I dream of numbers…

Let me prefix this blog post with a couple of apologies.

firstly i need to apologise for not posting in a while, life’s been a bit hectic and i’ve found it hard to keep the blog “regular”.

secondly, i need to apologise to Steven and Andy at bioware-mythic. Last night i didn’t have my thinking cap on, and must have come across as extremely dense in the tester IRC channel. i came out with a lot of sensationalist statements that really, after sleeping on it, don’t hold much water. it’s not like me to do something like that and i’ll try not to let it happen again.

thirdly, to you guys, the readers and players. i need to apologise to you, for giving you the wrong impression in this thread. in that thread i said this: “i’m pretty sure it’s designed to keep rr80’s who don’t buy the progression pack “competetive”. as an rr100 will hit an rr80, the same way another rr80 will. the problem is, an rr100 hitting another rr100, will be hitting for absolutely rediculous amounts due to the way the values scale.”

This post is going to be a bit numbers heavy, but it should provide some insight as to why what i said was wrong. I literally slept on it, and now i’m thinking a bit clearer.

Now, everything in war scales with rank. your player ranks up from 1-40. and then upon hitting 80, you gain a effective +1 rank, and all of your calculations are then based off of rank 41. a similar thing happens post-80. what mythic are doing, is giving you 5 additional effective ranks as you move up to rr100. you could assume from this, that you gain one every 4 renown ranks. so that when you’re rr100, you have an effective rank of 46 for all calculations.

you might want to know why this is important… well, firtly, your tooltips are all based on rank 40. so they are inaccurate as you gain renown. secondly, as previously stated, your rank affects everything, from how hard you hit, to how high your softcaps are, and even how likely you are to be crit. let’s take a look at a couple of calculations. i’ll do four, two rr80’s hitting each other, two rr100’s hitting each other, and an rr80 hitting an rr100 (and vice versa).

our toons will have the same weapons, but different armour (and therefor slightly different stats). both will be wearing medium armour, and have a two handed weapon who’s dps value is 101.5, they also have a +50% damage bonus from mechanic (can you guess the career yet?). please note that in an effort to limit variables i’ve chosen to use the same armour class, and the same toughness value (as they don’t change much anyway). the other stats do have considderable differences though.
at rr80, our toons have 1050 strength, 400 melee power, 300 toughness, 280 initiative and 600 weaponskill, with 3060 armour.
at rr100, our toons have 1400 strength, 400 melee power, 300 toughness, 320 initiative and 1000 weaponskill, with 4260 armour.

now for the calculations, Auto attack damage is calculated as:

  • <attackers weapon DPS> x <attacks weapon speed> = Base Damage
  •   <attacks weapon speed> x (<attackers strength, intelligence or ballistic skill> + <attackers bonus melee, magic or ranged damage> – <defenders toughness>) = Stat Bonus
  • ((<base damage> + <stat bonus>) / 10) x <attackers damage bonus> = Raw Damage
  • crit chance = (<attackers level x 7.5 + 50) / <defenders initiative> x 10
  • <defenders armor> / <attackers level> / 110 = Armor Mitigation %
  • <attackers weapon skill> / (<defenders level> x 30 + 200) = Armor Penetration %
  • <defenders armor mitigation> x (1 – <attackers armor penetration>) can’t be greater than 0.75
  • final damage = crit damage x (1 – (<defenders armor mitigation> x (1 – <attackers armor penetration> )))

our RR80 will hit for:
101.5 x 3.4 = 345.1
3.4 x ( 1050 + 400 – 300) = 3910
((345.1 + 3910) / 10) * 1.5 = 638.26 (rounded 638) raw damage.

against another rr80:
(41 x 7.5 + 50) / 280 x 10 = 12.75% chance to crit for between 957.4 and 1084.6 damage
3060 / 41 / 110 = 0.67 armour mitigation
600 / (41 x 30 + 200) = 0.42 armour penetration
1084.6 x (1 – (0.67 x (1 – 0.42))) = 707.15 max damage.

