Melee combat mechanics (wall of text)
ho trovato questo post in un blog mentre ero alla ricerca delle varie formule per calcolare il danno etc..
E' un post molto puntiglioso e ben fatto, in attesa di smentite (o di eventuali errori nelle formule) e' il primo cosi completo ad indicare l''innerworking del combattimento melee di war.
Se avete tempo e vi fate i seghini mentali sul voler a tutti i cosi capire perché fate tot danno e per cosa lo fate eccovelo.
Pigri del cazzo, analfabeti in inglese e gente col cervello di hudlok e' meglio che non continuino la lettura, per tutti gli altri enjoy.
Warhammer Online - Melee Combat Mechanics
INTRODUCTION
Based on my experiences in WoW, I developed a passion for simulating combat, especially melee combat. Finding the gear combinations for attaining my character’s maximum Damage Per Second (DPS) was the foundation of those exercises on both my rogue Discoepfeand and my shaman Disquette. The information in this post is intended to be the foundation for those people who wish to do the same in Warhammer: Age of Reckoning (WAR).
DPS AND THEORYCRAFTING IN WAR
WAR, for better or worse, is primarily a PvP (or RvR, actually) game at heart. As a result, sustained DPS is often not going to be the concern of the players, who will instead be focused on burst damage as much as sustained damage. There are, however, some high-end PvE aspects that the developer (Mythic Entertainment) has alluded to. I don’t particularly care how useful this information is to the “average RvR player”, to be quite frank. My desire in this game isn’t to gain knowledge for the purpose of using it as Mythic intended, but simply to know and explain it for those who might care about the PvE portions of the game. As might be evident from my writing style, I’m getting older and am finding happiness in different things than I used to. As such, this blog is here for my own edification, and if you don’t like it or my motivations, feel free to stop reading - I’ll never know the difference ;-)
So, with that all out of the way…
BASIC STATS TO KNOW
1. Strength - this increases your auto-attack melee dps, all other things remaining the same, by 0.1 dps per strength.
2. Toughness - this stat, which both players and mobs have as a characteristic, is the inverse of strength (with respect to damage - your strength also effects your target’s chance to parry your attacks. That’s irrelevant for this post). Explicitly, it reduces the dps done to you by 0.1 dps / toughness.
3. Weapon DPS - the damage per second inherent in every weapon. It’s interesting to note that WAR is not like WoW - there is no variability from hit to hit. It’s all a mathematical formula with no randomness to the outcome of each hit. Crits may be an exception (I haven’t started work on them yet).
4. Weapon Speed - how many seconds it takes for each auto-attack swing of your weapon.
OTHER BASICS TO KNOW
* Your combat log will show not only the damage you did, but also how much was mitigated by armor. As an example, you might see the following: Your attack hits Evil Ogre for 80 damage. (20 mitigated)
* Very Important Disclaimer!!! So far the formulas I’m comfortable sharing in this post have proved to be accurate within 1 point of damage in all the testing I’ve done. I cannot, however, say without a doubt that these are the formulas being used. The best thing we can do is test for ourselves and draw our own conclusions. Having other people confirm these formulas via in-game testing would be nifty, so drop me a line if you do so.
ON TO THE SHOW!
Basic Attack Damage when single-wielding
Your auto-attack damage is calculated by a fairly simple formula. We’ll use some of those stats we covered earlier. I’ll use the following variable names:
* Strength: Str
* Target’s Tougness: Tou
* Strength Bonus: StrBon (I’m going to use this so as to simplify the way the formulas look. So far I haven’t found any damage calculations which use Str but not Tou, or vice versa, and when they’re used together, so far they’ve always been seen in the form Str-Tou).
* Weapon DPS: Wdps
* Weapon Speed: Wspeed
* Armor Mitigation %: Armor
Please note - throughout this whole post I’ll just be using a single term for armor. Weapon Skill affects armor penetration. That’s a very uninteresting stat for me, as it’s essentially a linear effect. A fully accurate formula would use (ArmorMitigation =
TargetArmor%*(1-WeaponSkillArmorPenetration%). If you’re writing a calculator, be sure to include that term, but this thing is complicated enough without that uninteresting term to further expand these large formulas. Thanks to Wodin and Hermit for pointing out that I shouldn’t leave this out all together without and explanation!
* Damage per Attack: Dmg (I’m specifying this so that it’s not confused with Damage per Second).
