Guild Wars 2

How can you find the optimal stats and gear for your playstyle?

If you are into fine-tuning your build, chances are you have experimented with one of those spreadsheets, or sites like GW2Buildcraft. Simple questions have simple answers. For maximum direct damage you choose straight Berserker gear. And if you don’t want any other stats (say, defense or magic find), you can stop reading now. Full Berserker is the answer.

However, suppose you do want other stats. If you like to have 18k health, how can you maximize your damage? How does your maximal damage change if you put 17k or 19k in health? Is the tradeoff between offense and defense worth it?

Mathematically, this comes down to a problem of constrained optimization, which is much harder than finding single purpose builds. Rather than thinking too hard, I decided to take a short cut.

I wrote a short little program that looks at all possible combinations of equipment and computes the resulting stats. And since I like visuals, rather than looking at tables I plot the result. Examples are attached.

Disclaimer: The conclusions may be well known to some of us, but I hope you find the explanations helpful. Also, I never have bugs in my programs, and I never get downed in fractals ;-)

Let’s move on to the first plot!

Plot 1 shows a scatter plot where each point represents one particular gear combination. I plot effective health versus effective power. Effective health is your health plus the bonus for damage reduction due to toughness. Effective power is your power combined with the averaged effect from critical hits computed from precision and critical damage.

About the data:

- Level 80 exotic gear

- Light armor

- PvE gear only (no PvP amulets)

- Various options drawn from Soldier, Sentinel, Knight, Valkyrie, Berserker, Cavalier, Cleric, Carrion, Rabid, Rampager, Magi, Explorer, plus jewels; runes are too varied, but we allow orbs and crests

- To cut down the number of combinations, we vary things in groups: weapons, armor, trinkets, jewels, orbs/crests

- There are small inaccuracies, for example I didn’t bother figuring out the availability of back items.

- Looking at the plot, we do get a rather nicely filled out cloud of data points. There are more than 30000 points. The distribution would be smoother if we run through all single item combinations, but this doesn’t change things much. Also, we cover quite a range without major gaps in effective health and power despite the funny business of getting three stats per item, but not in all combinations.

We now can start answering some questions about optimal gear. If you really only care about effective health and power, you want to be at the upper-right edge of the cloud. For example, suppose you like 20000 efffective health. Then you would move to the right on the horizontal line at 20000 to the edge of the cloud to maximize your effective power.

The question is, what gear puts you at the upper edge of the effective health-power options?

First of all, you probably can guess what equipment gives you the point with highest effective power. What about the maximal effective health? Where is full Soldier, Knight or Valkyrie gear?

Happy surprise, I made more than one plot :-)

Plot 2 shows the same data as the first plot in red, and in green we mark the location of PVTPC gear (power, vitality, toughness, precision, critical damage). 3 out of 5 of the PVTPC stats you get for Berserker, Knight, Sentinel, Soldier, Valkyrie, plus a few special cases.

PVTPC gear does better than the rest because effective health and power are computed from pow/vit/tou/pre/cri – points in other stats are wasted. We discuss a direct damage build that ignores condition damage and healing, but does include vitality and toughness.

Plot 2 also shows five points in blue for stats that you get for a full Berserker, full Knight etc builds.

Berserker (pow/pre/cri) is the maximal damage point. Basically: power rules. For average direct damage, power is more important than precision, and precision is more important than critical damage. Berserker wins, but also gives you minimal health.

Sentinel (vit/tou/pow) gives you the maximum in effective health. Since we ignore healing, the formula for effective health tells you to, roughly, invest the first 750 points in vitality, and then to equal amounts in vitality in toughness. Sentinel is very appropriate for that. We can only hope that the prices come down, or we might as well ignore Sentinel as a practical option.

The three points around 2100 effective power are, from high to low effective health, Soldier, Valkyrie, and Knight.

The location of Soldier (pow/vit/tou) is not surprising. It gives you the most important damage stat, power, and it gives you lots of survivability. Soldier gear is therefore a very reasonable suggestion for beginners or for difficult content (read: content that challenges your player skills ;-)

Surprising may be the location of Valkyrie (pow/vit/cri) and Knight (tou/pre/pow) gear. Since there are no Knight jewels, I used Emerald (pre/tou/pow). Basically, these two options loose because critical damage, precision, or toughness are not as effective as power or vitality in giving you effective health and effective power. It’s in the formulas. (Note the differences to the stats in PvP.) Of course, they do become good options if you change your criteria.

