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Stats, what they mean, how they work

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    Stats, what they mean, how they work

    Hello, everybody. It's been a sleepless night for me, and the server is down as I write this. So, instead of just regretting to have started a 3hours upgrade instead of a 18h one, i figured i could use my time to write something useful. In this thread, we're going to go over defensive/offensive stats, so hopefully you can get a better understanding of exactly what they mean, what they're worth, why you shouldn't trust the green numbers, and why the game game seems to have some special new kind of maths, where 76*1,16 = 180.
    Keep in mind this is not some kind of advanced science, this is simple maths. In fact : This thread is useless if you can do the following

    We're gonna start with damage, then toughness, then recovery. But before that, we have to explain what diminishing returns are.

    Diminishing returns are one of the most common ways for developpers to avoid stacking a certain stat, and end up with a ridiculous result (as in, stacking enough armor to get "100% damage reduction", or more than 100). The other, less elegant way, is capping that stat to a certain maximum (dodge,block, parry are capped at 95%).
    The basic logic behind diminishing return for a stat is : the more you have of it, the more you need to achieve the same increase. Which leads to the conclusion: the more you have of it, the less valuable it becomes. This can be attenuated by certain things, but i'm saving this for later.

    There are 2.5 types of diminishing returns in this game:

    This means that the stat efficiency is not proportional to the stat score. For instance : to get 10% chance to crit at level 70, you need about 389 crit rating. Now to get 90%, you'd expect 9 times what you need to get 10%, right ? Wrong ! You need 31500 crit rating to get 90% chance to crit. Affects crit chance, armor, and ability rate.

    This means, that the more you get of a certain stat, the less valuable it becomes, not because it gives less, but because being additive makes it give proportionally less. This sentence barely makes sense, even to me (and i'm the one who wrote it), so i'm gonna give an example to illustrate : let's take power. A certain amount of power always increases the "bonus damage" by the same number. But let's take two cases:
    - Going from damage increased by 0% to damage increased by 100% : this means that you're going to do double damage
    - Going from damage increased by 1000% to damage increased by 1100% : even though it still gave you "100% more", the result is merely a 10% increase in your damage. Because power is additive (Your_Power + bonus) and not multiplicative (Your_Power * bonus) Affects Power.

    As it's the case for critical damage or attack speed. When you see "+ 14,4%"atsp, it doesn't increase your atsp by 14,4%, but rather by 14,4% of your base atsp, which is 1. Regardless of what your atsp is, 14,4% more is always gonna give you 0,144 more attacks per second. This makes it go back to type 2 diminishing returns. Affects attack speed, critical damage.

    First, let's take a look at what stats affect your damage :
    - Weapon Damage : where it all starts. It's a range, which means each time you hit, a random number is chosen between the two numbers displayed in the weapon stats. Even if it does the same on average, hitting between 90k and 110k is less boring than always hitting exactly for 100k;
    - Power : Increases your damage by a certain %age. One point of power gives a 0,5% damage increase;
    - Attack Speed : How many times you attack per second. X% atsp is always gonna give X more attacks per second (50% = 0,5 att/s, etc.);
    - Critical Rating : Gives you a certain chance to score a critical strike, which is a hit that deals more damage. The percentage is calculated as follows : P=C/(C + 3500), where P is your crit chance percentage, and C your crit rating;
    - Critical Damage : How much a critical strike hits for. NOT THE BONUS DAMAGE A CRITICAL HIT GETS, BUT THE TOTAL DAMAGE IT DOES. The game calculates the damage as if it was the bonus damage, but ingame testing proves that it's the total damage, as indicated on the character sheet.

