Post by DoroFuyutsuki on Jun 15, 2008 20:13:33 GMT -5
As the original thread got so full of idiots posting into it asking questions that were answered in the post, I have deleted it and re-instituted it here.
Note that asking a question already answered in the body of the original post will result in an automatic ban and no lesser punishment. This is non-negotiable.
Common Misconceptions
Strength
Every point of strength gives you 20 HP and 0.25 hp (Credit to Dako) per second regeneration. If you are a strength hero, this will increase your damage
Agility
Every one point in agility gives you .2 armor, 1% IAS, and if you are an agility hero, more damage
Intelligence
Every one point in INT will give you an extra 15 mana and a .01 MP per second (Credit to Good4UtoMunchOn and Crojan) mana regen bonus.
Critical Strike
Critial Strike as an innate skill STACKS with critical strike granted from items. On top of this, Critical Strike from multiple items stacks up. The chance is what stacks though... not the multiplier. Crit multipliers never stack despite the red numbers.
When it comes to doing the math on critical strikes and how much bonus damage you receive from them the math is very easy for the first bonus, but for each bonus beyond the first, it becomes fiendishly difficult.
1 Bonus: (.75 X Damage) + (.25 X (Damage X Multiplier)) = Average Damage (Here, it is (assuming a 2X multiplier) 125% of your normal damage)
Before I go on, understand that calculating multiple bonuses is a pain in the rear like you wouldn't understand.
2 Bonuses:
If you have two multipliers, one at 25%2X and the other at 15%3X then you need to do some statistics math to come to the right number...
The question you have is this: "What percent of my attacks will have both of my critical strikes take effect?" Well, that's relatively easy...
(25/100)*(15/100) = 3.75%
On the cases where the 2X multiplier does not happen, you have a 75% chance for a 15% multiplier which reduces the 15% down to 11.25
21.25% of attacks will strike for 2X Damage
15% of attacks will strike for 3X damage
63.75% of attacks will strike for 1X damage
Final Damage = 0.6375x + 0.425x + 0.45x = 151.25% damage (Credit goes to htb for correcting my original numbers in this example)
If you were to do a calculation involving 3 bonuses it would look something like this:
Instance A: Whatever your percentage of not actually critting would be (You don't know this number until you have the additive % from B-H)
Instance B: Crit 1 only (but not 2 or 3)
Instance C: Crit 2 only (but not 1 or 3)
Instance D: Crit 3 only (but not 1 or 2)
Instance E: Crit 1 + Crit 2 (but not 3)
Instance F: Crit 1 + Crit 3 (but not 2)
Instance G: Crit 2 + Crit 3 (but not 1)
Instance H: Crit 1 + Crit 2 + Crit 3
And the math would look like this:
(Instance A% X Damage) + (Instance B% X Damage X B Multiplier) + (Instance C% X Damage X C Multiplier) + (Instance D% X Damage X D Multiplier) + (Instance E% X Damage X Multiplier) + ... + (Instance H% X Damage X H Multiplier)
Remember though that C and E use multiplier two and D, F, G, and H use multiplier three. What you notice here is that the first multiplier ends up being almost completely wasted as it is only calculated in instance B. In effect, what you notice is a virtual change in the distribution of your critical bonuses and the change is only negative because of two factors: exclusive statistics calculations and subtractive statistics.
Exclusive Statistic the largest multiplier overwrites the other multiplier(s) and this means that the rate of occurrence for the overwritten multiplier is essentially wasted as it was consumed, but not applied.
Example of a Subtractive Statistic: You have a 50% chance of it raining, a 25% chance of receiving $10 back from your friend, and a 10% chance of seeing a polka-dotted car. The chance that it rains and your friend pays you back but you don't see a polka-dotted car is calculated from the 10% of statistics which do not include you seeing the car. To do this, you have to use a ratio to find the new % chance of each instance (50/100 divided by (X/90) = new%) and then multiply those numbers together.
Evasion
Evasion from two different items / skills, or a combination of item / skill does not stack in any way. The higher percentage will take precedence.
Block
Blocking stacks with evasion and dodge.
Block is not an effect that is shown like "MISS" is in the game.
Also, it is a diminishing stack (it CAN stack with itself)
.75 DODGE * .75 MISS * .75* BLOCK = .42 attacks will actually do damage to you.
This means that if you possess a 25% dodge, block, and chance for enemies to miss, then you will only be hit (and take full damage) from 42% of incoming enemy attacks. This number is derived from the probability of one event checked against three flags (your block, dodge, and miss%)
Miss Chance[/size]
Miss chance is an effect that gives your attacker a chance to miss. Stacks with evasion. Miss chances on target stack in a multiplicative form. Note that any unit attempting to deal an attack to an uphill opponent has an inherent 15% to miss.
