### TSW Fist Healer Theorycrafting

TSW Fist Healer Theorycrafting by Shadai

There is a lot of information (and misinformation) floating around on the forum boards about this ability or that ability. Mostly it is spouted theorycraft from people who haven’t tested what they are spewing, or guys who have always done it this way… and it works damnit, so clearly this is the only way. I’m not really one just to spout things I don’t really have a lot of first-hand knowledge of; so in my attempt to understand game mechanics, I really like proof. Proof as in hard numbers, not napkin math where you just vaguely defend your position and expect everyone to agree with you for whatever reason.

There have been a lot of fist healing threads and guides and rotation theory running around, but no one has taken the time to really get behind the mechanics and massage the math. I’ve spent the last few days testing and running numbers, and I have found some interesting truths about fist healing. Kick back, in the next few posts (or however long it takes me to post my findings) I’m going to share what I’ve found.

This all started when I was told “no this is better” in regards to Empowerment when I suggested that Out of the Woods would be a good ability to take. And when I asked why, no one could really give me the answer. So I set out to figure it out. What is better? And why? When does one become better then the other? And what IS the optimal rotation for fist?

Definitions

The question soon became, “How can I compare Empowerment to Out of the Woods in real numbers?” Indeed, it’s not like they are the same ability.

Empowerment: Whenever a heal over time effect critically hits, the target is healed for XXX

Out of the Woods (OOTW): Whenever you heal a target to above 80% of their maximum health, you gain a beneficial effect that increases all direct healing done by 27.5% for 8 seconds.

At first glance, it’s obvious which one is better. Fist is more a HOT style healing, and Empowerment seems to directly buff that. Whereas OOTW buffs… direct healing? Well we don’t really do a lot of that in fist right? Or do we?

Assumptions

In order to answer the question I need to somehow translate both abilities into real numbers that I can then compare. But in order to do that, I have to isolate the variables. To do this, I ran numbers based on my healing numbers with several assumptions in place. These were just to ensure I was getting fair numbers across the board, and not to mention make the math easier to see and understand.

1. Round down – occasionally I came up with a remainder that was not a whole number. Instead of complex rounding, I just simply dropped it and round down on all numbers.

2. EDIT: Healing Sparks crits AND will proc Empowerment.

3. Consumers are a flat 20% increase per resource – again, fact, but at the time I started I wasn’t sure.

4. HOTs refresh on cast

5. OOTW affects not just direct healing, but the HOT part of Creature Comfort AND Surgical Steel. For some reason. I don’t really know why. But when I was testing it in game, with the OOTW buff up (and no other buffs) I would see the numbers jump up 27.5% on Creature Comfort and both the direct and HOT portion of Surgical Steel. This was confirmed by writing the tooltip numbers down and doing the math. An exact 27.5% increase. Oddly enough, it only affected the HOTs on the consumers, but not the builders. I don’t know if its a bug or a feature, but for the math and comparison, you will see the numbers go up for those two abilites.

6. Empowerment has a 1 second cooldown like all passives, meaning it can only trigger once per second.

7. All of my numbers are based on my healing gear with a 2% buff from PVP (cause I couldn’t turn that off). Your numbers will obviously vary, but it wasn’t the exact NUMBERS I was really interested in, rather the trends they produced. So your numbers may be larger or smaller, but the trends will stay the same.

8. I ran the tests with both Creature Comfort (CC) and Surgical Steel (SS) to see the differences. Mostly because I was curious on the break point between these two abilities as well. It just so happens that some people here on the forums champion the use of one or the other. So I included them both so you can compare which is better using hard numbers.

Empowerment and Probability

So now we get to the probability portion of the math. Empowerment is directly dependent on critical rating. That is to say, the higher your crit chance, the more benefit you will see from Empowerment. But how can I put that into numbers?