    So that we know what the stats are, how do we calculate the damage ?
    It's fairly easy, the way to go is basically this:
    - You take the average damage you get from your weapon(s) (add the tome damage if tome equipped, but take the average of the max hit and min hit from both weapons if dual wielding). We'll call it WD, where WD = (MaxHit + MinHit)/2
    - You multiply it by the damage increase from power. We'll call your total power P, and as 1 power increases the damage by 0,5%, the power factor is P/200. As the power gives bonus damage and isn't the "total damage", we'll need to add 1 (so, 100%) before multiplying WD by the power factor
    - You multiply it by your attack speed (we'll call it S). Since we're calculating how much damage we do per second, we need to know how much each hit deals for damage, and multiply it by how many times per second you attack.
    - You multiply it by the expected damage increase from crits. Which means : let's take the critical percentage (to simplify then we'll get back to the real deal) CC, and the damage your critical strikes do CD. Since the critical damage displayed is the total damage, we need to be careful not to count it twice. We'll call the crit rating CR. So, if Da is your damage without factoring in crits, and Db the damage with crits (regardless of power/atsp and stuff for now), the "normal strikes" will be (1-CC) (*1 since they do normal damage), and since CC is your crit percentage, the critical strikes will do CC*CD damage, which gives us:
    Db = Da*[(1 - CC)*1 + CC*CD] which becomes Db = Da[1 + CC(CD - 1)]

    The formula to get the dps, based on what i said above, gives us :
    DPS = [(1 + P/200)*WD]*S*[1 + CC(CD - 1)]
    DPS = [(1 + P/200)*(MaxHit + MinHit)*0,5]*S*[1 + (CR/(CR+3500))(CD - 1)]

    Where do i put my Champion Points to get the maximum DPS ?
    You can check out this thread if you want to know.
    - Why does the formula there use CD and not CD - 1 ?
    As i said before, the formula the game uses assumes CD is the bonus damage from crits, not the total damage. Ingame testing proves it's actually the total damage.

    Time for ability rate, i didn't really know where to put it
    - Ability rate : Reduces your and your minions' cooldowns by a certain %age. P = AR / (AR + 1000), where P is the cooldown reduction %age, and AR your ability rate score.
    NB : Base attacks have a 25% chance to reduce the remaining cooldown of your spells by 2s

    Now that we're done with damage, let's take a look at toughness :

    It's described at "your ability to withstand damage, mesured in how much damage you can take before falling". It's not very clear, so i'll detail a bit. It basically means how much "raw" damage the enemies need to shoot, so that the actual damage you take after damage mitigation (blocking, armor, etc.) takes you down. Let's take an example, but kind of backwards, it's clearer that way:
    Suppose an enemy shoots "100k worth" of damage. You have enough armor to reduce damage taken by 60%, and you have 50% dodge chance. It means out of the 100k he shot, you're gonna only "receive" 40k, of which you'll avoid on average 20k (you don't avoid part of the damage from a single hit with dodge, i mean on average, on several hits, you'll avoid half). So, on average, 100k damage shot = 20k damage taken. It means that if you have 20k HP, you'd have 100k toughness with these defensive stats, because enemies need to shoot "100k worth of damage" for you to actually take 20k damage and die.

    After this quick overview, let's take a look at our defensive stats :
    - Armor : Decreases the damage taken, by P = A/(A + 3000) where P is the damage reduction percentage, and A your armor;
    - Block chance : Percentage of chance to block a hit. A blocked hit deals only 25% damage (prevents 75% damage); Don't forget you cannot block if you don't have a shield equipped, so don't take into account block in toughness if you don't play with a shield.
    - Parry chance : Percentage of chance to parry a hit. A parried hit deals no damage if it's melee, and parried ranged attacks deal half the damage (not sure about this one, you'll have to verify)
    - Dodge chance : Percentage of chance to dodge a hit. An avoided attack deals no damage at all, obviously.

    Now, how do we calculate toughness ? I'll start with a little example again, to get the formula. We'll ask our little guy above for his help again.
    20k hp = 100k toughness because you avoid 80% of the damage (60% dmg reduc => 40% damage taken, multiply it by 50% damage avoided by dodge, 0,4*0,5 = 0,2 => 20%).

    Which gives Toughness * %DamageTaken = HP
    Now bear with me. I said %DamageTaken, so it's 1 -
    Which gives us Toughness * (1 - %DamageAvoided) = HP
    So Toughness = HP/(1- %DamageAvoided)
    Let's see how to get the damage taken, by using each stat.

