Lately, I've had some discussions about how to increase my DPS. People have been telling me - try to squeeze more skills in your rotation (specifically your spammable) or try to count your light attack (LA) ratio and improve it. Well, I tried and failed. My DPS didn't increase. When I thought about it more, I called it BS and here is a proof why.

Who am I? A woodelf stamSorc with 2100 base stamina regeneration parsing 62k (party) DPS. And a redguard stamSorc with 900 base stamina regeneration parsing 62k (party) DPS. My goal is 65k DPS. Nice to meet you.


Please note that all calculations are valid for both static or dynamic rotations. It does *NOT* apply to rotations with proc skills, specifically to nightblades. I will explain the reason later.

1) Let's define some skills:

S_dot - A skill with or without initial damage which main component is damage over time
S_spam - A skill with or without damage over time which main component is direct damage, aka your spammable
LA - Light attack
HA - Heavy attack

Let's say our rotation is a static one and assume that we use LA between each skill:

S_dot > S_dot > S_dot > (swap) > S_dot > S_dot > S_spam > ... > S_spam > (swap)

There is no point to overcast your S_dot abilities, because you won't get any more DPS from it (except the initial damage it does, but for the cost it will always be a DPS loss). So as long as we keep uptime of our S_dot abilities at 100%, we can get more DPS only by including more S_spam abilities in our rotation.

Let's define some more abbreviations:
DMG - Our overall damage within 1 cycle of our rotation
DMG_spam - Our overall damage within 1 cycle of our rotation for S_spam abilities
DMG_dot - Our overall damage within 1 cycle of our rotation for S_dot abilities

It's obvious that
Because S_dot abilities have 100% uptime, we can say that
It means you can't increase your DPS by spamming S_dot abilities or casting them faster or more often.

This all leads to an easy conclusion that
And people will pragmatically tell me that the more S_spam abilities I cast, the better DPS_spam I get, and thus I get better DMG. Is it really true? No, it isn't, because this applies only to 1 cycle of your rotation! For the whole fight, there are more variables, so let's define them:

R_regen - Our main pool regeneration. It includes our base regeneration, skills (redguard), external resource gain (orbs and other synergies), and other mechanics in the game (regeneration areas)
R_drain - Our main pool drain. It includes our base drain (skills), external resource drain (block, roll dodge), and other mechanics in the game (degeneration areas)
DEG = R_drain - R_regen - Our overall main pool degeneration
DEG_dot - Our overall main pool degeneration for S_dot abilities
DEG_spam - Our overall main pool degeneration for S_spam abilities

I intentionally call it degeneration, because you want R_regen < R_drain, so the formula DEG = R_drain - R_regen gives positives numbers. We will work with it soon, and working with positive numbers is easier.

Now, when we do our rotation, we spend our pool resource. Because DMG_dot = const, DEG_dot is const too, therefore
So we can work just with DMG_spam and DEG_spam. The point is that the more S_spam we put into our rotation, the greater DEG_spam is (and also your DMG_spam). Due to R_regen < R_drain, we will definitely reach a point where we're out of our main pool, so we have to start doing HA, which means slowing down our rotation. For the whole fight, our overall DMG is combination of our DMG per rotation and our degeneration, thus
The greater N is, the greater impact our DEG has. Simply said, the less bursty combat, the more DEG impacts us (we don't need regeneration for a short burst).

Let's explode our formula:
We said that DMG is inversely proportional to DEG, so for N -> inf., DMG is balanced by DEG.
So we can say:

Hypothesis 1:
For reasonably long fight, our DPS will remain the same no matter how many spammable abilities we squeeze into our rotation.

Mathematically:
It has some limitations and conditions, but I will explain them later.

2) There is another conclusion to the first point which is a matter of discussion often. The question is simple: how much regeneration should I have?

Well, let's see. We said we expect our characters have DEG > 0. With higher regeneration, our offensive stats drop. So lets define these variables:

OFF - Sum of our offensive abilities, including spell / weapon damage, max resource pool, crit rate, and external buffs
DEF - sum of our defensive abilities, including spell / physical resistance, max health pool, health regeneration, and external buffs
R_regen - (see above)

Because the number of points we can put into these stats is limited, we can say:
For most players running trials, Def stat is defined pretty precisely and we can expect that most of the players have similar defenses, like 17k Health. So we can't reasonably lower our defense to increase our offense. Thus we can presume:
While I know we can work around it a bit, the effect is small and in a group of end game players, there won't be any difference in Def stats anyway.