Crit is a fickle rating. To understand what I mean by that, think of coin. A coin has only two sides, heads and tails. When you flip a coin in the air, you have a 50-50 chance of it landing on heads. Same as our healing. Let’s assume for a minute that we have a 50% crit rating. Each hot that ticks on the target has a 50-50 chance of triggering Empowerment. Our HOTs have only two options, hit for normal, or crit. We don’t have to worry about penetration, blocks or glances. Each second, we can either crit or we do not.

Back to our coin example. If we flip a coin once, we have a 50% chance it lands heads. However, if we flip that same coin say, ten times, do we have a 50% chance of getting 5 heads? If you said no, you can skip the next part. If you said yes, keep reading.

The coin is 50% each flip. But that doesn’t mean that over time we will get the exact same number of heads and tails on each even flip. You could flip a coin 10 times and get 7 heads. Or you could get 1 head. The short sample size becomes a problem. The only way to even it out is extend the same. Now if I flip that coin say… a thousand times… the chances of me having exactly 500 heads is still small, but the chances are it will be a lot closer to 500 then it will be to 700. So even if I assume a median baseline for Empowerment, there are just some days where you will be above the median, and some days where you will be below.

Back to our crit problem. Let’s say we have 20% crit. That means for every 10 seconds of HOTs ticking, we can assume that 2 of those will crit, triggering Empowerment twice. Or in other words, one out of every five. So by taking our crit percentage and multiplying it into our Empowerment number, we get the same number but in a per second ratio, since it can only trigger once per second.

So: .2 * 400 = 80. So Empowerment heals 80 points per second. If this doesn’t make sense, think about it this way. One crit out of every 5 is triggers for 400 more right?

Well: 80 + 80 + 80 + 80 + 80 or 80(5) for 5 seconds = 400

Alright sweet. But this is only for 1 HOT. What happens when we have more then one HOT ticking? If you said add another 80, go back to playing WoW.

An additional HOT ticking on the target crits at the same 20%. However, since we can only trigger Empowerment once, we don’t care if both crit. We only care if ONE of them crits. If you flip two coins in the air at the same time, your chances of getting at least 1 head is a lot better then getting no heads. In this case, our crit percentage actually increases for each additional HOT.

For some people it is actually easier to think of it this way: What are the chances that neither one crits? Well that’s easy. The first one won’t crit 80% of the time. The second one won’t crit that same 80% of the time. For both of them to not crit? That’s .8 * .8 = .64 You have a 64% chance of them BOTH NOT CRITTING. So what are the chances at least one crits? The opposite of 64% or 100 – 64 = 36%

Your crit rating just jumped from a mere 20% with one HOT to 36% with two. That means that the per second benefit we get for using Empowerment jumps from 80 per second to .36 * 400 = 144. So not an 80 point increase, but still a nice jump to healing power.

In order to figure out where Empowerment is better then OOTW, I picked two crit points; 20% and 30%. Since we don’t really know what our crit percentage is, from my play experience most MMOs have a crit percentage around those two numbers.

So for a 400 point Empowerment:

20% crit would be 80 for 1 HOT, 144 for 2 HOTs, and 196 (49% to crit) with 3 HOTs

30% crit would be 120 for 1 HOT, 204 (51% to crit) with 2 HOTs and 264 (66% to crit) with 3 HOTs

Notice how with each HOT added the chance to crit goes up less and less. This is because even at 20%, and you have 5 HOTs on the target, a 1 out of 5 chance would lead you to believe that you would be guaranteed at least one crit a second. But this clearly not the case.

Math

I laid out each rotation as it were to the second. This allowed me to calculate when HOT’s were added, when they dropped off, and at what point and second allowing for an accurate Empowerment calculation. I could simplify them but I wanted to show the work in case I got something wrong (it has been known to happen).

First, I will start out with using Out of the Woods. I will break it down into two sections, the first being using SS with OOTW and the second using CC with OOTW. During each rotation, I’m starting from nothing with 5 Cauterize Spam then the Consumer. HAx is the prefix I use to denoted Cauterize HOT being applied.

