Mathematics Never Fails — Intepretations of Formulas in CyberChess
Contrary to our common impressions that games are just for fun, mathematics is in essence an inseparable part of various games. There are many in-game values and properties that can be calculated, which will help you better understand the game’s mechanism. This rationale works for CyberChess as well.
During the game in ranked mode these days, have you seen devastating damage figures of the Mage’s [Thunder] skills?
Do you want to know how much higher the Mage’s [Thunder] skill’s damage is than other heroes’ single damage skills?
Here you may find the answer you want, we will only explore the formulas provided by CyberChess Wiki and how to make sensible calculations through simple data analysis. You can do it yourself to solve the confusion about the damage figures in the game.
So, are you ready to do the math now?
The Conversion Of Heroes’ 4-Dimensional Attributes
First of all, let’s talk about the concept of the 4-dimensional attributes. Four-dimensional attributes are the attributes that are converted from the basic attributes, and only the 4-dimensional attributes are shown in the match, which are Melee/Spell attack, HP, P.DEF(Physical.DEF), and M.DEF(Magical.DEF).
Melee Hero ATK = STR*(1+0.05*(Hero Level-1))
Spell Caster ATK = INT*(1+0.05*(Hero Level-1))
HP = 50*COM*(1+0.05*(Hero Level-1)）
P.DEF = MND*(1+0.05*(Hero Level-1))
M.DEF = SPI*(1+0.05*Hero Level-1))
The [0.05 * (Hero Level-1)] part of above conversion formulas, is used to calculate the extent of increase in the 4-dimensional attributes when we upgrade heroes. A simple understanding is that when each hero upgrade 1 level, there will be an additional 5% increase in the 4-dimensional attributes .
These conversion formulas look quite complicated, right?
Then let’s simplify the conversion formulas:
ATK = STR/INT
HP = 10*COM
P.DEF = MND
M.DEF = SPI
For heroes from level 2 to level 9, multiply the converted 4-dimensional attributes by [ 0.05*(Hero Level-1) ].
In other words, the extent to which the 4-dimensional attributes are enhanced is equal to 1+0.05*(Hero Level-1), which I will call Extent of Improvement.
Upgraded 4-dimensional attributes = 4-dimensional*Extent of improvement
For example, check the attributes of he level 1 Knight below.
We can use the basic attributes to convert them to the 4-dimensional attributes:
- Strength = ATK = 85
- Constitution * 10 = HP = 790
- Willpower = P.DEF = 58
- Spirit = M.DEF = 48
Assuming that this knight is upgraded to level 5:
- The extent of upgraded four-dimensional attribute growth (AKA extent of improvement) = 1+0.05*(5–1) = 1.2
- Upgraded ATK = ATK*extent of improvement of Attribute growth = 85*1.2 = 102
- Upgraded HP = HP*extent of improvement of Attribute growth = 790*1.2 = 948 ≈ 950
- Upgraded P.DEF = P.DEF *extent of improvement of Attribute growth = 58*1.2 = 69.6 ≈ 70
- Upgraded M.DEF = M.DEF *extent of improvement of Attribute growth = 48*1.2 = 57.6 ≈ 58
Therefore, the 4-dimensional attributes of this level 5 knight is:
- ATK = 102
- HP= 950
- P.DEF = 70
- M.DEF = 58
It would be much easier to understand the conversion formula in the way above.
How to Determine the Main Hero When Merging
Warrior, Ranger, Knight, and Rouge will base their combat attribute on **STR** while Druid, Mage, and Priest are based on **INT**. To calculate the main hero who will be the main for upgrading into 2 stars or 3 stars.
📝 Total Combat Power = (STR or INT + CON + (0.5 * MND) + (0.5 * SPI) + (0.5 * AGI)) * (1+0.05 * (Hero Level -1))
Heroes with the highest combat attributes in the 3 heroes will be determined as the main hero when upgrading.
To simplify the analysis of the formula, we can conclude that it actually consists of two parts.
The first part is the hero’s basic combat power, which is its combat power in level 1.