The question is, what is the optimal effective health-power gear somewhere between Soldier and Berserker? Are you able to guess?

Surprise, I made yet another plot :-)

Plot 3 adds two things to the discussion.

First of all, in a real build you also want to add other sources of stats, so I decided to look at traits 20/30/0/20/0. This gives you 200 power, 300 precision, 30% critical damage, and 200 vitality. This could be a burst build for a scepter/dagger elementalist. Comparing with plot 2, this gives us a shift to bigger health/power values. If you look closely, it’s not just a shift, because our investment in precision and critical damage becomes more effective.

The hand picked points correspond essentially to mixing Soldier and Berserker gear. Even when mixed, these types remain optimal for effective health and power.

Starting with Berserker, we fill our equipment slots as follows. Recall that jewels and orbs (or runes) are more efficient in giving you critical damage, which partially explains the order in which we switch.

Armor Jewels Orbs Trinkets Weapons
Bers Ruby Ruby Bers Bers
Bers Ruby Ruby Bers Sold
Bers Ruby Ruby Sold Bers
Bers Ruby Ruby Sold Sold
Sold Ruby Ruby Sold Bers
Sold Ruby Ruby Sold Sold

Not all of the near optimal points are of this type. For example, different combinations of toughness and vitality give you similar effective health, so you may choose to mix in some Knight gears if you prefer toughness over health.

Can you guess what happens close to the Soldier point? (I’ll leave this as an exercise ;-)

Suppose you could wish for a new type of equipment with a new set of attributes. The way effective power works, it would be very interesting to get some pow/pre/vit equipment. This could beat Berserker in the inbetween region.

Well, you didn’t ask for it, but yes, I made one more plot :-)

Plot 4 is an alternative way to plot the data in plot 3 for PVTPC gear.

We can look at the relative effectiveness of the builds by considering the product of effective health and effective power, let me call it EHP. (I haven’t seen precisely this before, but wouldn’t be surprised if it was discussed before, please comment below.)

Look at it this way. Twice the effective power means that you do twice the damage in any given time. Twice the effective health means that you live twice as long to do your damage (assuming some given amount of damage dealt to you per second that you don’t/can’t heal). So the product of effective health and power tells you correctly that you are able to do four times the damage before you are downed.

What do we do with that? Well, we plot it. Plot 4 shows EHP normalized by some constant to keep the numbers reasonable. We plot EHP versus effective power. As you can see, for 2200 to 3000 the effectiveness of the builds is roughly the same. In other words, you get what you pay for in return for your point investment. However, towards higher effective powers, your effectiveness in EHP drops. Berserker is not very effective on that scale, but of course EHP is a special way to look at things.

What does that mean? I can offer some nice visuals for that, too. Go, play the game to find out how well Berserker really works for you ;-)

I did not consider condition damage or magic find. But most importantly, I would like to have a good model for healing, which in turn makes toughness more important. The numbers already do change if you allow, say, one heal before you go down.

Outstanding work!
I am glad to see that there are more and more people in the elementalist community that are interested in theory crafting

A few remarks:

Why not include ascended gear?

For effective power, did you just multiply actual power by crit chance and crit damage modifiers? I tend to call this raw damage = power . ( 1 + (precision – 822) / 21 / 100 . crit damage / 100 )
(Base crit damage being 50)
And effective health = vitality . 10 . total defence ?
Did you take into account the base class vitality of 164.5 (Which is not disclosed in the stats panel)?
Total defence being base toughness (916) plus additional toughness from gear plus defence from gear (920 for light armor)

I would not say that precision is more important than critical damage. To an extent you are right, but there is no direct link in the allocation of stats between the two, so the ratio may vary and it makes comparison more likely to be inaccurate. Also their effectiveness is interdependent.

I agree with your zerker-PVT conclusion. Although you would have to consider the idea that effective health is not being used at all times (your health is not always threatened, because of pro-active defence, dodges, etc) so I tend to use a coefficient of effective health usefulness, usually around 0.5 in PvE, and I use this to min-max my gear. With that in mind I still find that changing the zerker pieces that have a bad crit damage ratio to PVT is a positive move.

