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WARCRAFT III MATHS FAQ BY DAVZZ
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Copyright (c) 2004 Davzz. (Contact info at bottom of Faq)

Do not sell this Faq or edit it by removing my name from it.
Do not post it on any other website without my permission. 
Do not incorporate any part of this FAQ into your own guide
without obtaining my express written permission.

Warcraft III (c) and related materials owned by Blizzard
Entertainment.

=================
TABLE OF CONTENTS
=================

 1.  History
 
 2.  Introduction

 3.  Teh Formulas!!!

 4.  Modders Section

 5.  Misc

 6.  Contact info

==========
1. HISTORY
==========

07-01-06
Version 1.2
(The only real update here is really a global e-mail address 
change, if you've sent an e-mail to the old address between this 
update and the last update, it probably went poof)
(I would also like to note that at this point of time, a lot of
information in this FAQ has been made obselote by recent patches
and I'm afraid I lost my love of this game to correct them.
You may still find the information useful however)

07-13-2004
Version 1.1
(Some 1.16 patch changes and some questions answered,
small update really)

02-22-2004

Version 1.0
(FAQ done. Released to GameFAQs)

===============
2. INTRODUCTION
===============

"If a unit has 50% evasion, then it has 50% more hp!!!"

"...So a unit with 100% evasion... it has 100% more hp?"

Don't laugh, I actually seen this happen why too many 
times, which is what this FAQ is for. This FAQ is made to 
store all the formulas of Warcraft III that I know.

This is probably of more use to map modders, who need to 
find out whether a unit with 100 hp and 5 armor is better 
than a unit with 130hp with 0 armor.

Or people who like to theorycraft on how Abominations 
beat other tier 3 melee, I'm looking at you, troll guy.

=================
3.TEH FORMULAS!!!
=================

------------------------
Calculating Effective HP
------------------------

Each point of armor gives you 0.06% more EHP.

Therefore...

eHP = bHP * (100/(100-ev%)) * (1+(arm*0.06))

bHP = Base HP
ev% = Evasion percentage (100% means you can't be hit, duh.)
arm = Armor of unit.

E.g: A Demon Hunter with at level 1 with lvl 1 Evasion has
575 bHP, 5 armor and 10% evasion, therefore he has...

575 * (100/90) * (1+(0.3))
= 830 eHP

Note that this only applies to damage taken from normal
attacks. The poor DH will still drop like a fly when hit
with the UD nuke. 

This also means that high armor, low HP units benefit more 
from Periapts of Health while low armor, high HP units
benefits more from Rings of Protection.

------------------------------------------
Average Damage Increase Of Critical Strike
------------------------------------------

Avg Dam = Crit% * (Crit Multipler - 1)

Meaning a level 2 critical strike will increase the average
damage of the unit by about 30%... not exactly a very good
skill unless you have lots of claws of attack, is it?

-----------------
Damage per Second
-----------------

Dps = ((Max damage + Min Damage)/2)/ Cooldown

Feel free to substitute Max Dam + Min Dam for Avg Damage,
if it isn't obvious already.

This one's too easy I'm not gonna give any examples.

----------------------
Effective Attack speed
----------------------

I have no idea how multiple attack speed buffs stack, but
assuming there's only 1 buff.

EAsp = base speed * (100/(100+(Multiplier)+(Agility Bonus))

Agility Bonus = 2% increase per point of agility.

E.g: A level 1 blademaster (24 agility) with Bloodlust on him
will have a cooldown of...

1.77 * (100/(100+40+48))
= 0.94 (2 decimal places :p)

UPDATE: Multiple attack speed buffs, oddly enough, stack
themselves linearly instead of exponentially.

E.g A level 1 blademaster (24 agility) with Bloodlust, Unholy 
Frenzy and Lvl 3 Endurance Aura on him will have a cooldown of...

1.77 * (100/(100+(40+75+15)+48))
= 0.64 (2 dp yet again)

If the implications aren't obvious, this means that after a
few attack speed upgrades, you might want to consider boosting
something else.

-------------------------------------------
Bounce Attack (Huntress or Chain Lightning)
-------------------------------------------

The formula for finding the damage at a specific amount of
hits is

BaseDmg * ((DamReduc/100)^(Bounce No.))

Base Dmg = Base Damage
DamReduc = Amount of damage left after reduction.
Bounce No. = The no. of times projectile has bounced.

E.g: The 2nd bounce of a huntress will deal...

17 * ((50/100)^2)
= 4 damage

...which is why no one bothers upgrading the bounce upgrade

...while the 8th hit of level 3 Chain Lightning will deal

180 * ((85/100)^7)
= 57 damage

...which barely scratches a wisp for a 120 mana spell. :p

==================
4. MODDERS SECTION
==================

-----------
Damage Dice
-----------

Warcraft III, having RPG aspect, gives a nod to the old Pen
and Paper RPGs by using "dice" to determine random values.
2d6 for example, means "throw 2 6-sided dice and take 
the result." All you need to know though is

Min Damage = Number of dice.
Max Damage = No. of dice * Number of sides
Average Damage = (Min Damage + Max Damage) / 2

For mercenary units, feel free to set dice to something dumb 
like 18d3, it probably won't matter. However for racial units 
however, damage upgrades are determined by adding an extra
dice, so keep the numbers reasonable unless you want the
upgrades to be extra weak or strong.

--------------------
The Making of a Hero
--------------------

If you plan to change strength to give 666 hp per point,
agility to give 2 armor per point and intelligence to 
decrease your mana by 15 each, don't read this.

