28 April 2010

The non-linearity of the ICC zone-buff

Today (or yesterday, depending on which continent your WoW servers are) the ICC zone-buff was increased from 10% to 15%. That's an increase of your DPS, HPS and HP by 4.5%. I think that the main benefit of this buff is the DPS component, not only does it affect more people, but 4.5% more HP or HPS doesn't drastically alter your ability to survive poorly handled boss-abilities. Sure, there may be borderline cases where those few percent are enough to save you, but in general that Malleable Goo or Vengeful Shade will kill you just as hard today as it did last week.

So why then does this not apply to DPS in the same way? Knocking a few percent of the duration of a 5 minute fight is not a major difference. Except for two things. The first is the enrage timer. On heroic modes, enrage timers on some bosses are a real threat. Especially since we typically have someone die here and there, bosses like Festergut and Blood Queen can end up being close calls, especially on earlier kills.

The time-based add-spawn mechanic
The second effect is far more interesting. Quite a few boss-encounters involve some type of spawns or secondary targets that need to be killed. These spawns are almost always on a fixed timer. In ICC we have Marrowgar (bonespikes), Deathwhisper (cultists), Saurfang (blood beasts), Putricide (oozes) and the Lich King (val'kyr, vile spirits). I've skipped over Gunship and Valithria because the "boss-kill" mechanics are very different from the regular boss-encounter.

Now, with this type of add-spawning, you will have to divert your DPS to the adds before going back to the boss. And this is where the fun kicks in: Higher DPS means the adds go down more quickly and you spend more time on the boss with your higher DPS. The effect of a DPS-increase on your effective boss-DPS (which is what determines the length of the fight) is amplified by the fact that there are periodic adds that need to be killed.

Enough talk, let there be math!
Assume a boss with B HP. Let R denote the raid DPS on the boss and f R the raid DPS on the adds (In case of single-target adds 0 < f < 1, as you lose DPS by swapping to an unbuffed target and having to ramp up your rotation. For AoE adds, f can be larger than 1.). We have adds with a total of A HP spawning every Ta seconds.

To kill the adds, we need A / (f R) seconds, which leaves us with Tb = Ta - A / (f R) seconds to DPS the boss per wave of adds (Pro-tip: If Tb < 0 then you're doing it wrong). Divide by the interval between two waves, Ta and we obtain the fraction of time we can spend on the boss:
1 - A / (f R Ta)
Multiply by raid DPS on the boss to find the effective raid DPS on the boss:
R - R A / (f R Ta) = R - A / f Ta

Not a big surprise, eh? If you have adds with a total of 300K HP spawn every 30 seconds, your effective DPS on the boss is lowered by 10K, divided by the DPS-correction-factor caused by the difference in DPS between boss and adds. Could've worked that one out without the whole derivation...

Buffing your DPS
So now we get 5% more DPS from a new ICC buff (Yeah, I know it's actually 4.5% for this weeks change as I said before, but I'll take 5% for simplicity). How does that change our effective boss DPS?
1.05 R - A / f Ta
So the term that adds a positive contribution to effective boss DPS is increased, while the term that adds a negative contribution remains unchanged. The net effect will be a greater positive contribution on effective boss DPS.

An example
Lady Deathwhisper has 6.7M HP on 10-heroic. In phase 2, she will summon a single add every 40 seconds. The add has 176K HP (averaged between a Fanatic and an Adherent). Lets assume that raid DPS is 30K on the boss and 20K on the adds (So f = 0.667). Your effective boss DPS will be 16.8K. Now, add 5% raid DPS (31.5K on boss, 21K on adds). Your effective boss DPS will increase to 18.3K, an increase of about 9%.

This effect becomes more noticable, the more time you spend on adds. The most notable example was pre-30% nerf M'uru (which I never had the pleasure of fighting, unfortunately), where the tuning was so tight that there was very little time to DPS the boss. Small increases in raid DPS had large effects on the time it took to burn the boss down.

Conclusion and take-home message
We've seen a quick analysis of how the commonly used add-spawn mechanic can amplify the effect a DPS increase has on your raids performance. The effect becomes stronger the longer you take to kill the adds. Obviously, there are all kinds of other benefits to having the adds down more quickly (preventing the Val'kyr from dropping your buddies off the ledge in the Lich King encounter is one such benefit), but from a mathematical point of view, the boss DPS effect is the most interesting.

22 April 2010

How stuff scales

I'm currently working on getting some equations for threat-generation of a Bear as a function of a bunch of stats to see how strongly (or weakly) we scale with certain stats and how powerful some of the threat talents are. As an intermediate step, I had to determine how much damage each ability does with different amounts of AP. The effect of haste, hit, expertise, crit and ArP are well-documented or easy to deduce, but there wasn't much on how things scale with AP. So I made the Heroic Training Dummy my new best friend for an evening.