Against an rr100  
(41 x 7.5 + 50) / 320 x 10 = 11.17% chance to crit for between 957.4 and 1084.6 damage
4260 / 41 / 110 = 0.94 armour mitigation
600 / (46 x 30 +200) = 0.38 armour penetration
1084.6 x (1 – (0.94 x (1 – 0.38))) = 456.24 max damage

and now for the rr100 hits:
101.5 * 3.4 = 345.1
3.4 x (1400 + 400 – 300) = 5100
((345.1 + 5100) / 10) x 1.5 = 816.76 (rounded 817) raw damage

against an rr80 
(46 x 7.5 + 50) / 280 x 10 = 14.10% chance to crit for between 1225.5 and 1388.9 damage
3060 / 46 / 110 = 0.6 armour mitigation
1000 / (41 x 30 + 200) = 0.69 armour penetration
1388.9 x (1 – (.6 x (1 – .69))) = 1130.56 max damage  
 
against another rr100
(46 x 7.5 + 50) / 320 x 10 = 12.34% chance to crit for between 1225.5 and 1388.9 damage
4260 / 46 / 110 = 0.84 armour mitigation
1000 / (46 x 30 + 200) = 0.63 armour penetration
1388.9 x (1 – (.84 x (1 – .63))) = 958.34 max damage


so, as you can see. an rr100 vs an rr80 will definitely have a distinct advantage, and even vs another rr100 the damage should scale fairly well. one of the reasons for people hitting so hard last night on the pts, was that some abilities seemed to scale “wrong”. this was confirmed by mythic shortly after Steven and Andy came to test with some core testers and regular members in eataine, where they decided to take down the PTS to fix the errors.

i look forward to testing out the new, working armour sets soon. and hopefully now we can copy our regular characters to pts, we can arrange some actual rr80 vs rr100 fights, to see how big the difference really is.

Thanks to Moromer for proof reading this to make sure my math was sound. also, if any other theorycrafters can point out inaccuracies in the formulae for future, that would be great.

edit: a question was raised in the thread as to why should someone bother to level past 80, would they not gain anything out of it if they didn’t manage to get hold of warpforged gear etc.

in the example i gave, both weapons had the same dps values (rr75 weapons). the only thing that changed were the character rank, and the stats that the improved armour allowed.
if i were to further narrow down the changes and go for an rr80 vs an rr100, with the same initiative and strength, and armour values etc. essentially have both toons wearing full sovereign, it would look like this:

RR80 will hit for:
101.5 x 3.4 = 345.1
3.4 x ( 1050 + 400 – 300) = 3910
((345.1 + 3910) / 10) * 1.5 = 638.26 (rounded 638) raw damage.

against another rr80:
(41 x 7.5 + 50) / 280 x 10 = 12.75% chance to crit for between 957.4 and 1084.6 damage
3060 / 41 / 110 = 0.67 armour mitigation
600 / (41 x 30 + 200) = 0.42 armour penetration
1084.6 x (1 – (0.67 x (1 – 0.42))) = 707.15 max damage.

Against an rr100  
(41 x 7.5 + 50) / 280 x 10 = 12.75% chance to crit for between 957.4 and 1084.6 damage
3060 / 41 / 110 = 0.94 armour mitigation
600 / (46 x 30 +200) = 0.38 armour penetration
1084.6 x (1 – (0.94 x (1 – 0.38))) = 456.24 max damage

and now for the rr100 hits:
101.5 * 3.4 = 345.1
3.4 x (1050 + 400 – 300) = 3910
((345.1 + 3910) / 10) x 1.5 = 638.26 (rounded 638) raw damage

against an rr80 
(46 x 7.5 + 50) / 280 x 10 = 14.10% chance to crit for between 957.4 and 1084.6 damage
3060 / 46 / 110 = 0.66 armour mitigation
600 / (41 x 30 + 200) = 0.42 armour penetration
1084.6 x (1 – (.66 x (1 – .42))) = 670.28 max damage   
 

against another rr100
(46 x 7.5 + 50) / 280 x 10 = 14.10% chance to crit for between 957.4 and 1084.6 damage
3060 / 46 / 110 = 0.66 armour mitigation
600 / (46 x 30 + 200) = 0.38 armour penetration
1084.6 x (1 – (.66 x (1 – .38))) = 640.78 max damage
so what you can see from this, is that an rr80 will hit an rr100 considderably less than another rr80, but an rr100 in sovereign instead of doomflayer (ie. identical stats) will only hit for moderately more damage.
with that in mind though, some of the non-set items i saw on pts last night had some amazing stats at rr98 or so. which leads me to believe you could possibly see “better” than sovereign stats on non-set items, but you won’t get things like the sovereign proc bonuses.

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10 Responses to “I dream of numbers…”

  1. isn’t armour mitigation capped at 0.75? that would cause the rr 80 to do 580,261 damage in your last example. So “only” 90 damage difference or the rr80 does 13% less damage.