Your fourth plot is daring!
I also have a hard time modelling healing and linking it to the rest of the models.

Thanks a lot! I would be more than glad to discuss all this with you.

Enjoyed this very much. Great job!
Glad that you came to the same conclusion Soldier Ruby Ruby Bers Soldiers (combination not in your list but its juts minor difference) is what I have always advocated in wvw. I guess the second from left, in the plot4 is Sold Ruby Ruby Sold Bers?

I am not sure I agree with your conclusion that ruby orbs are the best option.
I find that they provide about the same bonus as runes of strength when you have low might stacks (6-7) but the runes’ effectiveness is increased and outshines ruby orbs as soon as you pass that mark.

(I am talking about a set-up with 0/30/x/x/x zerker with 50% fury uptime, I put 0 in fire for pessimistic reasons, more points in fire will only confirm my conclusions, and replacing some zerker→PVT also goes my way)

Raw data vs. how that data is applicable to actual game play can be vastly different.

I agree, that’s why i use this “coefficient of effective health usefulness” to determine the value of my EHP. This coefficient is arbitrary and is meant to reflect the practical use of my passive defence.
It could be objective: I would just have to fraps my gameplay and see the proportion of time that my HP is not full.

Thanks for the comments!

@Zelyhn:
I really like your suggestion to use effective health with some coefficient. As given, effective health is a very conservative estimate of our survivability. It is the one-hit survivability, i.e. we do not allow time for healing or other skills to save our skin.
Yes, ascended gear is certainly something worth looking at as well.
I’ll get back to you with the actual formulas that I used later.
(If you haven’t done this yet, Zelyhn’s guide is really worth reading.)

@Sabull:
Good point, it is not in the list, but very similar. Perhaps I misunderstand, but I think it is the fourth point from the left. I find
Sold Ruby Ruby Sold Bers 3116 eff.power
Sold Ruby Ruby Bers Sold 3319 eff.power
Bers Ruby Ruby Sold Sold 3319 eff.power
The reason for the last two is that I have lumped together the Back Item with Armor so that 6xArmor + Back gives almost the same major/minor stat contribution as 5xTrinkets: 337/240 and 336/240.

@covenn
I agree: this is just “raw” data. They might tell us something about an isolated part of the game, but your own ingame experience is key.

@Zelyhn
Good point, for a well-founded discussion you need to know the formulas that I actually used. The basic calculations come from the Wiki, but people seem to round-off differently, and there are different ways to define “effective” power and health. (The following does agree mostly with what Zelyhn suggested.)

For effective power I define
ep = p * (1 + q * (0.5 + d))
where
p = power
q = (precision – 832)/2100 = critical chance, capped at 1.0
d = critical damage/100

Note a small difference to the Wiki. I am not sure how I got there originally, but the formula for q assumes an exact value of 4% for the base value of precision of 916: (916-832)/21 = 84/21 = 4. The Wiki uses 822 and talks about rounding off the result. Perhaps someone can comment on rounding effects and what one should actually do here. Numerically and in the plots the differences would be small.

I compute effective health relative to light armor,
eh = h * a / al
where h is your health, a is your total armor (defense + toughness), and al is the base value for light armor 920 plus 916 for base toughness. We have
h = 10805 + 10 * v
a = al + t
al = 1836
where v and t are the extra points in vitality and toughness added beyond the basevalue of 916 at level 80. So we get
eh = (10805 + 10*v) * (1836 + t) / 1836

This is awesome work thanks. I shall enjoy watching the discussion unfold.

I agree with Zelyhn about ruby orbs. The effective power of ruby orbs is comparable to runes of strength (still bugged). If you are a thief then I would say ruby orbs over runes of strength or you are a scepter ele burst maybe. In a fight that won’t be over in 15 secs runes of strength are definitely better. Ruby orbs are good reliable Solid Safe dps.

I always speak from a 0/10/0/30/30 D/D perspective just as a note.

Healing exponentially increases the value of toughness but when it comes to vitality it is linear. Which I believe you pointed out.

Zelyhn.8069:

I would not say that precision is more important than critical damage. To an extent you are right, but there is no direct link in the allocation of stats between the two, so the ratio may vary and it makes comparison more likely to be inaccurate. Also their effectiveness is interdependent.

Abilities/Procs based off of crits greatly influences actual worth of crit damage vs. crit chance as well.