Most of the testing was performed by testing the damage of an ability at different levels of AP by taking off gear. Most of the testing was done with my Moonkin spec, to prevent pesky talents from obscuring the raw data. Master Shapeshifter was clicked off, so there were no damage-increasing talents or buffs. I kept all gear with ArP off for the entire test, as it complicated calculations. This immediately meant that 2pc T10 was also not used, which was useful to keep Swipe and Lacerate testing clean.

At each level of AP, several attacks were made to determine the damage of the ability. Other than abilities that scale with the Druids weapon-damage (Maul, Mangle, auto-attack), all abilities have a fixed damage value rather than a damage range. A non-integer value means you can get both the integer below and the one above the precise damage value as outcome. Simply dividing the increase in damage by the increase in AP gives the scaling factor. For Maul and Mangle a larger number of attacks was needed. I took samples of about 40 hits and averaged the results.

Some results
  • The initial hit from Lacerate is affected by armor, it is not buffed by the Mangle debuff, but it is affected by the 2pc T10 set-bonus.

  • Faerie Fire (Feral) is a spell in all aspects: It uses your spellhit chance (17% chance to miss against a boss-mob without hit), your spellcrit chance and it crits for +50% damage rather than +100%. It deals Nature damage and is not affected by armor.

  • Maul and Mangle do not scale as their tooltip would have you think. First of all, they seem to double-dip from Naturalist: The talent increases your normal melee damage by 10%, but Maul and Mangle scale with this melee damage and are increased by another 10%. This double-dipping, coupled with Savage Fury, makes the predicted scaling match what I observed from hitting the dummy. For Maul, there is a 10% discrepancy (the measured scaling is higher). In my result, I've taken the measured value. I still have to work out where this comes from.

  • Maul and Mangle deal damage based on melee damage plus some bonus component. The bonus component in the tooltip does not seem to match the actual bonus component when hitting a target at all, no matter how I twist all the talented buffs that affect it. I will keep looking.

The numbers!
In the following table you'll find how much the damage from an ability increases when you add 100 AP. This includes any talents or debuffs that you can reasonable expect to be part of a Ferals spec or to be active on the boss: Savage Fury, Feral Instinct, Rend and Tear, Naturalist, Mangle/Trauma, a bleed effect, Blood Frenzy / Savage Combat and Arcane Empowerment / The Ret Paladin buff whose name I forgot.

Note that by 100 AP I mean a character screen difference of 100 AP. Talents (such as Protector of the Pack) and buffs (Trueshot Aura and such) increase the amount of AP you get from gear and buffs. I assume we're fighting a L83 boss-mob with appropriate armor value. Below you'll find the results for a fully sundered and Faerie Fired mob with 500 armor penetration rating (which is a typical value for a Druid gearing up with ilvl 264 T10 and similar offset items). Values are for non-crit attacks.

AbilityDamage increase from +100 AP
Faerie Fire (Feral)15.5
Swipe (2pc T10)8.4
Lacerate hit0.85
Lacerate hit (2pc T10)1.02
Lacerate 5-stack tick7.66
Lacerate 5-stack tick (2pc T10)9.19

Well, the numbers speak for themselves, I'd say. Maul is easily the best-scaling attack, trailed by Mangle and FFF. The initial hit from Lacerate scales horribly with AP, which explains why Swipe takes over as filler-attack at pretty much any L80 gear-level.

This is just the start of my little research. It's all just damage, but what really matters is threat. I'll continue to work with these results, couple them with other stats, threat-modifiers, etc... Hopefully I'll find out what causes the strange discrepancies between the predicted and measured damage-values for Maul and Mangle in the mean time.

13 April 2010

The Cataclysm Druid Preview

Last friday Blizzard posted the preview of upcoming changes to the Druid class with the Cataclysm expansion. I'll take a quick peek at what will change for Bear Druids.

Thrash (Level 81): Thrash deals damage and causes all targets within 10 yards to bleed every 2 seconds for 6 seconds. The intent here is to give bears another button to hit while tanking. Talents will affect the bleed, such as causing Swipe to deal more damage to bleeding targets. 5-second cooldown. 25 Rage.

More variety to our AoE tanking rotation! That must be good. Swipe dealing more damage to bleeding targets is also mentioned, which will couple nicely to Thrash. My main concern though, is that this still looks like a rather static rotation: Thrash -> Swipe -> Swipe -> Swipe -> Thrash -> repeat. I'd much rather see some procs and similar mechanics that will force us to change our rotation on-the-fly. But, this is just the initial preview, there's bound to be more to come.

Stampeding Roar (Level 83): The druid roars, increasing the movement of all allies within 10 yards by 40% for 8 seconds. Stampeding Roar can be used in cat or bear form, but bears might have a talent to drop the cooldown. The goal of this ability is to give both bears and cats a little more situational group utility. 3-minute cooldown. No cost.

AoE Dash. Whether this will be a powerful new tool or just another gimmick will only be clear once we know what the encounters look like. It has the potential to be very useful though.

  • We want to add tools to cat form and depth to bear form. If a Feral cat is going to fill a very similar niche to that of a rogue, warrior or Enhancement shaman, it needs a few more tools -- primarily a reliable interrupt. Bears need to be pushing a few more buttons just so the contrast between tanking and damage-dealing is not so steep.

