Guild Wars 2

what would output more damage
45% crit chance and 66% crit damage or 50% crit chance and 50% crit damage

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

There is a nice table if you scroll down displaying how much your dps increases for crit chance/crit dmg.

Your critical Damage multiplier is:
1 + crit chanche x crit damage

45% crit chance and 66% crit damage:
1 + 0.45 × 0.66 = 1.297 (~30% more damage)

50% crit chance and 50%
1 + 0.5 × 0.5 = 1.25 (25% more damage)

In other words, just multiply those stats. The bigger, the better

its weird how low both are. is that tpvp stats or pve ?

dae.1865:

its weird how low both are. is that tpvp stats or pve ?

Why low? Maybe he just isn’t zerk? It’s still high in some aspects of game.

pve ranger power spec usualy reach 94%crit damage and 40% crit chance without any as ended jewelry

Molch.2078:

Your critical Damage multiplier is:
1 + crit chanche x crit damage

45% crit chance and 66% crit damage:
1 + 0.45 × 0.66 = 1.297 (~30% more damage)

50% crit chance and 50%
1 + 0.5 × 0.5 = 1.25 (25% more damage)

In other words, just multiply those stats. The bigger, the better

Not quite. The expected damage is more like this:

(1-crit chance)x1 + (crit chance)x(1.5+crit dmg) = 1 + (crit chance)x(0.5+crit dmg)

So, 45% crit chance and 66% crit damage:

1+0.45(0.5+0.66)=1.522 —> 52% more direct damage on average

50% crit chance and 50%

1+0.5(0.5+0.5)=1.5 —> 50% more direct damage on average

You’re forgetting the 0.5 added to base damage multiplier when critting.

Pardon my ignorance but while looking over the chart, it looks as if Critical Chance is more important (or has a higher effect) then Critical Damage. Is this true? I always thought it was the other way around.

Yeah it’s true. The gain from 1% crit chance will always be greater than the gain from 1% crit dmg (unless you somehow get over 100% crit chance… then it’s better to spec all the extras to crit dmg).

And this is even more the case if you have an “on crit” sigil on your weapons (which is affect only by chance, not crit damage)

Faux Sheaux.6179:

Yeah it’s true. The gain from 1% crit chance will always be greater than the gain from 1% crit dmg (unless you somehow get over 100% crit chance… then it’s better to spec all the extras to crit dmg).

Only until 50% critchance once you’re at 50% critchance or higher they are equal.

That doesn’t take into account any on crit sigils though I should also say.

Manekk.6981:

Faux Sheaux.6179:

Yeah it’s true. The gain from 1% crit chance will always be greater than the gain from 1% crit dmg (unless you somehow get over 100% crit chance… then it’s better to spec all the extras to crit dmg).

Only until 50% critchance once you’re at 50% critchance or higher they are equal.

That doesn’t take into account any on crit sigils though I should also say.

Ehh… I’ll change my above “always” to “almost always”, but you’re still pretty far from the actual case.

Let CD = Crit Dmg %, CC = Crit chance, and F = 1+CC(0.5+CD)

Then, for the partial derivatives:
dF/dCD = CC
dF/dCC = CD+0.5

This just basically says that the marginal effect of adding 1 CD to adding 1 CC is usually going to lean towards CC. It does cap off at CC=1 though. You can’t go any higher. But until then, aiming for more CC will benefit you more than aiming for more CD.

Look at CC=0.99 and CD=0.99. Let’s add one to each while keeping the other static and see how it changes:

CC = 1, CD = 0.99;
F = 1+1(0.5+0.99) = 2.49

CC = 0.99, CD = 1;
F = 1+0.99(0.5+1) = 2.485

See? Still slightly higher. However, with that said, I wouldn’t suggest traiting for higher than CD=0.8 since you won’t get additional effects from fury. If you’re running that type of a build, you will definitely be taking advantage of fury.

