I came across this thread on Reddit yesterday where someone asked whether CHD or CHC is better on a ring. Obviously, the immediate quick answer in my head was "CHD". However, the answer is not always correct - as so often, the right answer is "it depends". As the math went on crazy in this thread, it occurred to me that people were doing more calculus than required to solve the Schrödinger Equation, when actually it's completely independent of your DPS and all other stats besides CHC and CHD. So... I built a super quick single-service webpage that answers that question on first glance - and you don't need a degree in mathematics for that ;-)

(Note: the table looks completely weird in IE... use Chrome or Firefox, please.)

It's pretty simple: On the left, you enter the competing stats on an item (for example, in Reddit OP's case 6% CHC vs. 50% CHD on a ring). In the middle, you enter your current stats - don't forget to include buffs like Bait the Trap or Crusader's Judgement-Resolved or Laws of Valor that you anticipate to have in a rift; at the same time, obviously remove the stats you gain from the item slot you're currently comparing (e.g., in this case, the ring you want to replace).

You'll see the "winner" on the right and how much better the given stat is. Adjust your CHC/CHD value (because let's be serious, getting perfect rolls isn't exactly easy) to see how non-perfect rolls turn out. The table at the bottom will automatically update - and show you how much changes in gear (or buffs) will skew the result in favor of the one or the other stat.

Let me know if you spot any mistakes, or have any suggestions for improvements. Thanks!

remember to take into account also proc on crit (like solanium) and skll that interact with crit (battle rage - bloodshed)

Well... there's no way to quantify if you're using something like Solanium or Nightstalker. In those cases you probably won't ever ask that question, but you'll always want both CHD and CHC and in case you have to make a choice (rings) you'll go for CHC, no matter the DPS. This calculator cannot take such factors into account and is not made for this; it's only for the majority of players that does not have any "on crit" procs.

I wonder why you would make a calculator for this. It is known you have to aim for a 10:1 CHD:CHC ratio for the best damage output.

If your calculator would take other things into account (ambush on a dh for example might oneshot a mob with a crit if you have more CHD, other procs that happen on crit, ...) it would be good, but a complete post with a link to a website, where you enter numbers, that basically says 10:1, seems a bit much.

PS: I'm all for theory crafting and calculations to optimize your setup, so keep it up

I wonder why you would make a calculator for this. It is known you have to aim for a 10:1 CHD:CHC ratio for the best damage output.

Go to the website and look at the default values: 450% CHD, 50% CHC on your char, and you find a ring and want to know whether it's better to go for 50% CHD and 6% CHC. Simple, right? Go for 10:1 ratio by choosing 50% CHD, and you end up at 500 CHD and 50 CHC, perfect, isn't it? Well... it's not. As you can see, CHC is better.

The 10:1 ratio is a rule of thumb, similar to the 10:1 armor:allres ratio, but it's not the general "always right" answer. The devil is in the detail. That's why this calculator can indeed be useful. Granted, probably only for rings because in all other cases the item slot tells you what to do (amulet always CHD over CHC, gloves always CHC over CHD, and on no other slot than rings do you ever have the choice between both stats).

according to calculator, the rule of thumb 1:10 should be updated in 1:8,33

Haha
It's just due to the fact that you're comparing 6% CHC vs 50% CHD, which is not a 1:10 ratio either. If you compare 5% CHC with 50% CHD then it's back to 1:10 ratio again ;-)

I wonder why you would make a calculator for this. It is known you have to aim for a 10:1 CHD:CHC ratio for the best damage output.

Go to the website and look at the default values: 450% CHD, 50% CHC on your char, and you find a ring and want to know whether it's better to go for 50% CHD and 6% CHC. Simple, right? Go for 10:1 ratio by choosing 50% CHD, and you end up at 500 CHD and 50 CHC, perfect, isn't it? Well... it's not. As you can see, CHC is better.

The 10:1 ratio is a rule of thumb, similar to the 10:1 armor:allres ratio, but it's not the general "always right" answer. The devil is in the detail. That's why this calculator can indeed be useful. Granted, probably only for rings because in all other cases the item slot tells you what to do (amulet always CHD over CHC, gloves always CHC over CHD, and on no other slot than rings do you ever have the choice between both stats).