Range vs. Melee vs. Intermediate affects sustainability, which increases/decreases the effectiveness of healing/Tough/Vitality themselves on sustainability. Sustainability directly impacts ability to do damage in a fight outside of initial burst. All this without taking into consideration play ability or traits/utilities.

Minor example:

Staff + good mitigation via play will allow that player to sacrifice toughness/vitality/heal power (in regards to self only… might want it for group support) in lieu of power/precision/crit dmg.

Daggers + poor mitigation from play mean toughness/vitality/heal power must come at the sacrifice of damage. Dead people do no damage….

covenn.7165:

Range vs. Melee vs. Intermediate affects sustainability, which increases/decreases the effectiveness of healing/Tough/Vitality themselves on sustainability. Sustainability directly impacts ability to do damage in a fight outside of initial burst. All this without taking into consideration play ability or traits/utilities.

Minor example:

Staff + good mitigation via play will allow that player to sacrifice toughness/vitality/heal power (in regards to self only… might want it for group support) in lieu of power/precision/crit dmg.

Daggers + poor mitigation from play mean toughness/vitality/heal power must come at the sacrifice of damage. Dead people do no damage….

This is pretty much everything in a nice neat package. Spot on! Unless you want to be daggers = poor mitigation go in burst pop mist to get out if that is your role.

@Abraxax

For the crit chance, the wiki is correct: it is precision – 822 and it gives 4.47% crit chance. Since the game takes only integers into account it is displayed and used as 4%, but as soon as you reach 927 precision it becomes 5%. This is a minor difference indeed, and we are not going to use the rounding up in our calculations anyway (the maximum deviation from not rounding up is 0.79%).

I do not understand why you would compute EHP in relation to light armor. Why dividing by the base defense? When you take a hit the damage is first divided by your armor then subtracted to your HP, or equivalently: divided by armor then divided by HP to give the percentage of health lost, so the correlation is linear and the base defense is not involved at any point. But maybe I am forgetting something?
This is important because if you want to compute the absolute marginal benefits from extra vitality or toughness you need this calculation to be correct.

Apart from this, and if I am not mistaken, you did everything right! Good job again

One thing that could be interesting would be to show what pieces of zerker you need to change to PVT as a function of effective health usefulness coefficient to be optimal.

I have some preliminary thoughts on healing and survivability, I will write about this soon, but I definitely not master this subject at the moment.

Very nice work. I used to do something similar with pen and paper. (Obviously not 30k data points.)

You may have come across this in your research but here’s the only post I found around healing back when I was doing this http://www.guildwars2guru.com/topic/60838-math-damage-reduction-toughness-and-vitality/

Lanny.6987:

Very nice work. I used to do something similar with pen and paper. (Obviously not 30k data points.)

You may have come across this in your research but here’s the only post I found around healing back when I was doing this http://www.guildwars2guru.com/topic/60838-math-damage-reduction-toughness-and-vitality/

That post is really a good read. The OP is the creator of the buildcraft.com site

I wish he’d update the buildcraft website with all the changes that have happened.

Hasn’t been updated in months and manually adding in stats can be annoying :/

Nice work. I use any and every type of stat to achieve the right stat balance that I’m looking for.

I’ve done a lot of build optimization, minmaxing, and research on effective health and how certain important yet difficult-to-measure variables, i.e. condition damage received and healing received, hurt/help you over time. My notes, critiqued by many peoples, can be found here.
I actually created a time2death calculator using HTML+JavaScript, though I haven’t had any time to work on it or test it, so it’s still in an alpha state.

While the effective health algorithm is technically health * armor, condition damage and healing can not be ignored, as they both directly interact with health or/and armor in such a way that is not easily calculated as the variable can fluctuate, potentially quite wildly, depending on who you’re fighting, how you’re playing, and how the overall battle goes.
Thus effective health isn’t as important as just building with your play style in mind. How well can you remove conditions? How often and how much do you heal? Etc etc.

In regards to effective power, I usually use the following formula (Edit: formula not algorithm, thanks Zelyhn):

Average dmg: (power * (1 – critrate)) + (power * critrate * (1.5 + critdmg))

When it comes to effective power, while, in comparison to effective health, it is easier to come to a more certain mathematical conclusion as to what’s best, you still have to judge by your play style.
Bursty builds may care about on-crit dmg more while bunker/hybrid builds may care about overall dmg more.

