Aemon Algiz
Member
City of Heroes and Villains as we all know has a rather intricate mathematical structure behind its comic book appearance. Recharge rates, endurance recovery, endurance reduction, regeneration rate, and a multitude of other things. In this "guide" I would like to discuss the various formulas, and provide a simple explanation as to how they function in the game. I will focus alot of time on the more important equations to PvP'ers such as: accuracy, recharge rate, regen rate, recovery rate, endurance reduction, and the new Defience. I will spend some time on as many of the other known equations as I can.
<font size=4>Index
</font>
I. Recharge and Endurance Recovery
a. Endurance Reduction
b. Recharge Reduction
II. Chance to Hit (Also called, Accuracy)
a. Tohit Buff
b. Accuracy Modification
c. Defense
1. How Defense is hurt in PvP
2. How to fix Defense in PvP (Based on Arcanaville's theory)
d. Tohit Debuff
III. Regeneration Rate
a. Equation and Example
b. Application
1. Blaster
2. Controller
3. Defender
4. Scrapper
5. Tanker
6 Peacebringer
7. Warshade
8. Brute
9. Corruptor
10. Dominator
11. Mastermind
12. Stalker
IV. Recovery Rate
a. Base Endurance (100%)
b. Modified Endurance (Over 100%)
V. Mezmerization Duration
VI. Defience
a. Before
b. After
VII. Fury
a. Versus Minions
b. Versus Liuteniants
c. Versus Bosses
d. Versus Elite Bosses
e. Versus Heroes and Archvillains
VIII. Criticals (Scrappers)
IX. Domination
a. Basics
b. Permanent Domination
X. Travel Power Speed and Distance
a. Super Speed
b. Super Jump
c. Teleport
d. Fly
<font size=4>I. Recharge and Endurance Reduction</font>
Lets start with the basic and mostly easy endurance and recharge reduction. The equation for both of them looks like this:
(Base recharge rate)/(1+.(Enhancement value))
(Base endurance use)/(1+.(Enhancement value))
In mathematics these are considered asymptotes, as they approach zero across any value of x (except for infinity where it actually does reach zero). Since they function in this manner there will be a steep decline in benefit from endurance reduction beyond some point. Lets take a look at some examples, and for these I will use Knockout Blow. Knockout Blow has a base endurance usage of 18.5 endurance and a base recharge of 25 seconds. For both examples I will use even level SO values.
A. Endurance Reduction
First the endurance reduction.
(18.5)/(1.33333~) = 13.875 endurance
(18.5)/(1.66666~) = 11.100 endurance
(18.5)/(1.94933~) = 9.490 endurance
As you can see, from the first SO used, we saw a reduction in endurance usage equal to 4.625, from the second a further reduction of 2.275, and from the third another reduction of 1.61. As you can see, after each SO was slotted there a drastic decrease in benefit. This is something you should take into consideration when deciding whether or not to increase your endurance reduction over another modification since beyond a point you get a nominal bonus.
B. Recharge Reduction
Now, using Knockout Blow once again to calculate recharge reduction we will observe how three recharge reduction SO's affect the value.
25/(1.33333~) = 18.750 recharge
25/(1.66666~) = 15.000 recharge
25/(1.94933~) = 12.825 recharge
As you can see the reduction in recharge time from the first enhancement is equal to 6.25, from the second 3.75, and from the third 2.175. Now I realize alot of people, including myself, don't care about the drop in benefit and will continue to do increase it with set bonuses until we have perma-hasten, an eight second KO Blow, or whatever else we feel we need. It is just important that other players not as interested in minimizing recharge rates realize this fact.
<font size=4>II. Chance to Hit (Also called, Accuracy)
</font>
Chance to Hit is actually one of the coolest mathematical properties in City of Heroes/Villains, due to the fact that there is actually five major properties that go into calculating a characters chance to hit. Tohit, Tohit Buff, Tohit Debuff, Defense, and Accuracy. The base equation for Chance To Hit looks like this:
((Base Tohit) + (Tohit Buff) - (Defense) - (Tohit Debuff)) * (1 + .(Accuracy modification))
As is made clear by the equation, Tohit is the base value for calculating Chace to Hit where any Accuracy Modification made to power is a multiplier. To express this I will once again use Knockout Blow as an example, although I will also use Haymaker as a comparison. Knockblow has a base Tohit value of 75% and Haymaker has a base Tohit of 75%. I will use various examples of how Chance to Hit is modified across the board. The reason I want to include Knockout Blow in these calculations is due to the fact that it's base Chance to Hit is different than the other powers in the set.
A. Tohit Buff
The first example will include Knockout Blow and Haymaker modified with an unenhanced Rage, which provides a +20% Tohit Buff to all powers. There will be no Defense or Tohit Debuff accounted for in this calculation nor will there be an accuracy modification.