I’ll make another post on it though… Let’s say that CD = 0.2, CC = 0.8, then

F = 1+0.8(0.5+0.2)=1.56

Adding one point to either side will give:

CC = 0.81, CD = 0.2;
F = 1+0.81(0.5+0.2) = 1.567
CC = 0.8, CD = 0.21;
F = 1+0.8(0.5+0.21) = 1.568

So adding 1% to CD is more worthwhile than adding 1% to CC in this case.

It basically comes back to:

dF/dCD = CC
dF/dCC = CD+0.5

Assume CC > CD+0.5:
dF/dCD > dF/dCC by substitution.

Basically, this means you only get a larger marginal benefit by adding a point into CC if CC > CD+0.5… You need a full 50% more in critical chance than you have in critical damage % for a point to be more worthwhile in damage than chance.

For those who don’t know what dF/dCC and dF/dCD mean, they are measures of marginality in this respect (derivatives if you’re a math person).

Good analysis, always love a bit of maths to support a position.

Given a trait like precise strikes though there might be a good reason why you want to take a bit more CD when you feel you have a reasonable amount of CC in your build, say 40-50% not including fury 20%, if you are building a spike dps build which is designed to kill as quickly as possible. More CD in that scenario to frontload that first strike is quite fun assuming you can land it.

Of course CC is nice for lots of other reasons as well given runes,sigils etc.

Faux Sheaux.6179:

I’ll make another post on it though… Let’s say that CD = 0.2, CC = 0.8, then

F = 1+0.8(0.5+0.2)=1.56

Adding one point to either side will give:

CC = 0.81, CD = 0.2;
F = 1+0.81(0.5+0.2) = 1.567
CC = 0.8, CD = 0.21;
F = 1+0.8(0.5+0.21) = 1.568

So adding 1% to CD is more worthwhile than adding 1% to CC in this case.

It basically comes back to:

dF/dCD = CC
dF/dCC = CD+0.5

Assume CC > CD+0.5:
dF/dCD > dF/dCC by substitution.

Basically, this means you only get a larger marginal benefit by adding a point into CC if CC > CD+0.5… You need a full 50% more in critical chance than you have in critical damage % for a point to be more worthwhile in damage than chance.

If those who don’t know what dF/dCC and dF/dCD mean, they are measures of marginality in this respect (derivatives if you’re a math person).

I have no kittening idea what you just said but according to wiki chritchance is better until 50% point for point

Wiki is wrong ;( Mind sending the link to it so I can edit the page? I looked, and I didn’t see where it said that.

I edit the wiki all the time for mistakes. You’d be surprised how often they show up, especially for stuff you’d assume to be rock solid by now. I had to fix the graphics descriptions for two legendaries, both pretty recently (you’d assume they’d be right after almost a year into the game). Misinformation is everywhere.

Not true, Manekk. The table supports Faux. It’s just simple calculus and what he proved was that you need chance to be at least 50% greater than CD for another 1% CD to be greater damage than another 1% chance. Indeed, the table shows exactly this. In many cases, I should point out that the difference in damage of having either 5% more in CC vs CD is generally really small but Faux’s theorem holds. Although this is all rather academic as a proper analysis would compare how much precision gets you CC on a primary or secondary stat. It might be that critical damage scales better as a secondary stat, if that makes sense. Faux, please, if you feel like it, extend the analysis to answer that question?

Faux Sheaux.6179:

Wiki is wrong ;( Mind sending the link to it so I can edit the page? I looked, and I didn’t see where it said that.

Wiki is correct, manekk misread the axis on the table.

Sorry, you’ll have to spell it out for me Chopps. To answer which question?

Well, do you always get 5% crit chance from a two handed weapon secondary precision stat? Or is it a little less? How does precision and CD compare as secondary stats? What about when precision is primary stat? And does this support my theory than max ranger DPS would use rampager gear? I know those are sort of ill-defined questions, but that’s what I was getting at.

Okay, I’m assuming you are still talking about CD as critical damage %, not condition damage.

You get 6-7% crit chance from a two handed weapon minor stat. The actual calculation would be:

delta(CC) = rounddown((128 + P(mod 21))/21), where

delta(CC) = change in critical chance (by percent)
P = Precision before equipping weapon
P(mod 21) = remainder after dividing P by 21 —> P(mod 21) is an integer between 0 and 21

So using tables on the wiki, minor attributes in CC and CD give 6-7% and 9% increases, respectively.

