Pierce, there is no arguing about that it's valuable. But, how often is it really utilized in the game? With a really fast attack speed, does it really matter if you have a 30% chance or a 95% chance? How often do the monsters line up correctly so it can be used to it's full potential?
I'll be doing the calculations agian. And this time, I'm sure they are correct - just had an exam of statistics. All who don't believe me, stick it where the sun don't shine,
or try to convince me.
Lets assume at all times, thier will be 6 monsters in a line so the maximum number of pierces is 5. This seems like a nice number, some claim that this really is the maximum number of pierces and don't forget, this is just a number, just take an other number if you believe 5 is to much or to little.
Lets start with
30% pierce. Your chance-tree will look like this.
Code:
|--70%--1 hit
|
|--30%--pierce
|--70%--2 hits
|
|--30%--pierce 2
|--70%--3 hits
|
|--30%--pierce
.......
Note, you need an other 2 branches to get to the total number of 5 pierces.
Lets sum the chances at the end of the branches and see that it will be 1.
P[1 hit]+P[2 hits]+P[3]+P[4]+P[5]+P[6*]
=0.7+0.3*0.7+0.3²*0.7+0.3³*0.7+0.3²*0.3²*0.7+0.3²*0.3³
=1
*: if you pierce 5 monsters, you will hit the first monsters, the first monster of the first pierce, the first monsters after the second pierce...
Total number of monsters hit = 6
The average is.
P[1 hit]*1+P[2 hits]*2+P[3]*3+P[4]*4+P[5]*5+P[6]*6
=...
=1.42753 hits.
This means that if you were to do 100 damage without any pierce, you will be doing 142 damage with 30% pierce.
Nice you say?
95% pierce
we can do the same calculations and reasoning as we have done above. Lets have a look at the average.
5.298 hits.
This means that if you were to do 100 damage, you'd be doing 529 damage with 95% pierce.
So don't come and say pierce isn't worth it in general play. Even with only 3 monsters to pierce, the extra damage is huge. The only time when pierce isn't usefull is when you kill the monsters with a single hit. Though that ain't often the case, now is it?
note that extra fast throw speed doesn't chance much. You'll still have the same extra damage as you would have with a slow attack speed.
No ranged zon worth their salt would play without 8-9 points (65-69%) into pierce.