Now be forwarned, Knockout Blow according to Mids has a base Chance to Hit of 90%. This is not because it has a base Tohit of 90%, but rather there is a hidden Accuracy Modification on the power. To discover this hidden modification we simply take 90%/75% and find an Accuracy Modification of 1.2.
Knockout Blow:
(75% + 20% - 0% - 0%) * (1.2) = 114% Chance to Hit
Haymaker:
(75% + 20% - 0% - 0%) * (1) = 95% Chance to Hit
According to how this equation works adding a modifier directly to Tohit allows for a great increase in Chance to Hit, although this alone is a powerful increase in a characters ability to effectively connect most shots Accuracy Modifications must also be taken into consideration.
B. Accuracy Modification
For consistency I will once again use Knockout Blow and Haymaker as the powers that will have Accuracy Modifiers placed into them. For simplicity even level SO's will be used for comparisons and no Tohit Buffs, Tohit Debuffs, or Defense will be applied to equation.
Knockout Blow:
(75% + 0% - 0% - 0%) * (1.2 + .33333~) = 115.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.2 + .66666~) = 140.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.2 + .94933~) = 161.2% Chance to Hit
Haymaker:
(75% + 0% - 0% - 0%) * (1.0 + .33333~) = 100.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.0 + .66666~) = 125.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.0 + .94933~) = 146.2% Chance to Hit
While SO's provide a good increase in Chance to Hit up to Three SO's, you can get substaintally more of a boost from using Accuracy Modification IO's and Set Bonuses in conjunction with one another. This is because set bonuses ignore Enhancement Diversification and it is relatively easy to achieve a Accuracy Modification of 3.0 and above.
C. Defense
Defense and Tohit Debuff work very similarly, but they will be discussed seperately due to the issue of Defense in PvP and how it is hindered. Defense is a value stated in percentages in Mids' Hero Designer and the various other "hero creators" due to how it directly affects Tohit.
Defense actually comes in two flavors: positional and conditional. The positional Defense values come from AoE Defense, Melee Defense, and Ranged Defense. The conditional Defense values comes from Smashing Defense, Lethal Defense, Energy Defense, Negative Defense, Fire Defense, Cold Defense, and Psionic Defense. Now, when the game engine considers which Defense value to use when calculating Chance to Hit it will always chose the greater between conditional and positional Defense. For example, if a Ninjitsu Stalker has 37% Smashing Defense and 75% Melee Defense and he is fighting a Super Strength Brute. If the Brute were to use Knockout Blow, which a Melee and Smashing attack, the game engine will automatically use the 75% Melee Defense to calculate the Chance to Hit.
<font size=4>Index
</font>
I. Recharge and Endurance Recovery
a. Endurance Reduction
b. Recharge Reduction
II. Chance to Hit (Also called, Accuracy)
a. Tohit Buff
b. Accuracy Modification
c. Defense
1. How Defense is hurt in PvP
2. How to fix Defense in PvP (Based on Arcanaville's theory)
d. Tohit Debuff
III. Regeneration Rate
a. Equation and Example
b. Application
1. Blaster
2. Controller
3. Defender
4. Scrapper
5. Tanker
6 Peacebringer
7. Warshade
8. Brute
9. Corruptor
10. Dominator
11. Mastermind
12. Stalker
IV. Recovery Rate
a. Base Endurance (100%)
b. Modified Endurance (Over 100%)
V. Mezmerization Duration
VI. Defience
a. Before
b. After
VII. Fury
a. Versus Minions
b. Versus Liuteniants
c. Versus Bosses
d. Versus Elite Bosses
e. Versus Heroes and Archvillains
VIII. Criticals (Scrappers)
IX. Domination
a. Basics
b. Permanent Domination
X. Travel Power Speed and Distance
a. Super Speed
b. Super Jump
c. Teleport
d. Fly
<font size=4>I. Recharge and Endurance Reduction</font>
Lets start with the basic and mostly easy endurance and recharge reduction. The equation for both of them looks like this:
(Base recharge rate)/(1+.(Enhancement value))
(Base endurance use)/(1+.(Enhancement value))
In mathematics these are considered asymptotes, as they approach zero across any value of x (except for infinity where it actually does reach zero). Since they function in this manner there will be a steep decline in benefit from endurance reduction beyond some point. Lets take a look at some examples, and for these I will use Knockout Blow. Knockout Blow has a base endurance usage of 18.5 endurance and a base recharge of 25 seconds. For both examples I will use even level SO values.
A. Endurance Reduction
First the endurance reduction.
(18.5)/(1.33333~) = 13.875 endurance
(18.5)/(1.66666~) = 11.100 endurance
(18.5)/(1.94933~) = 9.490 endurance
As you can see, from the first SO used, we saw a reduction in endurance usage equal to 4.625, from the second a further reduction of 2.275, and from the third another reduction of 1.61. As you can see, after each SO was slotted there a drastic decrease in benefit. This is something you should take into consideration when deciding whether or not to increase your endurance reduction over another modification since beyond a point you get a nominal bonus.