    - Armor gives you A% damage reduction. So the damage taken is (1 - A);
    - Parry makes you avoid damage (we'll forget about the possible 50% dmg reduction instead of 100% as it it's not taken into account in the ingame toughness calculation, or so it seems at least). If you parry P% of the hits, you take (1 - P) of them;
    - Dodge : same as parry. You take (1 - D) where D is your dodge chance;
    - Block : just a tiny bit trickier. You avoid 75% of the damage, but only in B% of the cases. So the damage taken is (1 - B*0,75) where B is your block chance.

    The formula gives us :
    Toughness = HP/[(1 - A)(1 - P)(1 - D)(1 - B*0,75)]
    By the way, before i forget, each vitality point seems to give 50 hp (1 brilliant vit gemstone gave me 2500 hp)

    Before we get to recovery, i'd like to add a few things :
    - Parry and dodge have a lot of weight in toughness due to them being considered pure damage avoidance, but are unreliable. If you have 20k HP and take 80% "less" damage only because of armor, you'll survive a 99k "raw" hit provided you are full hp, everytime. If you have 20k HP and take 80% "less" damage only because of dodge, you'll survive sometimes and then you'll get oneshotted.
    - You can dodge/parry/dodge most attacks, but not all. For instance, you can't parry Elban's lifedrain. However, you can parry/dodge/block reflected damage or dot damage from the immolator buff, which gives a very interesting effect when coupled with in the zone for example. Throw in a cleave in a group within a reflecting enemy and you'll start parrying 13421413 hits because of the dot + the multistrike of cleave, and with enough mobs your cooldowns will go down to 0 (really close to 0 i mean, as in shorter than it takes to draw the sign again). At lower trials anyway.
    - I said in the beginning that diminishing returns can be "attenuated". It's the case for armor. The more you have of it, the more valuable a %age becomes. For example, let's take how adding 5% to the damage reduction displayed affects the damage you take. Going from 0 to 5% damage reduction makes you take 95 instead of 100% damage, so it's effectively a 5% reduction. But going from 90 to 95% damage reduction makes you take 5% damage instead of 10%. It's effectively a 50% damage reduction. It stills ends up being a diminising return, but when you compare the efficiency, it's not "as DRed" as it looks. This is why lowering armor is dangerous, because the increased damage taken is higher than you think. If i take down my damage reduction from 60% to 50%, i'm taking 50% damage instead of 40%. Effectively, it means i'm taking 25% more damage, not 10%. The higher you go, the bigger the gap gets. Going from 99,9% damage reduction to 90 is not about 10% more damage, it's 100 times more damage.

    We're almost done, there's only recovery left

    I'll start with how to calculate the total hp gained back per second, then we'll see what exactly recovery is and finally how to calculate it.
    What stats affect the HP you get back in combat ?
    - Life Regeneration : gives you back a certain amount of HP per second, in or out of combat. We'll call it LR;
    - Life on hit : heals you for a certain amount each time you hit. We'll call it LOH;
    - Attack Speed : since you get back hp from loh at each hit, more hits/s = more hp/s. We'll call it S.

    Which one is better ? The FAQ answers this, but i'll add in a detail. If your concern is your own survival, go for LOH. If your concern is your minions' survival, put your CL points in life regen. They benefit from it, but not LOH.

    The hp you get back per second (we'll call it HPS) would be:
    HPS = LR + LOH*S

    But the ingame tooltips says recovery is how much toughness you get back per second, not how much life. So we have to multiply the HPS by the toughness you get for each HP which gives us : Recovery = HPS * Toughness/Life
    Recovery = (LR + LOH*S)*Toughness/Life

    This means a few things.
    - Increasing only toughness, not life, would increase your recovery even without touching your HPS. This is why block, dodge, parry and armor increase your recovery;
    - Increasing both toughness and life proportionnally would have no effect on recovery. This is why vitality increases toughness and not recovery.

    That's all. I may add a few things (such as screenshots to illustrate) later. I hope you found this helpful. Tell me if you find any mistakes.
    I'd like a moment of silence for damage reflect. It's the worst stat of the game that is linked to combat, be cause you still take the damage reflected, and you reflect a miserable amount of damage anyway.
    Last edited by Schmilo; 06-08-2017, 07:40 AM.

