r)

h = Chance to hit, expressed as a percentage. This doesn't exceed .95 (unless you autohit for whatever reason) and never goes below .05.
d = Normal damage. This is any damage that happens any time you hit.
s = Damage which isn't multiplied on a crit. "s" stands for sneak attack, but this includes elemental/alignment properties on weapons, manyshot damage, and so on.
t = Chance to roll a threat. This is the threat range of your weapon or your chance to hit, whichever is lower.
f = This is your chance to confirm a threat. Most of the time, this is equal to h. If you have Critical Focus, it's (h+.2) or .95, whichever is higher. If you auto-confirm crits, as with a level 20 fighter or Bless Weapon, this is 1.
c = This is the number of bonus multiples you get from a crit. A 2x crit weapon is 1, a 3x crit weapon is 2, etc.
b = This is elemental burst damage, such as from fiery burst weapons and thundering. Such enhancements self-multiply based on your crit multiplier; if they don't, then they're added to r and not b.
r = This is fixed bonus damage dealt on a crit. No such abilities exist in PF core, to my knowledge.

Using that formula, I can easily calculate his expected weapon-based DPR, which includes counting the additional attack from spellstrike. What that formula doesn't seem to let me do is add the shocking grasp in there. It can only hit once, after all, and is delivered on any of the attacks... the formula just doesn't isn't cutting it for me.

So, I'd be awesomely appreciative if someone could walk me through the math on how to figure out the DPR of the following magus:

Spoiler:
BAB +12/+7/+2, STR 26 (+8), +5 keen speed scimitar (after arcane pool), Power Attack (-4/+8), Weapon Focus {+1/+0)
Spell combat + Intensified shocking grasp (35 average damage) through spellstrike, grants one extra full-BAB attack.

+22/+22/+22/+17/+12 for 1d6+21, 15-20 crit range for 2d6+42
The first successful hit discharges the shocking grasp.

Assume he's fighting AC 27.

For simplicity, assume no other buffs or feats.

It's quite possible that there's some ridiculously easy way to do this that I'm just overlooking. So, if that's the case and the above is answered easily, then I have a second question:

Using the same magus, how easy would it be to factor the potential DPR gain of a Quickened Intensified shocking grasp prior to the full attack pattern, and what is that gain?

Thanks in advance for any help!

cant you also empower it for moar damag

cant you also empower it for moar damag

For sure, and there's about a million other ways to increase the damage, but I'm keeping the base example simple for now.

Once I can actually reliably calculate out the expected DPR, then I'll worry about full optimization :)

technically yes a magus with multiple metamagics can have lots of shocking grasps and against a target that must die post haste at higher levels you can quicken one shocking grasp and then pop another shocking grasp for a total of 2 spells for the round added to a full attack with the blade in hand.

Asta

Am I missing something here? Is this something you do just randomly to take a given build and optimize it's output, or are you actually min-maxxing your fellow gamer's characters?

Is it the Magus class itself throwing off the calculations? Because the existing math seems sound for weapon damage.

Is there a similar formula for magic users to calculate their spell DPR? I know it wouldn't work EXACTLY the same, but given a base formula, we could tweak it for the spellstrike hits.

(pointedly not going into my anti-DPR frustration/rants in an effort to actually be helpful.)

Barry: To answer, I'm always trying to optimize some random build or another, but in this case, I am indeed min/maxing fellow gamer's characters - in this case, converting them from 2.5 to Pathfinder (lol, don't judge :P /shame)

Yes, it is the magus that is throwing off the calculations. It's not the physical part that's the problem, it's tacking in the actual DPR effect of the shocking grasp that would be part of the full attack action + extra physical attack.

I'd think that for casters to calculate spell DPR, we'd average its damage, look at if the spell offers a save, and multiply average damage vs. average save chance, or something like that. For a shocking grasp, the save chance is replaced by a single attack chance, so that's about that - that by itself would plug into the formula fine.