Precision as a major stat gives 8-9% CC (using same formula).

[Edit] I don’t want to draw any conclusions for you, but hopefully you can use some of this to draw your own.

That’s enlightening, thanks Faux.

Sorry if your math already encompasses this faux but isn’t there also a large variable of how many times you hit?

Eg. If you only hit twice 50/50 is better. But if you hit 3 times 45/66 is better.

So, in layman’s terms, the extra damage provided by 1% CD is equal to CC/100. The extra damage provided by 1% CC is equal to (.5+CD)/100.

There’s another layer to this when you start looking at gear though. 1% CD always has less cost than 1% CC. You need 21 precision to boost CC by 1%. The trade off between CD and primary stats is between 16:1 and 5:1.

Chopps.5047:

Faux Sheaux.6179:

Wiki is wrong ;( Mind sending the link to it so I can edit the page? I looked, and I didn’t see where it said that.

Wiki is correct, manekk misread the axis on the table.

Did I? where did I do this? I’m thinking you’re misunderstading me more than I do you.

Here’s what I mean:

If you have 45% critchance you gain more by adding 5% more critchance than adding 5% critdamage.

If you have 50% critchance you gain the same from adding 5% critchance or 5% critdamage.

If you have 55% critchance you gain less by adding 5% critchance than adding 5% critdamage.

That’s what I meant and that’s what the wiki says, I can’t see where I misread that table.

If the wiki says that, then it’s definitely wrong. Would you mind linking that exact page please so we can fix it? I’m still not seeing it.

Also, are you sure you aren’t interpretting it incorrectly? If you were saying…

• “If you have <50% more critchance than critdamage then you gain more from adding 5% critchance than 5% critdamage”…
• “If you have 50% more critchance than critdamage then you gain the same from adding 5% critchance or 5% critdamage”…
• “If you have >50% more critchance than critdamage then you gain less from adding 5% critchance than 5% critdamage”…

…then it’d be correct. In fact, that’s exactly what I’m saying as well. The effectiveness of CC is dependent on CD is all I’m trying to explain.

For the math freaks, I will add my grain of salt. The wiki is correct. In fact from Sheaux’s formula (call it a theorem then!) the derivative with respect to CC is proportional to CD+0.5.

Go to the table in the wiki. Pick a column: move along the rows. Calculate the change in damage. What you are looking at is the increment in damage as a function of CC with CD constant. This increment is always constant (by Sheaux’s theorem). You can check that from the table.

Same thing if you pick a row: the increment in damage is proportional to CC, and therefore constant.

The point where the change in damage with CC and CD is the same is when CC=CD+50%.

Check for example CD=0 and CC=50% (first column, middle row): 1.250. Observe how the entries to the right are the same as the entries below. The increments are equal. Since increments are constant inside each row or column, we have proved that the row CC=50% is the same as the column CD=0 (past row CC=50%). In fact, in mathematical terms, that part of the matrix is “symmetrical” (A_ij = A_ji).

If Faux feels like fixing this table, there is a row that is wrong. Check CC=95%. The last 5 entries in that row are wrong (wrong copy/paste I assume). They should be:
… 2.140 2.188 2.235 2.283 2.330 2.378 2.425
instead of
… 2.140 2.188 2.230 2.278 2.320 2.368 2.410

The correct increment is 0.0475 for that row.

Faux Sheaux.6179:

If the wiki says that, then it’s definitely wrong. Would you mind linking that exact page please so we can fix it? I’m still not seeing it.

Also, are you sure you aren’t interpretting it incorrectly? If you were saying…

• “If you have <50% more critchance than critdamage then you gain more from adding 5% critchance than 5% critdamage”…
• “If you have 50% more critchance than critdamage then you gain the same from adding 5% critchance or 5% critdamage”…
• “If you have >50% more critchance than critdamage then you gain less from adding 5% critchance than 5% critdamage”…

…then it’d be correct. In fact, that’s exactly what I’m saying as well. The effectiveness of CC is dependent on CD is all I’m trying to explain.