    Thank you! I'm bookmarking this one.
    This is incredibly helpful reference.


      Great Post, voting for Sticky here.

      I have a question, do you know how to calculate the potential cdr from Attackspeed?
      KAJE TIJI REGA 5325


        Originally posted by soios View Post
        Great Post, voting for Sticky here.

        I have a question, do you know how to calculate the potential cdr from Attackspeed?
        It would be something like 0.25*2*Atsp, so ATSP/2. That being, the average cooldown reduction per second, in seconds. But practically it's useless, because it doesn't factor in abilities and specifics that interact with each other. Like the extra hit from frenzy, the bonus atsp from battlerage / rapidfire / bloodlust. Bloodlust would make you have a lower-than-expected CD, which means more frequent use of warp time, which means an even lower cooldown. You'd have to know the average uptime of such buffs to make use of it.
        BUZE TALO PEBA 0409




            Corrected a mistake, 1 vit is actually 50 hp and not 62.5 .
            I'd forgotten i had +25%hp from CP
            BUZE TALO PEBA 0409


              stat name?
              'recovery' to 'hps' (healing per second) or 'rps' (recovery per second), vitality increasing overall amount of time to recover and needing less per second. or can vitality be figured in? or armor, parry, dodge, block be taken out as doing the same as base life and vitality and increasing time to heal? just have a flat hps of loh and regen?
              Last edited by Bishishi; 06-29-2017, 04:56 PM.


                Means I have to know this huge amount of math for.playing a game? Don't I better quit?
                FIGU BUXU YOXU 3083
                Last edited by Debanjan; 08-19-2017, 08:49 AM.


                  Originally posted by Debanjan View Post
                  Means I have to know this huge amount of math for.playing a game? Don't I better quit?

                  Or just use the general guidelines!
                  VOWO TOSO QEME 4656


                    You don't need math. Math just allows you to fully understand what's going on and try to tune your character to a finer degree. Or you can just follow the green numbers, if you die easy increase toughness, if you don't kill fast enough increase damage. It's only as hard as you make it.
                    ROJO CIXA XITO 9019


                      Originally posted by Debanjan View Post
                      Means I have to know this huge amount of math for.playing a game? Don't I better quit?
                      No need to fret.
                      It's usually pretty much common sense. Like Xeros said:
                      • If you're dying, you need more defensive skills.
                      • If you're taking too long to kill things but rarely dying, try upping your offensive skills.
                      Even people who understand what all the numbers mean and how they're related will still tell you to just do what works. Experimentation is more helpful than math.
                      SESA YIFI CICE 9356


                        Would you need to update this with Haste now or do we just substitute it?
                        Novex WARRIOR LEVEL 70 , CHAMPION LEVEL = 1085
                        XP Build I'm using at the moment:
                        Damage = 437k
                        Toughness = 391k
                        Recovery = 69k
                        EXP 808%
                        Add me + Join in Discord !!
                        TUMU DOMA NEGU 3613


                          Originally posted by Novex View Post
                          Would you need to update this with Haste now or do we just substitute it?
                          You sub it in, since Damage is still calculated using Attack Speed.

                          The change in Nov 2017 only means that Attack Speed is no longer a "base Atttribute/state" and is now calculated from Haste, plus other things (my latest post on Haste to Attack Speed calculations and one for Haste from Attack Speed)
                          Eternium Files - links and details Eternium Guides:


                            The constant used in the crit chance calculation (3500) appears to not be correct anymore.

                            I've taken 5 different data points on my Mage and they all match, to the limit of the accuracy of the numbers, the equation C / (C + 3000), implying that the constant should be 3000, not 3500.


                              Originally posted by Rannasha View Post
                              The constant used in the crit chance calculation (3500) appears to not be correct anymore.

                              I've taken 5 different data points on my Mage and they all match, to the limit of the accuracy of the numbers, the equation C / (C + 3000), implying that the constant should be 3000, not 3500.
                              That was announced in the 1.2.65 release notes months ago.