In the end, once you get used to build optimization/minmaxing, you’ll get a feel for what you’re looking for. It’s definitely not as straight forward to optimize for this game as it is in a game like WoW.

@TimeBomb
These are not algorithms, these are formulas
Develop and reduce your effective power formula and you will get ours.

P * (1 – C) + P * C * (1.5 + D)
P * [(1 – C) + C * (1.5 + D)]
P * [1 – C + 1.5C + CD]
P * [1 + 0.5C + CD]
P * [1 + C * (0.5 + D)]

I’ve always liked the following thought experiment. Consider D = 0 and C = 100. Every hit then does 1.5x damage so each percent of crit is 0.5% more damage. At D = 50 then every hit does 2x damage so each percent of crit is 1% more damage. 1% more damage from power costs P/100. 1% more crit chance costs 21/(0.5 + D). So until 2100 /(0.5 + D) power it’s “cheaper” to increase damage with power.

PS – Any well-formed formula is an algorithm since it can calculate a desired value in a finite number of steps. But yes, labeling such a thing “formula” or “equation” is more common.

With the availability of the numbers for celestial, where would that fall on the plot? I imagine it’s not even close to optimal, but it would be interesting to see where it lands.

Zelyhn.8069:

…….I would not say that precision is more important than critical damage. To an extent you are right, but there is no direct link in the allocation of stats between the two, so the ratio may vary and it makes comparison more likely to be inaccurate. Also their effectiveness is interdependent.

……..

http://wiki.guildwars2.com/wiki/Critical_hit

The table clearly details the direct link between critical chance and critical damage. In many cases the difference is negligible to be sure.

Baladir.2736:

Zelyhn.8069:

…….I would not say that precision is more important than critical damage. To an extent you are right, but there is no direct link in the allocation of stats between the two, so the ratio may vary and it makes comparison more likely to be inaccurate. Also their effectiveness is interdependent.

……..

http://wiki.guildwars2.com/wiki/Critical_hit

The table clearly details the direct link between critical chance and critical damage. In many cases the difference is negligible to be sure.

I’m pretty sure he meant the fact that the ratio of critical damage percent to raw stat numbers isn’t a constant. For example, jewels have the tightest ratio at 1:5 while legs, chest, and ring are 1:16.

Exactly.
This table is accurate but you need to pay attention to the ratio of critical damage to precision in order to read it correctly.

If you compare how often critical damage is better than precision in the table as it is you get a about 12%, which is in line with the idea that critical damage is less potent than precision as a general rule.
But this is only true for a 1:21 ratio (1% critical damage compared to 1% critical chance). In fact, the ratio of stats is always better than this. The wiki states an average ratio of critical damage to precision of about 1:11 (in fact it is even lower than this, around 1:9). So to read the table correctly you need to compare the increment in precision with double that increment in critical damage. The result of such comparison is that in around 50% of the cases critical damage is better than precision. If you take away the points that are covered by a basic berzerker gear this percentage goes up to 60.
Therefore no general rule can be made from this table.

I made a very simple spreadsheet that helps to compute the marginal benefits from each stats. It is easy to do, and quite useful although it does not provide as much insight as Abraxax’s data does. But everybody ignored it

My cat’s breath smells like cat food.

This is awesome and a lot of work I’m sure!
I’m not sure if there is one, but it needs a TL:DR. I’m at work, so it’s definitely TLDR, but perhaps I’ll ahve time when I get home
Also, would it be possible to add the new celestial gear in? In either these plots or the buildcalculator? I really want to try the new celestial gear.

Quick Mouse.7635:

This is awesome and a lot of work I’m sure!
I’m not sure if there is one, but it needs a TL:DR. I’m at work, so it’s definitely TLDR, but perhaps I’ll ahve time when I get home
Also, would it be possible to add the new celestial gear in? In either these plots or the buildcalculator? I really want to try the new celestial gear.

I think they already in there, but even if they are not, they are closer to the bottom left ( aka bad) corner. Because they have Healing power and condition damage. 2 stats that are totally ignored in direct damage calculations.

Avatara.1042:

My cat’s breath smells like cat food.

LOL i understand exactly how you feel with this nerdy math talk haha.