Dmg = ((StrBon/10) + Wdps)*(Wspeed)*(1-Armor)
Let’s do an example! Let’s say you’re a White Lion, fighting a Vicious Spider (made up name) and the actors have the following stats:
White Lion Str: 350
Spider Tou: 250
White Lion Wdps: 25
White Lion Wspeed: 2.0 seconds / swing
(thanks for catching this labeling error, DPS_squared)
Spider Armor Mitigation: 15% (Incidentally, this is about half of what is typical for even con’d mobs)
Using our formula above, each melee auto-attack will do…
Dmg = (((Str - Tou)/10) + Wdps)*(Wspeed)*(1-Armor)
Dmg = (((350-250)/10) + 25)*2.0*(1-15%)
Dmg = ((100/10) + 25)*2.0*85%
Dmg = (10+25)*2*0.85
Dmg = 59.5
This will appear in your combat log as:
Your attack hits Vicious Spider for 59 damage. (11 mitigated)
Ok, so what’s happening here? Lots of interesting things! To wit:
1. Rounding - It should come as no surprise that WAR, like other MMOs, rounds abilities to whole numbers for display purposes. This does not mean that the game doesn’t process fractions - I’ve seen one of my HoTs tick for varying amounts, sometimes 268, sometimes 267, which I can only imagine is the game keeping track of the fractions internally in the server (or perhaps the client, I don’t know).
2. There are two forms of damage mitigation, but you’re only seeing one explicitly - Only the armor mitigation shows up in the display window, but remember that the target’s toughness is also factoring in to reduce the damage.
Calculating Mob Damage Reduction
You might ask how to figure out the opponent’s armor and toughness values. I sure needed to know that in order to reverse-engineer the more complicated attack types. Let’s go through that process (Hey, I spent the hours to figure out how to calculate these, so you’re gonna read about it :p )
* Armor - this was the easy one. For every auto attack, on every character, it was pretty straightforward to see that comparing the amount mitigated in the combat log to the damage done always had the same ratio when all else remained the same (target mob, your str, weapon, etc). And that’s that! Ok, except for crits, which I keep coming back to as being special. Other blogs or articles will probably cover how that is working in game at the moment.
* Toughness - this was the harder one. The first thing is to realize that mobs have this! Coming from WoW where the only mitigation stat against physical attacks was armor, I had to expand my horizons a bit to understand that this was not only present, but was *invisible* (ooooh, ahhhhh). What I mean by that is that it doesn’t show in the mitigation portion of the combat log. However, if you do a few tests on mobs, you find that regardless of your weapon dps, your strenght, your weapon speed, etc, you are constantly hitting the mob for a consistent amount less than you would expect if you used just strength in a simple calculation.You might find it helpful, if you want to do dps testing for yourself, to have a set of guidelines to follow for calculating a mob’s toughness.
Here’s what you do - look at your stats, auto attack a mob, and back into the toughness using the following procedure:
1. Record your Str, Wdps, and Wspeed
2. Auto attack the mob, and add the mitigated and non-mitigated portions together. For instance, for the combat log entry Your attack hits Vicious Spider for 59 damage. (11 mitigated), The number you would want to record is 59+11 = 70. We’ll call this number TDmg (for Total Damage, including armor mitigation)
3. Use the formula below, which you can re-create yourself by undoing the process we used above if you like to prove things out to yourself:
tou = 10*((((0.1*Str + Wdps)*Wspeed)-TDmg)/Wspeed)
That might need an example to make sure I got my parentheses right! Let’s use the spider example from above. Remember from before, that:
White Lion Str: 350
White Lion Wdps: 25
White Lion Wspeed: 2.0 seconds / swing
Spider Armor Mitigation: 15% (this is completely unnecessary information for this calculation)
Add to that our two new data points:
Mitigated Damage: 11
Final Actual Damage to Mob: 59
TDmg = 70 (the 2 lines above added together)
Let’s calculate it out using the formulas shown above:
tou = 10*((((0.1*Str + Wdps)*Wspeed)-TDmg)/Wspeed)
tou = 10*((((0.1*350 + 25)*2.0)-(59+11))/Wspeed)
tou = 10*((((35+25)*2.0)-70)/2)
tou = 10*((120-70)/2)
tou = 250
Yay, it works! It matches the toughness we had in the assumptions used for the first example. If you’re theorycrafting/testing dps on mobs, build this formula into a spreadsheet - you’re going to use it a lot ;-)
Calculation Damage of Special Attacks
(Note: I haven’t looked at special attack damage while dual-wielding. This only works for single wielding at the moment)
(Edit for Update! Erdrick figured out the Dmg for special attacks while dual-wielding, yay!)