Movespeed
The maximum movespeed is 522 hex per second. This is achieveable in TBR with Boots of Hermes and a speed scroll.
Lifesteal
The bonuses from Blade or Ares / Blade of Command (pick one), Night Regalia, and Burning Hand of the War God all stack.
Base Attack Speed
Classes:
Assassin, Warlord => 1.6 BAS
Ranger => 1.8 BAS
Barbarian, Spartan Warrior, Guardian of Nature, Khaos Champion => 2.0 BAS
Cleric, Druid, Warlock, Mage, Temple Guardian => 2.25 BAS (Credit to EyeOfTruth)
Attack Speed Bonuses
The maximum attack speed is 400% of your normal attack. The game does not care how you get to 400. Every point of agility counts as 1% IAS.
Attack Speed Calculation
BAT = Base Attack Speed; IAS = Increased Attack Speed
Attack speed formula is BAT/(1+IAS*.01)
It's IAS*.01 if you look at IAS as being 1-400 obviously. You could say it goes from 0.00 by .01 to 4.00 and it would just be 1+IAS. (Credit to sdakfjlsk124)
Using the assassin's base attack speed of 1.6 as an example:
1.6 / (1+(400*.01)) = 1.6 / 5 = 1 attack every .32 seconds or roughly 3 attacks per second.
Spell Reduction
All heros in WC3 have an innate 25% damage reduction that can not be removed by spells... they will always have this reduction no matter how low their armor gets.
This reduction stacks ONLY ONCE and that is with a SINGLE ITEM. This item is selected based on the percentage bonus to your reduction that it grants you.
Divine Armor[/size]
Divine armor takes only 10% dmg from all types of atacks (Credit to Dako). After this flat reduction of 90% the reduction from the armor value is also applied.
Example:
I hit for 6000 damage
Divine Armor takes places and reduces it to 600 damage
Armor of 56% reduction takes place and reduces this damage to ~ 280 damage
Bash[/size]
Bash is an interesting calculation series in that the chances stack until one of them activates. If you have two different bash chances, each at 15%, then you actually have two different %'s to bash someone and stun them:
A) Chance that the enemy is bashed on the first strike: 15%
B) Chance the enemy is bashed on second strike (cumulative): 27.75% (I think this is the number that everyone is asking about as it means that 27.75% of the time, you will receive a bash)
If I missed anything, or a question has not been answered, please post it in a reply here.[/size][/color]
Note that asking a question already answered in the body of the original post will result in an automatic ban and no lesser punishment. This is non-negotiable.
Common Misconceptions
Strength
Every point of strength gives you 20 HP and 0.25 hp (Credit to Dako) per second regeneration. If you are a strength hero, this will increase your damage
Agility
Every one point in agility gives you .2 armor, 1% IAS, and if you are an agility hero, more damage
Intelligence
Every one point in INT will give you an extra 15 mana and a .01 MP per second (Credit to Good4UtoMunchOn and Crojan) mana regen bonus.
Critical Strike
Critial Strike as an innate skill STACKS with critical strike granted from items. On top of this, Critical Strike from multiple items stacks up. The chance is what stacks though... not the multiplier. Crit multipliers never stack despite the red numbers.
When it comes to doing the math on critical strikes and how much bonus damage you receive from them the math is very easy for the first bonus, but for each bonus beyond the first, it becomes fiendishly difficult.
1 Bonus: (.75 X Damage) + (.25 X (Damage X Multiplier)) = Average Damage (Here, it is (assuming a 2X multiplier) 125% of your normal damage)
Before I go on, understand that calculating multiple bonuses is a pain in the rear like you wouldn't understand.
2 Bonuses:
If you have two multipliers, one at 25%2X and the other at 15%3X then you need to do some statistics math to come to the right number...
The question you have is this: "What percent of my attacks will have both of my critical strikes take effect?" Well, that's relatively easy...