However, it's really only the magus that can basically get more than one attack in a round thanks to spell combat, so their average value of a shocking grasp is far higher than that of a normal wizard. Adding a grasp onto a single attack doesn't really measure that fact. So, I'm not sure how to go about calculating its value.

I was considering taking average grasp damage, adding (damage times threat range) - that would give me grasp damage if it always hits, on its own, in a vacuum. Then, I'd multiply by the chance the magus misses all of his attacks in the round... but something about that doesn't feel right. Couldn't begin to tell you what that may be, but I dunno, it seems wrong.

Thanks for not ranting, though, and you were helpful by letting me clarify a few things :)

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Short-ish answer: to get DPR for an ability like shocking grasp that can only trigger once, and that triggers on any successful attack use the following formula:

(1-(m1)*(m2)*(m3)...)*D+(t1*f1+m1*t2*f2+m1*m2*t3*f3+m1*m2*m3*t3*f3...)*c*D

where:
m# = the chance that the #th attack will miss
D = the average damage that the ability will do
t# = the chance that the #th attack will be a critical threat
f# = the chance a critical threat on the #th attack will be confirmed
c = the number of bonus multiples you get from a crit, as it applies to this ability

I hope the sequences are clear with regards to how to change them for more or less attacks.

m1 = .2
m2 = .2
m3 = .2
m4 = .45
m5 = .7
D = 35
t1 = .3
t2 = .3
t3 = .3
t4 = .3
t5 = .3
f1 = .8
f2 = .8
f3 = .8
f4 = .55
f5 = .3
c = 1

Plugging that in, you get a DPR of .99748*35+(.332493)*35 or 46.55 for just the shocking grasp ability.

The formula I provided consists of two terms, the first is the chance that any one of your attacks hits times the damage a hit will do, the second is the chance that the first successful attack you make is a critical hit times the bonus damage a crit will do.

To calculate the odds that an event will happen given a number of tries, you have to think about the odds that it will not happen, and subtract that value from 1, to get the chances that your desired event will not not happen.

Your second question significantly complicates things, because you cannot have two charges of shocking grasp active at once, and because you must make your attacks in order of decreasing base attack bonus, you must hit with the quickened shocking grasp in your first three attacks in order for it to be used before the second shocking grasp is triggered.

This leaves us with a probability chain that I don't know how to simplify, that is going to be a really long equation, so I'm only going to describe it.

You have to consider four different situations: that the first attack hits, that the first misses and the second hits, that the first and second hit miss and the third hits, and that the first three attacks all miss.

This equation will end up looking similar to the 4 copies of the equation I posted earlier, each with a different coefficient and number of attacks based on the probability of the preceding event happening.

Reading back through this post, it seems pretty hard to follow so if you have any questions I'll try to clarify.

doublebear: That is exactly what I was looking for. I wouldn't have figured it out on my own, but I can understand the logic and math behind it just fine.

One internet for you, along with my thanks!

About adding a Quickened grasp in there, yea, I know it's weird. There are basically just two scenarios that can happen, though:

If the Quickened spellstrike hits, then we'd just add its damage on top of the "normal" attack routine, progressing exactly the same as if it didn't exist, looking exactly like what you typed above.

If it misses, then we progress into the normal attack pattern (speed attack + three BAB attacks) in order to try and discharge the spell; assuming one of these attacks hit, it looks exactly like the "normal" attack pattern, except for one little fact - he's still got his normal spell combat spell available (which, by RAW, he can now take after his full attack).

So I think there's only two things to worry about there, since one way or another, adding a Quickened spellstrike in there basically just results in adding one full-BAB physical attack + shocking grasp combo on there, either as the first, or last attack (we can't interrupt the attack pattern once it starts to inject the second spell charge).

Granted, I'm not sure how to figure that... man, I suck at actually determining on my own how to math things >.< I feel like this image applies to me.