On the other hand, if you want to make a hero that pretty
much confirms to melee map standards, read on.

~~~~~~~~
The Base
~~~~~~~~

First, let's start with speed,there are 3 speeds 
most heroes have.

Medium: 270 speed (e.g anyone who looks like a buff tank.)
Above Average: 300 (e.g Blademaster and BloodMage.)
Fast: 320 (e.g Way too many heroes.)

Update: Blademaster now has 320 speed.

Note that because of the huge number of fast heroes, medium
speed heroes might actually seem pretty slow, it's just an
"illusion" though.

Depending on your primary stat, the hero will get different
damage dice.

Strength: 2d6
Agility: 2d12
Ranged Hero: 2d4

This is added to your primary stat, so the dice doesn't
really make much of a difference except for agility heroes,
which is the only stat type where the primary stat actually 
starts at a pretty crappy amount instead of the highest.

Cooldown usually doesn't matter, since who cares how much
damage you do when you can deal 330 damage in an area with
flame strike? Heroes with passives and arrow type spells
might need to start with a decent or even low amount though.

Update: Bloodmage now sucks giant goat balls because of cap,
so maybe you can replace this with "Frost Nova" instead.

Each hero has a base armor of 0 to 2, usually 2 for strength
heroes and 0 for the agility, so their armor points won't be
TOO far apart.

~~~~~
Stats
~~~~~

Each hero has about 50 to 60 stat points. Note that the
base of each stat is 5 points. What that means is that
5 is taken as 0, any other number below 5 will be taken
as a negative amount. Each hero also gains 6 stat points
per level (exception: Lich).

As long as you don't try to severely make a 1 sided hero,
your stats shouldn't make much for a difference.

On the other hand, if you make a agility hero with 40 
agility and 5 strength, he's going to die to nukes so fast
it's not funny while overpowering everything else.

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
All stats are not created equal
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Anyone who has played a hero arena knows of the dreaded
999 (or worse) agility blademaster who dominates the map
and makes it unfun, which is why recent versions have
made agility tomes much more expensive than the other types.

When stats get out of hand, intelligence is unfortunately
the worse, since it offers you no increase in your 
survival rate and you extra points of mana doesn't help as 
much, as you can already cast your spells without wasting 
mana at all!

Because of Strength's linear and Agility's exponential
growth, Strength beats Agility early game while Agility
gets out of hand late game. Also, strength protects against
magic while agility does not, such even agility heroes will
need a good amount to prevent getting murdered.

Oddly enough, if stats DON'T get out of hand, the opposite
is true. In melee, intelligence heroes are highly prized
as they have a huge pool of mana to cast their spells while
agility heroes such as the blademaster are regarded as a
joke or FFA only heroes, where they can be boosted up to
high levels of insanity with items.

~~~~~~
Skills
~~~~~~

If your skill does more instant damage than storm bolt, is 
more powerful at immobilizing units than entangling roots 
or does more AOE damage than flame strike, you're probably
doing something wrong.

Normal spells should NOT have extremely high cooldown or
mana cost to make up for overpowerness, that's an ultimate's
job. If you can't cast a spell at level 1 about 2 or 3 times, 
you might want to rethink.

Some spells are never a good idea, such as Charming heroes.

Fit the skill to the primary stats. Strength heroes usually
need extremely powerful spells to make up for their crappy
base stats and low mana pool, while agility heroes should
get passives that make use of their good damage dice and
other base stats.

On the other hand, never give the blademaster bash, unless
you like to see perma-stunned units.

If you want to know Blizzard formula for determining hero
skills, it usually goes like this...

Warrior hero: DD spell, DD spell, Passive, Ultimate.
Intelligence hero: DD spell, Summon, Passive, Ultimate.
Agility Hero: Singl-target spell, Ultility, Passive, Ultimate.

Oddly enough, the PotM and Crypt Lord has the Intelligence
hero spell set while the Farseer doesn't have a passive at all!
Dark Ranger and Naga Sea Witch are an odditities too.

=======
5. MISC
=======

---
Q&A
---

Q. How does Attack speed stack?

A. This is answered in it's own section, but I'll just repeat
it for the lazy ones. It stacks linearly instead of exponentially.

For an example, let's take an imaginary unit with 1 sec cooldown
and two spells which increase AS by 100% each.

CORRECT: Unit gets 0.33 cooldown (1 * 100/(100+200))
INCORRECT: Unit gets 0.25 cooldown (1*100/(100+100)*100/(200))

Simplified: IAS gets less valuable as you get more of it.

Q. Does Evasion stack?

A. The folks at the Defense of the Ancients board have proved
that no, Evasion does not stack. Not even the 100 x 15% x 15%
x 15% x 15% thing. Item and Ability don't stack, neither does
item and another item. It doesn't stack, period.

If you have the Evasion skill, it will be used, otherwise the
item will be used.

Q. Does Critical Strike stack?

A. You would expect it to be no, but yes, it does stack. I
guess it's because there isn't any item in melee maps that
give you the critical strike ability (Searing Blade is one
of the items that give crit to you in custom ones.)

It is even possible for 2 critical strikes to be activated
at once. I am still working out the formulas for that.

===============
6. CONTACT INFO
===============

You can e-mail me at Davzz666@gmail.com if you have any need to
contact me. Make sure your e-mail subject is something like 
"[Warcraft III] FAQ" or I'll probably delete it immediately 
because of the massive spam I recieve.

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FAQ END
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Faq copyright (c) Davzz 2004. Warcraft III (c) by Blizzard
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