    • on second thought you claim that the capping is done after considering armor penetration so you can disregard my comment.
      you wouldn’t happen to have a link on how that information was obtained? i never considered the calculation to happen that way. i should probably get more armor now 😉

  2. as far as i’m aware, armour mitigation is calculated in two ways, firstly by the defenders rank compared to the amount of armour he has, this gives the mitigation amount. and then penetration is based on the attackers rank compared to the defenders.

    this is why higher rank players will deal more damage to lower rank ones, and why for example, a rank 48 lord would require in the region of 110% (on paper doll) physical mitigation to achieve the hardcap of 75%.

    the figures are taken from a couple of places, firstly, research i did a long time ago reading through the mechanic analysis pages on warhammer alliance, secondly from my own testing, and thirdly from talking with other core testers. thanks 🙂

  3. Yeah, there’s a big misunderstanding in that thread I think.
    It WOULD be nice if people did the math out like this (or looked for someone who did) before they go off on wild tangents raging about how there’s no benefit to being higher rank and in better gear. Bah.

  4. […] if you would like to know more about the reason for the change and why the damage was so high, read Bruglir’s post. So for us Shaman this means we get the following changes, one thing to note is that currently the […]

  5. Steven posted today and said that against lower rank targets your armor mitigation will max at more like 100.6% but vs. someone the same rank as you it will cap at 79% or something.

    It’s hard to figure out this scaling; on the one hand they say it was implemented to prevent high ranks farming low ranks, then on the other they say you will only notice an increase in damage or mitigation against lower rank opponents… /boggle

  6. well you can use the above formula to work out why for yourself. if someone say… rank 38, was hitting an rr100, and say he got a lucky crit for 1600 damage, and 350 weaponskill. it would work out like this:

    4260 / 38 / 110 = 1.01 armour mitigation
    350 / (46 x 30 + 200) = 0.22 armour penetration
    1600 x (1 – (1.01 x (1 – 0.22))) = 400 max damage
    note: the actual physical mitigation (1.01 x (1 – 0.22)) = .78, so the hardcap of 0.75 is applied.

    then 2 ranks later, he gets the same lucky crit off, with the same weaponskill etc.

    4260 / 40 / 110 = 0.96 armour mitigation
    350 / (46 x 30 + 200) = 0.22 armour penetration
    1600 x (1 – (0.96 x (1 – 0.22))) = 416 max damage
    note: this time the armour mitigation/penetration values take it to 0.74, below the hardcap.

    and finally, our guy has dinged 80, his effective rank moves up to 41, but he’s been slacking and still has the same WS values.

    4260 / 41 / 110 = 0.94 armour mitigation
    350 / (46 x 30 + 200) = 0.22 armour penetration
    1600 x (1 – (0.94 x (1 – 0.22))) = 432 max damage

    and then our guy dings 100, still on 350 weaponskill, because well… i dunno, he’s a moron or something.

    4260 / 46 / 110 = 0.84 armour mitigation
    350 / (46 x 30 + 200) = 0.22 armour penetration
    1600 x (1 – (0.84 x (1 – 0.22))) = 560 max damage

    so actually, it scales pretty well, the higher up you go the less damage you’ll take from lower rank players, and the easier you’re likely to hit the hardcap on mitigation. however once you start playing with higher rank players you’ll start to feel the pain a little bit more, and it becomes more important to focus on your mitigation stats a little more.

  7. hey Bruglir! nice numbers, but you forget that >RR80 Armor is 66 armorpoints 1%physical mitigation, not 44 points… or am i wrong?

  8. both toons wearing full sovereign, it would look like this:

    RR80 will hit for:
    against another rr80:
    3060 / 41 / 110 = 0.67 armour mitigation
    600 / (41 x 30 + 200) = 0.42 armour penetration
    1084.6 x (1 – (0.67 x (1 – 0.42))) = 707.15 max damage.

    Against an rr100
    3060 / 41 / 110 = 0.94 armour mitigation
    600 / (46 x 30 +200) = 0.38 armour penetration
    1084.6 x (1 – (0.94 x (1 – 0.38))) = 456.24 max damage

    Bad Typo ? /Bad example

  9. Heya! I had a little discussion with some of my guildies a few days ago regarding a player’s chance to be critted/initiative and that of his enemy works together. My guildmates believe that if for example a toon has a 20% chance to be hit and an enemy toon has 50% chance to crit the total crit chance is lower than 70% because of some unseen interaction between both players’ initiative scores. Could you please shed some light on this subject?

    Oh, and a have a great time celebrating the upcoming New Year!

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