Some Interesting Math

Bhow · 07-15-2008, 02:11 PM

Not sure if this has ever been posted anywhere before but Ive been messing with it / using it for a while now. Let me know what you think of it.

With the addition of many items with +crit chance, its been a bit hard sometimes to decide on which items to use. Eg. BCG.

When you crit, you hit for more than 30% more than you would normally have hit for. Knowing this, you can determine about how much dps your going to gain from wearing, say a +5%crit item.
5% * 30% = 1.5% dps gain.

Therefore if youre parsing ~3k on average find your base dps by:
Base DPS = 3000/(1 + .3 * your current crit chance)

Next find your dps gain by:
DPS Gain = Base DPS * (.3 * (New Crit Chance - Old Crit Chance))

??Also, if your well above your +spell damage cap, your also effectively using more of the +spell damage when you crit.??

This is what happens when I get bored at work

Please look over the math / logic. If you see something that doesn't make sense, speak up and Ill see if I can fix it.

Im working on a way to relate Casting / Reuse speed to crit chance / %spell damage increase. Ill post it if I get it working.

Pinski · 07-15-2008, 03:59 PM

No, you aren't using more +spell damage when you crit. Your +Spell Damage caps are based on your Spell's Quality and the INT-based bonus. That's it. Crits, Base Damage, nothing increases your spell damage cap, ever.

Bhow · 07-15-2008, 04:06 PM

Unless Im interpreting Bigron's guide wrong:

+Crit.
This Improves your critical hit chance.Critical hits are a improvement to base damage of spell by up to 30 pct.Critical hits are applied before +spell damage and the hit rate is targets of your level.

Im @ work at the moment, so Ill check it when I get home. If you're right, Ill change it.

Pinski · 07-15-2008, 04:07 PM

His guide is wrong.

Also your math on 5% crit is wrong. That is only true if you're going from 0% to 5% crit. Since you already have some crit, the value is not as large as you make it out to be.

Bhow · 07-15-2008, 04:34 PM

As to Bigrons guide being correct or incorrect, I cant be sure till I get home. Ill check it when I log on.

As to the math:
Every player starts with an initial chance to critically spell cast of 1%, or .01.

Assume int stays constant and only %spell crit can change.

Let d = a players actual dps w/ a crit chance of 0%
A players initially measured dps (x) = (1 + (.01 * .3)) * d (An increase from 0 - 1% crit.)

If a player adds an item that does not modify int, but adds +5% spell crit then:

Let y = the change in dps.
x + y = (1 + (.06 * .3)) * d (increase from 1 - 6% crit chance)
(1 + (.01 * .3)) * d + y = (1 + (.06 * .3)) * d
1.003 * d + y = 1.018 * d
y = .015d or .05 * .3 *d

If I made a mistake in the logic let me know, but I do not see any flaw.

Pinski · 07-15-2008, 05:05 PM

If I do 3k DPS with 30% Crit, and go to 35% Crit with changing nothing else, I will go from 2730 DPS with 0% Crit to 3016.65 DPS. That being here's how to calculate it:

x=current dps
c=current crit
d=new crit

Base DPS=x(1-(c*0.3))
New DPS=Base DPS * d * 0.3
x*(1-(c*0.3))*d*0.3+x*(1-(c*0.3))
0.3(x d) - 0.09(x c d) + x - 0.3(x c)
x(0.3 d - 0.09 c d - 0.3 c) + x

Therefore, your change in DPS is "x(0.3 d - 0.09 c d - 0.3 c)"

With some changing of variables, this is what you have:

x + y = (1 + (d * .3)) * base
(1 + (c * .3)) * base + y = (1 + (d * .3)) * base
1+0.3 c * base + y = 0.3 * d * base
y = 0.3(d-c)*base

Which isn't true as I've just shown above.

Bhow · 07-15-2008, 07:16 PM

I concede. I bow down before you sensei. That is why you dont do math at work

Bhow · 07-16-2008, 02:19 PM

Ok, again, feel free to correct me if I'm incorrect, but something is still bothering me about this.

Your claim:
Base DPS=x(1-(c*0.3))

This, to me, is incorrect.
If EXPANDED:
Base DPS = Current dps - (c*.3)*Current DPS

This is not the case. The Crit chance is applied to your Base DPS.

So, IMHO, it should be x = (1 + (.3 * c)) * Base DPS
Which EXPANDED: x = Base DPS + (.3 * c) * Base DPS

My claim in my initial post is in fact wrong. I was applying the change in crit to current dps instead of base dps, however, I believe that the math in my later post was correct.

I apologize in advance if I'm being stupid.
If you prefer, I can be reached via AIM.

Pinski · 07-16-2008, 02:54 PM

First, it's if expanded, not factored.

Second. It's wrong, yes. It should be
Base DPS = Current DPS/(1+0.3 c)
Since Current DPS = Base DPS(1+0.3 c)

My brain farted, but you need to stop saying factoring, you are expanding. Factoring is going from your 2nd to 1st line.

Well this means that given:
c=old crit
d=new crit
e=diff in crit
e=d-c
e+c=d
c=d-e
Curr=Base(1+0.3 c)
Base=Curr/(1+0.3 c)
New=Base(1+0.3 d)

You get:
New=Base(1+0.3 (e+c))
New=Curr+Base(0.3e)

Our netgain is Base(0.3e). Which is what you said, meh. Your approach to the problem doesn't use enough variables so it got confusing with all the actual values.

Use variables, less actual values if they can change. Not to mention, learn the difference between expanding and factoring :P

destriel · 07-16-2008, 02:59 PM

pinski for the president of math!

also, newsig > old song lyrics...