The basic combat power = STR or INT + CON + (0.5 * MND) + (0.5 * SPI) + (0.5 * AGI)
The second part is the increase of the hero’s combat power when leveling up, which can also be called as the Extent of Improvement.
The Extent of Improvement for every hero after it upgrade to 1 level higher is 5%.
Therefore, we can simply conclude that the extent of improvement would be 20% if it upgrades from level 1 to level 5.
Lastly, we combine these two parts together and we will get the total combat power of the hero. And needless to say, for level 1 hero, we can use its basic combat power as its total combat power.
We can conclude that,
Total Combat Power = Basic Combat Power*(1+5%*(number of levels upgraded for the hero) )
We will calculate the Total Combat Power of the below Warrior.
Basic Combat Power = 100+73+0.5*49+0.5*38+0.5*52 = 242.5
So the Basic Combat Power for this Warrior is 242.5.
Since it is a level 5 Warrior, the Total Combat Power = 242.5 *（1+5%*（5–1））=291
Isn’t it simple to do the calculation?
We can apply Total Combat Power not only to determining the main hero when merging, we could also use it to filter quality main heroes and materials heroes as well as other potential aspects.
The Calculation Of Damage Dealt by Heroes
Do you want to know how to calculate the damage dealt by the hero? Are you curious about what the theoretical upper limit of the damage that a specific skill could deal? Have you ever wondered how high the damage of Mage’s [Thunder] skill could be, which makes it the most popular skill of recent games.?
I would like to know the answers to above all as well, but before that, we need to be clear of some basic theoretical concepts first.
Normal Damage
Normal damage is damage dealt by general/spell attacks when the hero is not using a skill, and is affected by the hero’s valid attributes, divided into general damage and spell damage, and affected by the target hero’s physical and magic defense.
Skills Damage
Skill damage is based on the hero’s ATK, after the characteristics of the skill impact and damage added to create the damage, generally with the release of skill effects and chanting a spell before attacking, simply put, it takes time to release skills.
Heroic skills can be classified according to their characteristics and effects as follows:
- Single damage skills: [Charge], [Thunder], [Knowing], for skills that deal high damage to a single target.
- Area of effect damage skills:[Whirlwind], [Blade barrier], [Blizzard], [Fiery], [Penetrate], [Bombard], for skills that deals damage to the target and the surrounding area.
- Passive gain skills: [Stick], [Bloodsucking], [Asylum aura], [Meditation], for skills that provide a beneficial effect on the hero himself or his team.
- Control skills: [Stun], [Icebound], [Freezing arrow], for skills that cause stun, freeze, slow down control effects on target heroes.
- Summoning Skills: [Shadow],[Dire wolf], [Grizzly bear], for skills that summoning a doppelganger or partner to assist in battle.
- Functional Skills: [Shield], [Resurgence], [Variant], [Wind armour], for skills that provide special effects on the hero himself or his teammates.
- Healing Skills: [Holy-light], [Recover], [Pray], for skills that provide HP recovery to the hero himself or his teammates.
- Special Skills: [Assassinate], for skills that provide special characteristics to the hero himself.
- Continuous damage skills: [Curse], for skills that deals continuous damage to the target.
Damage Output Per Second
Damage output per second refers to the average damage dealt to the target per second.
In order to compare the skill’s ability to deal damage, we will divide the value of the skill’s damage output by the skill’s cooldown time to calculate the skill’s damage output per second.
Before we begin, in order to exclude the impacts of heroes’ differences, such as differences in hero levels and 4-dimensional attributes, we’ll use a system whiteboard hero as the basic parameter for dealing damage and taking damage.
Damage received = Opponent’s ATK*(a random number between 0.5~1.5 )*100/(Hero’s Defense + 100)
The above is the formula provided by CyberChess Wikipedia, we briefly analyze the formula firstusing the system whiteboard hero’s data as a reference：
Damage received = Damage created
Opponent’s ATK = 30 （ Attacking hero’s melee/spell damage base value）
A random number between 0.5~1.5 = Affects the coefficient of actual damage range of the hero, is a random value
100 = Fixed base value
Hero’s Defense = 30（Physical/magical defense of the hero who suffers damage）
The above formula is for the general melee / spell damage calculation, but our calculations won’t stop here. Let’s do something more advanced:
The Damage received calculation formula can be converted into a skill Damage received formula by first calculating the skill damage from the hero’s attack value and then applying it to the following calculation formula.