That means we can say:
Which is obvious, the more OFF stats you put your points in, the less regeneration you have and vice versa. But how does it apply to our DMG_fight, aka your overall damage?

In part 1 we said it doesn't matter how many S_spam you put into your rotation. But the truth is that this is limited by your DEG. So with lower DEG (higher regeneration) we have our OFF lower, but it also means we can put more skills into our rotation, because DEG allows us to do it. And, of course, the higher DEG we have (lower regeneration), the fewer skills we can cast. You can easily see that it equalizes itself, thus:

Hypothesis 2:
For reasonably long fight, our DPS will remain the same no matter how much regeneration we have.

Mathematically:

Now it raises some questions:
1) Why META builds recommend low regeneration then?
It has generally two reasons:
A - Burst damage. Burst damage is very important in some trials to deal with mechanics. See the first hypothesis again:
But for burst it does not work, because n -> 1, so it's rather DMG_fight(n) = sum(1..1) {DMG(n)}, diminishing the DEG part, because we don't care about our DEG, wejust need to burn fast.

From the second hypothesis
Again, for n -> 1, the formula is rather DMG_fight(n) = sum(1..1) {OFF(n)}

Which means DMG = OFF for DEG -> inf.
High DEG (low regeneration) means we can invest more in OFF and thus has better burst.

B - Better control of our DPS and a better potential DPS overall.

Being able to deplete our resource pool is sometimes useful (apart from burst damage), it's again connected to mechanics. Imagine the boss gets a huge shield every 30 seconds for 10 seconds. For these 10 seconds we have to perform another mechanics which does not need much of our resource pool. The best strategy is to deplete our whole resource during these 30 seconds, so we can regenerate it back during the next 10 seconds. We just try to utilize our DPS to the max. If our pool is at its maximum, all the regeneration is wasted. The more regeneration we waste, the more DPS loss. Therefore the lower regeneration, the lower overall DPS the loss is. Both hypotheses still work, but with connection to mechanics, higher DEG (lower regeneration) is usually better.

Note. This does not apply generally, sometimes the mechanics favor higher regeneration over higher damage (Hel Ra upper boss), but it's quite scarce.
Note 2. This is also a reason why nerfing Dark Deal for Sorcerers is such a big deal even in PvE (although it's not used much).

2) What about Bloodthirsty traits?

Well, both hypotheses still apply, we just need to apply them separately for 100% - 25% HP of the boss and for the last 25%.

Ideally, if we want the best DPS, we have to start with full resource pool and end with 0 in our resource pool. It's obvious from both formulas. But for bloodthirsty, we get extra DPS boost for the last 25%, so we actually want to be at 100% of our resource pool on 25% of the boss HP, so we can utilize our DEG to the max.

3) So how do I increase my DPS?

A - Be nightblade. No, really, it works and it's quite obvious from my hypotheses. Look at the first hypothesis again:
Can you see the condition DEG > 0? If your DEG <= 0, then the formula does not work and the hypothesis does not apply. Nightblades have a proc skill that doesn't cost any resources. Then of course the more such skills you cast, the better DPS you have, effectively overcoming the limitation. With DEG <= 0, you can squeeze more S_spam without any punishment. Therefore the mentioned Light attack ratio actually matters!

Can it be done for other classes? Well, technically yes, but if you look at the second hypothesis - DMG_fight(n) = sum(1..n) {OFF(n) + DEG(n)} = const - our OFF will be so low, that our overall DPS will be lower then with DEG > 0. And over regenerating means loss of DPS.

As a bonus, this is a proof that nightblades are over-performing

B - Practice your rotation. What I didn't explicitly point out are secondary contributors to the DPS. It does not contradict my hypotheses, but it's included in the DMG part, actually in both S_dot and S_spam. And it's the mysterious light attack weaving. To get the best possible DPS, we have to light attack weave at 100%. 1 LA per 1 skill. 100% uptime of DOTs. External OFF and DEF buffs. External resource regeneration (healer's job). This is where you get your DPS.

C - Use proc sets. Aha! Here are our loved / hated proc sets. PvPers hate it, PvEers love it. Now you understand why it is like that - it's the same mechanism that works for nightblades - it's DMG without the DEG part! Moreover, some sets require player's skill to utilize them, for example Arms of Relequen. In hands of good players, it's a set that overshadows all other sets. In hands of bad players, it's a bad set.

Yes, you understand it - add resource cost to proc sets and they will stop over-performing.

I will stop here as it's already quite a long post. What do you thing about it?


EDIT: Clarification of DPS parse as it's meant as a parse in a trial party with trial setup.