B. Recharge Reduction
Now, using Knockout Blow once again to calculate recharge reduction we will observe how three recharge reduction SO's affect the value.
25/(1.33333~) = 18.750 recharge
25/(1.66666~) = 15.000 recharge
25/(1.94933~) = 12.825 recharge
As you can see the reduction in recharge time from the first enhancement is equal to 6.25, from the second 3.75, and from the third 2.175. Now I realize alot of people, including myself, don't care about the drop in benefit and will continue to do increase it with set bonuses until we have perma-hasten, an eight second KO Blow, or whatever else we feel we need. It is just important that other players not as interested in minimizing recharge rates realize this fact.
<font size=4>II. Chance to Hit (Also called, Accuracy)
</font>
Chance to Hit is actually one of the coolest mathematical properties in City of Heroes/Villains, due to the fact that there is actually five major properties that go into calculating a characters chance to hit. Tohit, Tohit Buff, Tohit Debuff, Defense, and Accuracy. The base equation for Chance To Hit looks like this:
((Base Tohit) + (Tohit Buff) - (Defense) - (Tohit Debuff)) * (1 + .(Accuracy modification))
As is made clear by the equation, Tohit is the base value for calculating Chace to Hit where any Accuracy Modification made to power is a multiplier. To express this I will once again use Knockout Blow as an example, although I will also use Haymaker as a comparison. Knockblow has a base Tohit value of 75% and Haymaker has a base Tohit of 75%. I will use various examples of how Chance to Hit is modified across the board. The reason I want to include Knockout Blow in these calculations is due to the fact that it's base Chance to Hit is different than the other powers in the set.
A. Tohit Buff
The first example will include Knockout Blow and Haymaker modified with an unenhanced Rage, which provides a +20% Tohit Buff to all powers. There will be no Defense or Tohit Debuff accounted for in this calculation nor will there be an accuracy modification.
Now be forwarned, Knockout Blow according to Mids has a base Chance to Hit of 90%. This is not because it has a base Tohit of 90%, but rather there is a hidden Accuracy Modification on the power. To discover this hidden modification we simply take 90%/75% and find an Accuracy Modification of 1.2.
Knockout Blow:
(75% + 20% - 0% - 0%) * (1.2) = 114% Chance to Hit
Haymaker:
(75% + 20% - 0% - 0%) * (1) = 95% Chance to Hit
According to how this equation works adding a modifier directly to Tohit allows for a great increase in Chance to Hit, although this alone is a powerful increase in a characters ability to effectively connect most shots Accuracy Modifications must also be taken into consideration.
B. Accuracy Modification
For consistency I will once again use Knockout Blow and Haymaker as the powers that will have Accuracy Modifiers placed into them. For simplicity even level SO's will be used for comparisons and no Tohit Buffs, Tohit Debuffs, or Defense will be applied to equation.
Knockout Blow:
(75% + 0% - 0% - 0%) * (1.2 + .33333~) = 115.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.2 + .66666~) = 140.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.2 + .94933~) = 161.2% Chance to Hit
Haymaker:
(75% + 0% - 0% - 0%) * (1.0 + .33333~) = 100.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.0 + .66666~) = 125.0% Chance to Hit
(75% + 0% - 0% - 0%) * (1.0 + .94933~) = 146.2% Chance to Hit
While SO's provide a good increase in Chance to Hit up to Three SO's, you can get substaintally more of a boost from using Accuracy Modification IO's and Set Bonuses in conjunction with one another. This is because set bonuses ignore Enhancement Diversification and it is relatively easy to achieve a Accuracy Modification of 3.0 and above.
C. Defense
Defense and Tohit Debuff work very similarly, but they will be discussed seperately due to the issue of Defense in PvP and how it is hindered. Defense is a value stated in percentages in Mids' Hero Designer and the various other "hero creators" due to how it directly affects Tohit.
Defense actually comes in two flavors: positional and conditional. The positional Defense values come from AoE Defense, Melee Defense, and Ranged Defense. The conditional Defense values comes from Smashing Defense, Lethal Defense, Energy Defense, Negative Defense, Fire Defense, Cold Defense, and Psionic Defense. Now, when the game engine considers which Defense value to use when calculating Chance to Hit it will always chose the greater between conditional and positional Defense. For example, if a Ninjitsu Stalker has 37% Smashing Defense and 75% Melee Defense and he is fighting a Super Strength Brute. If the Brute were to use Knockout Blow, which a Melee and Smashing attack, the game engine will automatically use the 75% Melee Defense to calculate the Chance to Hit.