Unlike DAoC, and like some classes in WoW, WAR intertwines special attacks with your auto attack, as opposed to having a queue’ing system. As a result of not using a queue system, Mythic did something very smart for calculating special attack damage - they treat the weapon speed for the damage calculations as if it were the speed of the ability. Most special abilities are instant. Since each instant attack invokes the global cooldown of 1.5 seconds, 1.5 is the speed value used for most specials, whether you’re using a big 2 hander or a quick dagger. This is in contrast to WoW in which weapon speeds are normalized for instant attacks by their type (2.4 for swords, 1.7 for daggers, 3.something for 2 handers).
Another wrinkle thrown into the special attack calculations is that strength counts for twice as much! Above we noted that, per the character screen, each point of Str added 0.1 dps to your attacks. Also per the character screen, you will see that for special abilities, each point of Str adds 0.2 dps. What the character screen does not tell you is that your opponent’s toughness mitigation is also doubled per point. This makes things very convenient for us, as that doubling for both means that we can continue using our meta-stat: StrBon (Your strength - Your target’s toughness)
Now we have two facts that help us calculate the damage - weapon speed of 1.5 (usually) and StrBonus doubling - but we need more. MORE BLOOD FOR THE BLOOD GOD!
First, we have the ability’s damage itself. An ability may something like “A cruel blow which does 63 damage to your target and causes it to hate you greatly”.
Second, we have the special attack weapon dps modifier. This modifier, from my testing, is set to 150%. This means that if your weapon was 100dps, the damage of your special attack would be increased by 150 due to its weapon dps.
As noted by EasymodeX in the comments section, that’s equal to the multiplier for strength, which is a pleasing number - it again is the swing time of an instant attack.
So, let’s put that all together into a formula that captures these different facts. We’ll use the term Admg to refer to any extra damage you get from the special attack, per its tooltip, and we’ll use the term Sdmg to refer to the total damage of your special attacks after all the calculations are done.
Sdmg = (((StrBon/10)*2 + Wdps)*1.5 + Admg)*(1-armor)
(single wield only)
(note that Wspeed doesn’t factor in here - the special ability damage calculation is completely weapon-speed-free. You’ll be seeing this fact referred to again later in this post.)
As usual, let’s do an example so you can see it working. Assume the following:
White Lion Str: 323
Spider Tou: 264
White Lion Wdps: 51
White Lion Admg: 62
Spider Armor Mitigation: 15%
Sdmg = ((StrBon/10)*2*1.5 + Wdps*150% + Admg)*(1-Armor)
Sdmg = (((323-264)/10)*3 + 51*150% + 62) * (1 - 15%)
Sdmg = (5.9*3 + 76.5 + 62) * 0.85
Sdmg = 156.2 * 0.85
Sdmg = Your special attack hits Vicious Spider for 133 damage. (23 mitigated)
Update as indicated above, big thanks to Erdrick for figuring out special damage while single *or* dual wielding. That dude has more patience than me, that’s for sure :D Here it is:
Sdmg = ((StrBon/10)*2*1.5 + MHdps*150% + OFdps*52.5%+ Admg)*(1-Armor)
(Update on 9/18/08 - OFdps coefficient may be 67.5% now. I’ll have to check when I have a reasonably high level dual-wielder. Right now I only have a WP)
Alrighty, I hope that’s all clear, because the next formula (the last in this article) is the real doozy. Or maybe it’s not. But the fact is, it was horrible trying to figure it the next formula, and I had a victory beer when I finally got it working. However, even though it has so far been within 1 damage of actual tests each time I’ve done this, it looks so odd that I don’t have 100% confidence in its accuracy. I do have enough confidence in it to post it, and hopefully it stands up to further testing. If it doesn’t, so be it, and I’ll be very open to seeing a more accurate formula. So then, without further ado, let’s talk about…
Off-Hand Damage, when it happens, and how it’s calculated
Mythic has taken a novel (to me at least) approach to the mechanics of dual-wielding melee weapons. Instead of the off-hand weapon always swinging as it does in WoW, the chance for the off-hand weapon to swing is a simple proc from the main hand. A certain percentage of the time when the main hand hits, the offhand will also hit as an auto-attack. I don’t know what that percentage is. It’s probably documented somewhere, and if not, that’s a trivial task to empirically determine the proc chance (probably, who knows if they threw in something odd in the determination).
Edit 9/26/08 - The poster Star in the comments sections has been awesome and tested offhand proc rates! Here are his findings (comment copied directly):
Just calculated the proc chance of the offhand hit, and it results 0?46. But should need a more extended review.