1. 357 HAx1
2. 357+357+26=740 HAx2
3. 740+357+52=1149 HAx3
4. 1149+357+78=1584
5. 1584+357+78=2019
6. 2019+344(3)+78=3129 HOTs applied 85 per 5 (SS) and 59 per 4 (Healing Sparks-HS)
7. 3129+357+78+85+59=3708
8. 3708+357+78+85+59=4287
9. 4287+357+78+85+59=4866
12. 5965+344(3)+78=7075 HOT applied 85 per 5 (SS) and 59 per 4 (HS)

Now for CC instead of SS using OOTW. Since casts 1 through 5 are the same (all still Cauterize spam), we’ll start at 5:

5. 2019
6. 2019+78=2097 HOT applied 330 per 6 (CC)
7. 2097+357+78+330=2862
8. 3862+357+78+330=3627
9. 3627+357+78+330=4392
10. 4392+357+78+330=5157
11. 5157+357+78+330=5922
12. 5922+78+330=6330 HOT reapplied 330 per 6 (CC)

A couple of things to notice about these two before I move onto Empowerment. First, the healing applied by the OOTW bonus is nothing to sneeze at. Second, I know it seems like SS is beating out CC, and it is at least initially, but you have to run the equations longer for CC to catch up. The best HPS you’ll put out is 7 through 12 on both runs, this is when all HOTs are rolling and nothing is really falling off. For SS, the amount of healing is 12-6 or 7075-3129=3946. For CC, the number is greater at 6330-2097=4233. So a rotation with CC will heal more then one with SS but only over several rotations.

Next, Empowerment with SS, 20% crit:

1. 280 HAx1
2. 280+280+26+80=666 HAx2
3. 666+280+52+80=1078 HAx3
4. 1078+280+78+80=1516
5. 1516+280+78+80=1954
6. 1954+270(3)+78+80=2922 HOT applied 67 per 5 (SS) and 59 per 4 (HS)
7. 2922+280+78+67+59+196=3602
8. 3602+280+78+67+59+196=4282
9. 4282+280+78+67+59+196=4962
12. 6211+270(3)+78+80=7179 HOT applied 67 per 5 (SS) and 59 per 4 (HS)

And now 30% crit:

1. 280 HAx1
2. 280+280+26+120=706 HAx2
3. 706+280+52+120=1158 HAx3
4. 1158+280+78+120=1636
5. 1636+280+78+120=2114
6. 2114+270(3)+78+120=3122 HOT applied 67 per 5 (SS) and 59 per 4 (HS)
7. 3122+280+78+67+59+264=3870
8. 3870+280+78+67+59+264=4618
9. 4618+280+78+67+59+264=5366
12. 6743+270(3)+78+120=7751 HOT applied 67 per 5 (SS) and 59 per 4 (HS)

Next is using CC with Empowerment at 20% crit. Again, since the values are the same for 1 through 5 for Cauterize spam with the same amount of crit, I’m starting at 5. Refer to the SS/Empowerment 20% calculations for the exact numbers:

5. 1954
6. 1954+78+80=2112 HOT applied 260 per 6 (CC)
7. 2112+280+78+260+144=2874
8. 2874+280+78+260+144=3636
9. 3636+280+78+260+144=4398
10. 4398+280+78+260+144=5160
11. 5160+280+78+260+144=5922
12. 5922+78+260+144=6404 HOT reapplied 260 per 6 (CC)

And finally using CC with Empowerment at 30% crit. Again, refer to SS/Empowerment 30% calculations for 1 through 5:

5. 2114
6. 2114+78+120+2312 HOT applied 260 per 6 (CC)
7. 2312+280+78+260+204=3134
8. 3134+280+78+260+204=3956
9. 3956+280+78+260+204=4778
10. 4778+280+78+260+204=5600
11. 5600+280+78+260+204=6422
12. 6422+78+260+204=6964 HOT reapplied 260 per 6 (CC)

Observations (What does this all mean???)