Skill Damage received = Opponent’s ATK*skill damage*( a random number between0.5~1.5 )*100/(Hero’s Defense + 100)
Heroic Damage Calculation
First, a simple calculation, let us set the dealing-damage hero’s ATK as 30 and the receiving damage hero’s Defense as 30.
Apply the values to the formula：
Heroic Damage = 30*( a random number between 0.5~1.5 )*100/(30 + 100) = 12~35
The results show that a reasonable range of melee/spell damage for this system whiteboard hero is 12~35.
Skill Damage Calculation
We will use the same system whiteboard heroes. Let us set the damage-dealing hero’s ATK as 30 and the damage-receiving hero’s Defense as 30.
We will choose a skill of which the characteristics is relatively simple, that is, single damage skills as mentioned above. Here, we will use [Charge] skill to do the maths.
Charge
Warrior Exclusive
Deal 300% general attack damage to the target. CD: 8S
Apply the values to the formula：
- [Charge] skill Damage = 30*300%*( a random number between 0.15~1.5)*100/(30+100) = 35~104
We can conclude from the calculation that the reasonable skill damage range of [Charge] skill is 35~104. And it is not hard to calculate that the average value of skill damage of [Charge] is 70.
Calculation of Skill Damage Per Second
The reasonable skill damage range for the [Charge] skill has been calculated earlier to be 35~104.
The CD of [Charge] skill is 8 seconds
- Damage per second of [Charge] skill = 35~104/8 = 4~13
As a result, it can be concluded that the skill damage per second of [Charge] is 4~13. Furthermore, the average skill damage per second of [Charge] is calculated to be 9.
Comparison of Single Damage Skills’ Value
[Thunder] skill is more powerful after the recent update, we all like to use it, we will take [Thunder] skill as the object of numerical comparison. I believe there will be a lot of people interested in its skill damage value comparison.
[Thunder] skill is a single damage skills. Meanwhile, [Charge] and [Knowing] are also single damage skills. We will take the value of these three skills for comparison.
Skill Description:
Charge: Deal 300 % general attack damage to the target. CD: 8S
Thunder: Summon lightning, deal 100 % -600 % spell damage to the target. CD: 5S
Knowing: Deal 200 %-300 % general attack damage to the target. CD: 8S
The calculation method is the same as before for skill damage and skill damage per second. We will use the system whiteboard hero as parameters of the calculation to figure out the value of the 3 skills for comparison.
The process of calculation will not be repeated, I used an Excel sheet to calculate.
The calculation results are as follows:
(Calculation results table note: Since there is also a minimum and maximum value in the damage bonus of the [Thunder] and [Knowing] skills, at this point, we just need to multiply the minimum value by a damage range factor of 0.5 and the maximum value by a damage range factor of 1.5, which does not affect the results.)
From the calculation results it can be seen that：
- The difference between the values of [Charge] and [Knowing] is minimum and the value of [Thunder] stands out.
- In terms of average skill damage, [Thunder]’s skill damage is about 60%-70% higher than the other 2 skills, and the average damage per second is about 140%-180% higher than the other 2 skills.
Even with the lowest minimum value of skill damage, the [Thunder] skill has a rather impressive potential to be a skill with a stable damage output, as the probability of the lower-limit value appearing is quite low.
Other skills, such as Area of effect damage skills, Continuous damage skills, perhaps the mechanism of skills is a little different, but the reasoning behind for calculations is the same. You just need to adapt the formulas and method of calculation to work out the effective range of damage / heal dealt by the skills.
In The End
Feeling the charm of math? The formulas may vary from time to time due to strengthening or nerf of different skills but the methodology stays the same.
For the current game version, I think the floor price of the [Thunder] skill is going to be raised by you guys again in the Marketplace.
I hope this content about the calculation and intepretaion of formulas in CyberChess Wiki can help you.
Happy Ranking!
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