I’m saying the same thing as you I’m just using diffrent terminology, it’s the same wiki that’s been posted in this thread several times, I’m using plain language aka once you go above 50% critchance is when you want to add crit damage since before that it’s never better point for point.

Sheaux’s Theorem xD It’s literally week 1 calc lol…

Manekk.6981:

Faux Sheaux.6179:

If the wiki says that, then it’s definitely wrong. Would you mind linking that exact page please so we can fix it? I’m still not seeing it.

Also, are you sure you aren’t interpretting it incorrectly? If you were saying…

• “If you have <50% more critchance than critdamage then you gain more from adding 5% critchance than 5% critdamage”…
• “If you have 50% more critchance than critdamage then you gain the same from adding 5% critchance or 5% critdamage”…
• “If you have >50% more critchance than critdamage then you gain less from adding 5% critchance than 5% critdamage”…

…then it’d be correct. In fact, that’s exactly what I’m saying as well. The effectiveness of CC is dependent on CD is all I’m trying to explain.

I’m saying the same thing as you I’m just using diffrent terminology, it’s the same wiki that’s been posted in this thread several times, I’m using plain language aka once you go above 50% critchance is when you want to add crit damage since before that it’s never better point for point.

50% isn’t a threshold. What it means is that if and only if the chance is 50% MORE than damage. In other words, if you have 65% crit chance and 5% crit damage, then 1% damage beats 1% chance. However, if you have 65% chance and 40% damage, the. 1% chance beats 1% additional damage. It’s the difference that has to be at least 50%.

But as others have said and Faux calculated, the armor doesn’t scale in equal increments of 5% crit damage corresponding to 5% chance from precision. What this means is that it’s never as simple as our straightforward cases are showing.

Chopps.5047:

Manekk.6981:

Faux Sheaux.6179:

If the wiki says that, then it’s definitely wrong. Would you mind linking that exact page please so we can fix it? I’m still not seeing it.

Also, are you sure you aren’t interpretting it incorrectly? If you were saying…

• “If you have <50% more critchance than critdamage then you gain more from adding 5% critchance than 5% critdamage”…
• “If you have 50% more critchance than critdamage then you gain the same from adding 5% critchance or 5% critdamage”…
• “If you have >50% more critchance than critdamage then you gain less from adding 5% critchance than 5% critdamage”…

…then it’d be correct. In fact, that’s exactly what I’m saying as well. The effectiveness of CC is dependent on CD is all I’m trying to explain.

I’m saying the same thing as you I’m just using diffrent terminology, it’s the same wiki that’s been posted in this thread several times, I’m using plain language aka once you go above 50% critchance is when you want to add crit damage since before that it’s never better point for point.

50% isn’t a threshold. What it means is that if and only if the chance is 50% MORE than damage. In other words, if you have 65% crit chance and 5% crit damage, then 1% damage beats 1% chance. However, if you have 65% chance and 40% damage, the. 1% chance beats 1% additional damage. It’s the difference that has to be at least 50%.

But as others have said and Faux calculated, the armor doesn’t scale in equal increments of 5% crit damage corresponding to 5% chance from precision. What this means is that it’s never as simple as our straightforward cases are showing.

It’s amusing cause you’re not realizing that you are contradicting yourself now anyways if I was unclear in some way apologies for that I can’t seem to tell you what I mean any more plain than I already have.

This is it, if the wiki is wrong you’ll have to point out where:

“If you have <50% more critchance than critdamage then you gain more from adding 5% critchance than 5% critdamage”…
“If you have 50% more critchance than critdamage then you gain the same from adding 5% critchance or 5% critdamage”…
“If you have >50% more critchance than critdamage then you gain less from adding 5% critchance than 5% critdamage”…

Afaik, I followed those rules in my examples, sorry if it’s confusing mannek. I don’t know though what the value of this argument is besides correcting the wiki. I hope that helps.