The difficulty is that, in the combat log, offhand hits appear just like the mainhand hits (so you have to play with the time of the attack and the damage).
Also, you can get parried or blocked you main hand attack, and the offhand attack may still proc.
The part that I cared about was how to calculate how much damage each off-hand swing would cause when one did happen. So then why go into the proc-chance explanation? It is because that concept is intrinsic to understanding how and why the off-hand damage is what it is. In contrast to the other sections, I’m going to start us off with the damage formula, and then explain it after the fact. First, however, we need some new terminology to add to our stable of stats:
* Our current familiar stats:
* Strength: Str
* Target’s Tougness: Tou
* Strength Bonus: StrBon
* Armor Mitigation %: Armor
* Off-Hand Damage per Attack: OHDmg
* Our new stats:
* Off-Hand Weapon DPS: OHWdps
* Off-Hand Weapon Speed: OHWspeed
* Main-Hand Weapon Speed: MHWspeed
* Off-Hand Weapon DPS penalty: OHWPen
* Off-Hand Strength penalty: OHSPen
Alrighty, so here’s the formula:
OHDmg / (1 - Armor) =
(StrBon*OHSPen/10)*OHWSpeed
+ (MHWSpeed-OHWSpeed)*OHWdps
+ OHWdps*OHWSpeed*OHWPen)
ZOMG! I thought I was going to cry figuring that out. 4 seriously.
At this point, you have to take on faith that through trial and error and a few beers, I figured out the following constant values, and that they’re correct:
OHWPen = 0.9
OHSPen = 0.5
By now, you know what comes next - An Example!
Let’s lay out the relevant stats…
Str: 391
Tou: 291
StrBon: 100 (Remember, this is just Str - Tou)
Armor: 15%
OHWdps: 38.0
OHWspeed: 2.2
MHWspeed: 2.6
OHWPen: 0.9
OHSPen: 0.5
OHDmg / (1 - Armor) =
(StrBon*OHSPen/10)*OHWSpeed
+ (MHWSpeed-OHWSpeed)*OHWdps
+ OHWdps*OHWSpeed*OHWPen
OHDmg / (1 - 0.15) =
(100*0.5/10)*2.2
+ (2.6-2.2)*38.0
+ 38.0*2.2*0.9
OHDmg / (1 - 0.15) =
(100*0.5/10)*2.2
+ (2.6-2.2)*38.0
+ 38.0*2.2*0.9
OHDmg / (0.85) = 5*2.2 + 0.4*38.0 + 38.0*2.2*0.9
OHDmg / (0.85) = 11 + 15.2 + 75.2
OHDmg = 101.4 * 0.85
OHDmg = Your special attack hits Vicious Spider for 86 damage. (15 mitigated)
hey.
HEY.
HEY!!!!! Wake up! You still with me???
Ok, good, we’re almost done. I want to explain what’s happening with the formula above so you can have a sense of how well thought out Mythic’s offhand damage mechanic is.
First, as we discovered before, note that your special attacks aren’t diminished by using a fast weapon since special attacks don’t factor weapon speed into the damage calculations. Since off-hand weapon swings are procs of main-hand attacks, Mythic wanted to make sure that people didn’t abuse this mechanic by having a really fast main-hand to proc a hard hitting slow off-hand. Thus, they prorate the damage of your off-hand attacks by the difference between it and your main-hand weapon speed. The part of the calculation where you see this is in the term: (MHWSpeed-OHWSpeed)*OHWdps. The first term in the formula is also interesting in that you see Mythic halving the Strength bonus compared to a main-hand attack. Both that, and the last term of the formula (in which you see that Mythic has reduced the standard (weapon dps * weapon speed) by 10%) seem to be their attempt to tune the offhand damage to whatever internal goals they have. That’s my guess, at least, because it’s pretty damn complicated if that isn’t why they made this monstrosity of an off-hand-auto-attack-damage-calculation!
Conclusion
Melee DPS calculations in WAR are not nearly as simple as one might expect at first glance. While even these very primal calculations are relatively complex, there are even more complex formulas that will need to be developed to explain things such as off-hand crit damage.
And finally, I must reiterate: These formulas are my attempt at matching up mathematical formulas with observed results in WAR. I cannot guarantee that any of these are correct. However, they match up with my in game experiences so far.
I guess this is then end of my first blog post EVAR! If you have any comments or questions, feel free to post them in the response section (assuming it works, we’ll see if i get this blog thing figured out or not) ;-)
- Disquette
(Shaman, Disciple of Khaine, and ElitistJerks.com forum member)