From what I can find, the "crit factor" is calculated like this:

Crit Factor = (Crit Chance * Crit Damage) +100%

The 100% at the end is because if it's a non crit, you can ignore that. So we can drop that. That means, whatever CHC*CHD is the highest, is the best

Now lets go with your example: 50%CHC and 450%CHD, adding 6%CHC or 50%CHD.

With 6%CHC: (1+0.56)*(1+4.50)=8.58

With 50%CHD: (1+0.50)*(1+5.00)=9

So, 50% CHD would give you better sheet dps, or am I missing something?

Edit: ok I see, if you go (0.56*4.50)>(0.50*5.00), will have to double check what the exact calculation is, cause they are both a bit different.

Edit2: did some new calculations, and seems you are right. Did my first calculations based on a slightly different formula I found.

We cannot ignore the "non-crit" at the end, because it affects the overall damage in the end. That being said, it never works in favor of CHC but always for CHD (as the number of non-crit hit goes down when stacking up more CHC). But anyways - let's take a closer look at the example. We hit for 1000 damage a hundred times (how convenient for math, isn't it?).

With 6% CHC we hit 56 times for 5500 damage (450% CHD means 450% additional damage to each crit) and 44 times for 1000 damage, for a combined 352k.

With 50% CHD we hit 50 times for 6000 damage and 50 times for 1000 damage, for a combined 350k.

CHC is winning the race by 0.57%... which is exactly what my calculator says. *Phew* I have to be honest, for a moment you had me thinking I forgot something there ;-)

The problem in your formula is that (CHC * CHD) + 1 does not equal (CHC+1)*(CHD+1); the latter would end up being CHC*CHD + CHD + CHC + 1.

Edit: Wow, just saw your edit right now... was being distracted. Clearly too late for that stuff, gonna log off ;-) Hope the issue is resolved. Thanks for checking though - it's always good to double-check those numbers and calculations!

Can you link me that thread from the official forums with that discussion? Sounds interesting.

As said in the first post, those 1:10 ratios (for CHC/CHD and armor/allres) are a rule of thumb and good for estimates, but applying that blindly to every decision is just plain stupid :-)

Thanks for the link and for plugging my website into that discussion

Yeah... that discussion isn't healthy. Whenever I read this I know why I stay away from the official forums. Even the knowledgeable, usually helpful members of the community in this thread say things that are flat out wrong. It seems that the offensive atmosphere of the official forums just poisons each and every discussion...

Even looking at your table shows that the 1:10 ratio is off, it's output is rather skewed towards CHC. Take 48% CHC / 400% CHD for example. Adding 6% CHC resulting in 54%/400% (far far away from 1:10) is as good as adding 50% CHD.

Yeah, but that's just because of the imbalance of stats that's provided on the ring slot. It's basically the only example; on gloves it's so obvious that we don't need to talk about it, on amulet it's even and you never want an amulet without CHD, and on no other slot do both CHD and CHC appear, which makes this discussion always just about rings. I know a lot of people that went religiously on a long farming trip to find a ~45%+ CHD RoRG because they thought it'd be better than 6% CHC. Talking to them makes you feel like telling creationists about Darwin - no matter how much proof you bring on the table, they're just gonna stick to their weird theories even more. Those people cannot be convinced by facts, so I've given up. They have to find out about it on their own ;-)

http://d3resource.com/critcalc/

(Note: the table looks completely weird in IE... use Chrome or Firefox, please.)

It's pretty simple: On the left, you enter the competing stats on an item (for example, in Reddit OP's case 6% CHC vs. 50% CHD on a ring). In the middle, you enter your current stats - don't forget to include buffs like Bait the Trap or Crusader's Judgement-Resolved or Laws of Valor that you anticipate to have in a rift; at the same time, obviously remove the stats you gain from the item slot you're currently comparing (e.g., in this case, the ring you want to replace).