(25/100)*(15/100) = 3.75%
On the cases where the 2X multiplier does not happen, you have a 75% chance for a 15% multiplier which reduces the 15% down to 11.25
21.25% of attacks will strike for 2X Damage
15% of attacks will strike for 3X damage
63.75% of attacks will strike for 1X damage
Final Damage = 0.6375x + 0.425x + 0.45x = 151.25% damage (Credit goes to htb for correcting my original numbers in this example)
If you were to do a calculation involving 3 bonuses it would look something like this:
Instance A: Whatever your percentage of not actually critting would be (You don't know this number until you have the additive % from B-H)
Instance B: Crit 1 only (but not 2 or 3)
Instance C: Crit 2 only (but not 1 or 3)
Instance D: Crit 3 only (but not 1 or 2)
Instance E: Crit 1 + Crit 2 (but not 3)
Instance F: Crit 1 + Crit 3 (but not 2)
Instance G: Crit 2 + Crit 3 (but not 1)
Instance H: Crit 1 + Crit 2 + Crit 3
And the math would look like this:
(Instance A% X Damage) + (Instance B% X Damage X B Multiplier) + (Instance C% X Damage X C Multiplier) + (Instance D% X Damage X D Multiplier) + (Instance E% X Damage X Multiplier) + ... + (Instance H% X Damage X H Multiplier)
Remember though that C and E use multiplier two and D, F, G, and H use multiplier three. What you notice here is that the first multiplier ends up being almost completely wasted as it is only calculated in instance B. In effect, what you notice is a virtual change in the distribution of your critical bonuses and the change is only negative because of two factors: exclusive statistics calculations and subtractive statistics.
Exclusive Statistic the largest multiplier overwrites the other multiplier(s) and this means that the rate of occurrence for the overwritten multiplier is essentially wasted as it was consumed, but not applied.
Example of a Subtractive Statistic: You have a 50% chance of it raining, a 25% chance of receiving $10 back from your friend, and a 10% chance of seeing a polka-dotted car. The chance that it rains and your friend pays you back but you don't see a polka-dotted car is calculated from the 10% of statistics which do not include you seeing the car. To do this, you have to use a ratio to find the new % chance of each instance (50/100 divided by (X/90) = new%) and then multiply those numbers together.
Evasion
Evasion from two different items / skills, or a combination of item / skill does not stack in any way. The higher percentage will take precedence.
Block
Blocking stacks with evasion and dodge.
Block is not an effect that is shown like "MISS" is in the game.
Also, it is a diminishing stack (it CAN stack with itself)
.75 DODGE * .75 MISS * .75* BLOCK = .42 attacks will actually do damage to you.
This means that if you possess a 25% dodge, block, and chance for enemies to miss, then you will only be hit (and take full damage) from 42% of incoming enemy attacks. This number is derived from the probability of one event checked against three flags (your block, dodge, and miss%)
Miss Chance[/size]
Miss chance is an effect that gives your attacker a chance to miss. Stacks with evasion. Miss chances on target stack in a multiplicative form. Note that any unit attempting to deal an attack to an uphill opponent has an inherent 15% to miss.
Movespeed
The maximum movespeed is 522 hex per second. This is achieveable in TBR with Boots of Hermes and a speed scroll.
Lifesteal
The bonuses from Blade or Ares / Blade of Command (pick one), Night Regalia, and Burning Hand of the War God all stack.
Base Attack Speed
Classes:
Assassin, Warlord => 1.6 BAS
Ranger => 1.8 BAS
Barbarian, Spartan Warrior, Guardian of Nature, Khaos Champion => 2.0 BAS
Cleric, Druid, Warlock, Mage, Temple Guardian => 2.25 BAS (Credit to EyeOfTruth)
Attack Speed Bonuses
The maximum attack speed is 400% of your normal attack. The game does not care how you get to 400. Every point of agility counts as 1% IAS.
Attack Speed Calculation
BAT = Base Attack Speed; IAS = Increased Attack Speed
Attack speed formula is BAT/(1+IAS*.01)
It's IAS*.01 if you look at IAS as being 1-400 obviously. You could say it goes from 0.00 by .01 to 4.00 and it would just be 1+IAS. (Credit to sdakfjlsk124)
Using the assassin's base attack speed of 1.6 as an example:
1.6 / (1+(400*.01)) = 1.6 / 5 = 1 attack every .32 seconds or roughly 3 attacks per second.
Spell Reduction
All heros in WC3 have an innate 25% damage reduction that can not be removed by spells... they will always have this reduction no matter how low their armor gets.
This reduction stacks ONLY ONCE and that is with a SINGLE ITEM. This item is selected based on the percentage bonus to your reduction that it grants you.
Divine Armor[/size]
Divine armor takes only 10% dmg from all types of atacks (Credit to Dako). After this flat reduction of 90% the reduction from the armor value is also applied.
Example:
I hit for 6000 damage
Divine Armor takes places and reduces it to 600 damage
Armor of 56% reduction takes place and reduces this damage to ~ 280 damage
Bash[/size]
Bash is an interesting calculation series in that the chances stack until one of them activates. If you have two different bash chances, each at 15%, then you actually have two different %'s to bash someone and stun them:
A) Chance that the enemy is bashed on the first strike: 15%
B) Chance the enemy is bashed on second strike (cumulative): 27.75% (I think this is the number that everyone is asking about as it means that 27.75% of the time, you will receive a bash)
If I missed anything, or a question has not been answered, please post it in a reply here.[/size][/color]