Chopps.5047:

This is it, if the wiki is wrong you’ll have to point out where:

“If you have <50% more critchance than critdamage then you gain more from adding 5% critchance than 5% critdamage”…
“If you have 50% more critchance than critdamage then you gain the same from adding 5% critchance or 5% critdamage”…
“If you have >50% more critchance than critdamage then you gain less from adding 5% critchance than 5% critdamage”…

Afaik, I followed those rules in my examples, sorry if it’s confusing mannek. I don’t know though what the value of this argument is besides correcting the wiki. I hope that helps.

I’m not confused about how cc/cd works out, I’m confused why you and others keep saying wiki and/or I am wrong because we are saying the same thing it’s only I am using a diffrent way of saying it in plain english rather than a bunch of confusing math equations.

The thing I really objected to originally was when Faux claimed you needed 100%crit chance for critdamage to become better otherwise critchance would always be better, this is plain false or the wiki has it’s math up it’s kitten in it’s chart.

Saying you need “50% CC” for CD to be worth more point for point is not the same as saying you need “at least 50% more CC than CD” for CD to be worth more point for point.

The “at least _ more _ than _” is what he says you are missing. Without it, what you’re saying is only right assuming that there is 0% CD. What you’re calling “plain English” is missing an important piece of language – the conditional. That condition, the inequality, shows that the effectiveness of CC is dependant on how much CD you have. Leaving that bit out completely neglects to show that dependency.

You were right though. Me saying CC always scales better than CD was wrong. I immediately corrected myself after your post, and the math was to show where I was coming from. Not understanding the math is fine, but I outlined exactly what it meant underneath in very “plain English”.

Anywho, that’s as layman as I can put all of this. If you still don’t see it, I really am sorry. I just don’t feel like dragging this out any further because it’s really just an argument for the sake of arguing at this point. Fighting over diction is the worst kind of nitpicking to get caught up in imo.

I was wrong. This is the most layman I can put it.

• Anything above or to the right of the ladder will get more benefit from adding CC than CD
• Anything in the ladder gets the same befenfit from adding CC as it will from adding CD
• Anything below or to the left of the ladder will get more benefit from adding CD than CC

You will also notice that for any given sum CC+CD, the boxed values are the maximum amounts you can get for all combinations of CC and CD (all values diagonal to the box running from the bottom-left to top-right).

Cheers.

Anyone want to take a crack at a spreadsheet that shows how much precision the next point of CD is worth? I’ve started one, but if what I’ve done is correct, CD is almost always better if you have to choose between precision and CD.

Yeah… for the most part CD will do better than precision since precision —> CC doesn’t scale quite as well as the direct CD benefits you get.

So in other words, the CC to CD comparison doesn’t mean much because CD competes with precision for stat allocation, not CC.

Meh, it still helps to know what’s going on with the numbers. You never know when they will be relevant to fine-tuning your build.

Faux Sheaux.6179:

Saying you need “50% CC” for CD to be worth more point for point is not the same as saying you need “at least 50% more CC than CD” for CD to be worth more point for point.

The “at least _ more _ than _” is what he says you are missing. Without it, what you’re saying is only right assuming that there is 0% CD. What you’re calling “plain English” is missing an important piece of language – the conditional. That condition, the inequality, shows that the effectiveness of CC is dependant on how much CD you have. Leaving that bit out completely neglects to show that dependency.

You were right though. Me saying CC always scales better than CD was wrong. I immediately corrected myself after your post, and the math was to show where I was coming from. Not understanding the math is fine, but I outlined exactly what it meant underneath in very “plain English”.

Anywho, that’s as layman as I can put all of this. If you still don’t see it, I really am sorry. I just don’t feel like dragging this out any further because it’s really just an argument for the sake of arguing at this point. Fighting over diction is the worst kind of nitpicking to get caught up in imo.

I know I was right and I know you corrected/clarified yourself in the next post too the only reason we are arguing despite agreeing is cause Chopps is busting my chops (pardon the pun) in a tone that implies I can’t read the chart and he also said several times I was wrong, to be fair I was not as clear on what I meant from the beginning as I’d hoped either but as I clarified once you have above 50% critchance point for point critdamage is always better and likewise when below 50% critchance point for point more critchance is always better starting from scratch (0% of either) this is entirely true.