The first thing I noticed is Empowerment does heal a lot but it is thoroughly dependent on having many HOTs on target. This doesn’t make as much difference as you approach 30% crit, as even with 1 to 2 HOTs rolling, you can expect that using Empowerment will yield the greater benefit.

The part I found fascinating is that OOTW actually held its own up until the 20% level. That to me suggests there is a level in the game where you have to be in order to get the most out of Empowerment. Clearly, having more crit then 20% you should be using Empowerment. With the finding that Healing Sparks crits AND procs Empowerment, SS is very strong. It is a single consumer that stacks 2 HOTs that increases your ability to trigger Empowerment.

In plain speak, that means if you have less then 20% crit, you should be using OOTW to get the most out of your healing. If you are above 20%, you definitely should be using Empowerment.

In a moment of clarity, at one point my character sheet seemed to work and under my healing abilities it said I had a 19.7% chance to crit with around 700 crit rating from gear (I think it’s 679 or something close to it, I’ll check and update later). That was with a 1% buff from PVP. So if it was right, that means almost 700 should get you near 19%. But again, assuming the numbers I was seeing were correct.

The differences between the consumers was telling as well. SS is clearly superior in short burst situations. It just brings more healing in that short burst scenario then CC does. However, in very long multiple rotations, CC is the winner. Each CC rotation during 7 through 12 output more healing in that 6 seconds then any of the comparable SS rotations.

What does that mean? Quite simply, if you find yourself coming off the tank to heal anyone multiple times in a fight, you are probably better off with SS. If you are in a fight where only the tank is taking damage, then CC is going to put more heals on him over time.

Optimal Rotations

But we don’t start spamming Cauterize… we start with full fist resources.

Right you are.

Running the numbers for 13 seconds, and inserting a full 5 point consumer at second 1, I got the following results:

For OOTW with SS: 8768 total healing
For Empowerment/SS 20%: 9076
For Empowerment/SS 30%: 9852
For OOTW with CC: 8310 total healing
For Empowerment/CC 20%: 8364
For Empowerment/CC 30%: 9064

See what I mean about CC needing several rotations to catch up? SS beat out all the comparative builds by a decent margin even giving CC the best possible chance by starting it first.

A couple of truths about optimal rotations:

1. If anyone tells you to blow a CC early or without 5 resources, they are WRONG. CC has a 6 second tick which means it will continue to carry through all five builders and the recast of CC. Meaning it will tick every second as long as you keep refreshing it after 5 builders. In addition, you get a tasty 20% increase to the HOT for each builder you put into it. Cast it early and you run the risk of overwriting your tasty 5 builder, 6 second CC with a less then optimal new 6 second CC that doesn’t heal nearly as much.

2. In order to get the most benefit from Empowerment, more HOTs are needed. I was able to throw together a rotation with Nurture that was able to get 7171 with 20% crit and Empowerment and that only used Nurture 3 times (on casts 1, 5 and 10) to keep the HOT from falling off. Expect that number to go up if you use the passive Nurturing Gift to extend that to 10 seconds. If so, I anticipate that the rotation would be much easier to use since you would only have to refresh Nurture once per round (ie, Nurture, Cauterize x4 then CC. Repeat til done). Using this rotation allowed me to have 3 HOTs ticking at the same time, yielding a 49% crit rate and a 196 per second from Empowerment. EDIT: Numbers are wrong in light of HS critting and proc’ing Empowerment, working on the new numbers.

3. Theoretically, the only consumer worth using with less then 5 resources would be SS. And interestingly enough, it would be SS with OOTW that would see the most benefit. After getting off the three stacks of Cauterize, a rotation of Cauterize, SS, Cauterize, SS, Cauterize, SS, etc would yield good burst results and most likely keep OOTW in the discussion far past the 22% crit break point. It is one of the things I’m still testing.

I’m still testing some other things. I will let everyone know what I find.

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