Yes! Right now, tanking is very straightforward. More depth is sorely needed as it will make the role more fun to play and it will create a larger difference between strong and poor players.

Mastery bonuses for Feral (Bear)
  • Damage Reduction
  • Vengeance
  • Savage Defense

They make sense, I guess. Vengeance is something that all tanks get. It will give the tank a stacking AP-buff whenever they get hit. The buff adds 5% of the damage dealt by the attack to your Vengeance-stack with a maximum stack-size equal to 10% of your maximum HP. This should make threat scale properly with new content without having to overload the tank gear with DPS stats (which, in our case, will happen regardless, since we share it with Cats and Rogues).

Overall it's looking promising, I'd say. It's still very early, so many things can and will change. But the promise of more depth to the Bear rotation is something that pleases me greatly.

The full preview, including changes for Cats, Moonkins and Trees (who will no longer be trees most of the time!) can be found on the WoW forums

06 April 2010

Rage changes in Cataclysm

Blizzard posters have shown us what's in store for Warriors and Druids when it comes to rage in Cataclysm. The full story is on the WoW forums.

The changes and how I feel about them:
1) Rage is no longer generated based on damage done by auto-attacks. Instead, each auto-attack provides a set amount of Rage, and off-hand weapons will generate 50% of the Rage main hands do. This amount is based on a constant formula which factors in the base swing speed of the weapon. This means the Rage gained should be averaged out between fast and slow weapons. The constant formula also gives us the ability to easily increase the rage gained if it feels too low (or reduce it if is too high). We are also implementing the following mechanics, which will still allow rage to improve to some extent as you improve gear:

  • If the attack is a critical strike, it will generate 200% Rage.
  • Haste will accelerate swing times to generate Rage faster.
Rage gains will no longer depend on the damage you deal with your attacks. This is nice. This mechanic was one of the main sources of the exceptional gear-scaling that Warriors had: Getting more gear means you hit harder which allows you to use your specials, which also hit harder, more often. In Cataclysm, the scaling will be far more linear, which makes it easier to predict and to plan for.
2) Rage from damage taken will no longer be based on a standard creature of the character’s level, but instead will based on the health of the warrior or druid. Again, there is a constant that is multiplied by the rage generated in order to allow for fine-tuning. This calculation ignores all damage reduction from armor, absorption, avoidance, block, or similar mechanics, so improving your gear will not reduce Rage gained.
This one confused me at first, but followup posts by Blizzard employees cleared it up: The amount of rage you get from a boss hitting you depends on two things: Damage done by the boss and player health. The more damage, the more rage, as it is now. But more health means less rage per damage. So in theory, the Cataclysm equivalents of Patchwerk and Festergut would give the same amount of rage to tanks geared for the individual bosses. But a T10 tank going back for the Naxx weekly would gain alot less rage from Patchwerk then he did before (due to the increased health). This mechanic seems a bit clunky, depending on how strong the inverse-health-scaling is.

On the other hand, rage-gains being the same regardless whether you got hit, blocked, parried, got missed or dodged is an excellent change. No more rage starvation due to avoidance-streaks.
3) We will provide warriors and druids with more instant sources of rage. For example, the warrior shouts are changing to work more like the death knight ability Horn of Winter. Instead of Battle Shout consuming Rage, it will generate Rage but have a short cooldown. Both classes will have additional methods to generate Rage in an emergency or bleed off Rage when they have too much.
That sounds nice. I'm not sure which ability would make sense here for a Druid (Demo Roar?), but more on-demand rage and rage being an actual resource to manage should make things more interesting.

4) All “on next swing” attacks in Cataclysm are being removed. Heroic Strike and Maul will be instant swings that cost a variable amount of Rage. For example, imagine Heroic Strike costs between 10 and 30 Rage. You must have at least 10 Rage to use the attack, but it will consume all available Rage up to a maximum of 30. Any Rage consumed above the minimum will cause the ability to hit harder, and in some cases much harder. We will tune the ability so that it’s generally not a good idea to hit it when you have low Rage (unless everything else is somehow on cooldown) but becomes a more attractive button the higher your Rage.
I like this as well. Maul (and Heroic Strike) have become things that you don't even think about using anymore, you just spam it every auto-attack (or macro it to all your instant abilities) and forget about it. Other than RSI, these abilities don't give you anything, yet they're essential if you want to generate enough threat. Together with the rage-generating shouts, this change should help make rage more of a resource to be managed, like energy is for Cat Druids and Rogues and not like mana is for most DPS casters.

I like most of the changes, they should make Warrior and Druid gameplay more interesting. All this obviously assumes that the new mechanics and scaling factors will be balanced properly. The rage from damage taken mechanic I'm not entirely happy with. Depending on how harsh the inverse-health-scaling will be, it might make revisiting older content an unpleasant experience.

In related news, the coming week will feature previews of Cataclysm changes for all classes (except Paladins, they have to wait one week longer because they're special). Druids are scheduled for friday.