You'll see the "winner" on the right and how much better the given stat is. Adjust your CHC/CHD value (because let's be serious, getting perfect rolls isn't exactly easy) to see how non-perfect rolls turn out. The table at the bottom will automatically update - and show you how much changes in gear (or buffs) will skew the result in favor of the one or the other stat.

Let me know if you spot any mistakes, or have any suggestions for improvements. Thanks!

also:

always good advice

thanks for this!

I wonder why you would make a calculator for this. It is known you have to aim for a 10:1 CHD:CHC ratio for the best damage output.

If your calculator would take other things into account (ambush on a dh for example might oneshot a mob with a crit if you have more CHD, other procs that happen on crit, ...) it would be good, but a complete post with a link to a website, where you enter numbers, that basically says 10:1, seems a bit much.

PS: I'm all for theory crafting and calculations to optimize your setup, so keep it up

The 10:1 ratio is a rule of thumb, similar to the 10:1 armor:allres ratio, but it's not the general "always right" answer. The devil is in the detail. That's why this calculator can indeed be useful. Granted, probably only for rings because in all other cases the item slot tells you what to do (amulet always CHD over CHC, gloves always CHC over CHD, and on no other slot than rings do you ever have the choice between both stats).

It's just due to the fact that you're comparing 6% CHC vs 50% CHD, which is not a 1:10 ratio either. If you compare 5% CHC with 50% CHD then it's back to 1:10 ratio again ;-)

From what I can find, the "crit factor" is calculated like this:

Crit Factor = (Crit Chance * Crit Damage) +100%The 100% at the end is because if it's a non crit, you can ignore that. So we can drop that. That means, whatever CHC*CHD is the highest, is the best

Now lets go with your example: 50%CHC and 450%CHD, adding 6%CHC or 50%CHD.

With 6%CHC: (1+0.56)*(1+4.50)=8.58

With 50%CHD: (1+0.50)*(1+5.00)=9

So, 50% CHD would give you better sheet dps, or am I missing something?

Edit: ok I see, if you go (0.56*4.50)>(0.50*5.00), will have to double check what the exact calculation is, cause they are both a bit different.

Edit2: did some new calculations, and seems you are right. Did my first calculations based on a slightly different formula I found.

With 6% CHC we hit 56 times for 5500 damage (450% CHD means 450% additional damage to each crit) and 44 times for 1000 damage, for a combined 352k.

With 50% CHD we hit 50 times for 6000 damage and 50 times for 1000 damage, for a combined 350k.

CHC is winning the race by 0.57%... which is exactly what my calculator says. *Phew* I have to be honest, for a moment you had me thinking I forgot something there ;-)

The problem in your formula is that (CHC * CHD) + 1 does not equal (CHC+1)*(CHD+1); the latter would end up being CHC*CHD + CHD + CHC + 1.

Edit: Wow, just saw your edit right now... was being distracted. Clearly too late for that stuff, gonna log off ;-) Hope the issue is resolved. Thanks for checking though - it's always good to double-check those numbers and calculations!

As said in the first post, those 1:10 ratios (for CHC/CHD and armor/allres) are a rule of thumb and good for estimates, but applying that blindly to every decision is just plain stupid :-)

Yeah... that discussion isn't healthy. Whenever I read this I know why I stay away from the official forums. Even the knowledgeable, usually helpful members of the community in this thread say things that are flat out wrong. It seems that the offensive atmosphere of the official forums just poisons each and every discussion...

Yeah, but that's just because of the imbalance of stats that's provided on the ring slot. It's basically the only example; on gloves it's so obvious that we don't need to talk about it, on amulet it's even and you never want an amulet without CHD, and on no other slot do both CHD and CHC appear, which makes this discussion always just about rings. I know a lot of people that went religiously on a long farming trip to find a ~45%+ CHD RoRG because they thought it'd be better than 6% CHC. Talking to them makes you feel like telling creationists about Darwin - no matter how much proof you bring on the table, they're just gonna stick to their weird theories even more. Those people cannot be convinced by facts, so I've given up. They have to find out about it on their own ;-)