Critical and Block v3.0

[Willowdreamer]

I can't tell if this is a joke or not... as engineers we generally use differentiation to find the rate of change of a surface (in multiple dimensions a gradient). In the case of a behaved surface we can solve for minima/maxima directly. In a more complex surface, we generally control the rate of an optimization solver. This isn't the only usage but it is the primary one. The picture looks like a straight forward math exercise but in practice we generally form a mathematical equation representing a cost function for a specific problem we are trying to solve. The partials (again I'm assuming multi-dimensional problems since this is usually the case) are used to control the step sizes (for more rapid convergence). For a split second, I thought about calculating and plotting the partial derivatives here but looked at the surfaces and realized I didn't need to in order to gain the appropriate insight.

I think that the joke is - those who don't use this type of math on a daily basis, especially if they understood it way-back-when in school - we find it to be hieroglyphics when we are older.

I found it funny.

Kudos to those who can do these calculations and keep the world turning!

[ValdusWildheart]

Something interesting I found after messing with the equations that I think @Eric Stormbringer would be interested in, especially now that Storm is considered the "critical" school. See attached.

This is great analysis. I definitely wanted to put together some strawmen (typical PvP gear sets, specific end world sets, etc.) and test real world effect of the change, but this definitely gets to the heart of it. The other thing I would be interested in is maybe some break even / rule of thumb type analysis. Maybe in December...

Haha, I can just imagine people reacting to storms wandering around with 2-3,000 critical ratings! Good times.

Now, back to Thanksgiving preps. Ugh.

[Flux]

Just gonna put this in here....

In college right now. Have a test today and I know the problems look similar to this, but still have no clue how to even remotely begin them. Envious that you could EVER solve that lol

[Eric Stormbringer]

Something interesting I found after messing with the equations that I think @Eric Stormbringer would be interested in, especially now that Storm is considered the "critical" school. See attached.

If someone has 200 block, you need 400 critical to do 29% damage, and 500 critical to do 35% damage.
If someone has 400 block, you need 800 critical to do 29% damage, and 1000 critical to do 35% damage.

I forsee a problem in the future. Right now, an average storm might be able to have about 100 more critical than the average fire (easy number for the sake of argument). But, in the long term, as block increases, the average storm will need to widen this gap to 200 to maintain this same level of critical dominance.

Let's say, today an average PvP fire has 400 critical, and an average PvP storm has 500 critical. The storm has 6% more damage from critical.
In the future, when an average PvP fire has 800 critical, a storm will need 1000 critical to maintain this 6% advantage.

Why is this a problem? For one: pets. Currently, an ice wizard is able to get the same amount of critical from a pet as a storm is. They will need to revamp pet criticals so that it's not equal for every school. Storm Assailant should be a greater rating than Ice Assailant. (Honestly, Storm Dealer should be more than Ice Dealer. But that's for another day).

For another: the gap between storm critical and every other school's critical needs to widen. BIG time. Right now, it's easy for all schools to reach 800+ rating without much sacrifice to their other stats. This future 200 gap I mentioned is between fire and storm. Between ice and storm, this gap would need to be 400+.

Overall, however, I think this has been a beautiful solution. It makes sense that critical needs to progress much faster than block, because it's easier to gain high critical to your own school vs. getting high universal block.

As an engineer, even I wouldn't be able to tell you. But isn't implicit differentiation just nice to know?


It's official.

I've been holding off on the school-specific feedback to give the Devs the chance to audit stats. It's a monumental undertaking so I've decided to give them a chance to address the principles before they tackle the specifics. Believe me though- I've noted these changes and the potential effect on the Storm school. Once the audits are completed these will be addressed. Luckily KI is open to feedback i.e I was not happy with Storm spell's initial effect and made it known.

[KieranCaster]

Valdus, like a hawk encumbered with his hood,
Explaining metaphysics to the nation.
I wish he would explain his explanation.

Let me try...(with apologies to Quaker Oats)

My eff of ex is better than your eff of ex
My eff is better than yours
My eff is better ‘cause it’s powered by Dev’lration
My eff of ex is better than yours

And everytime I see Eric posting, it reminds me again of his mega-group, Eric and the Minions, and their epochal mega-hit of 2003, "Crit This!"

(And, Valdus and Patrick, please, get a room...)

All my Ex's Live in Texas.


Regards,
George Strait

I appreciate all the math you're doing, but I'm going to stick with "more crit good."

This post, my friends, is Ockham's Razor. Sir William of Ockham, a 14th Century Philosopher would agree with Robobot1747.

Despite all the math, and using cave man talk:

More Critical - Good.
Less Critical - Bad.

I am appreciative of the math by Vladus and the tinkling all over it by Patrick. But most appreciative of the time and effort by both to provide the community with explanations.

Thank you, and happy thanksgiving!

[Cody Nightblade]

Great guide!

There are two things I've noted regarding the current version of the Critical / Block System....

[needs further testing]
The game might use the caster's level only as a determining factor for the chance to Critical or Block.

I went and tested equal levels of Critical and Block between two of my Wizards.
(the levels: 120, 19)
As expected, when testing for my level 120 Wizard's Criticals, he had ~75% chance to critical.
However, when I reversed it and tested for my level 19 Wizard, the chance was much lower.

I will have to do more testing on this to confirm, but an explanation I found was that it takes the caster's level only for both the Critical and Block chances.
For example, equal Critical / Block at Lv20 => 15% Crit Chance, 5% Block Chance.
(The idea was that Level was a direct multiplier to Critical and Block chances, and that the multiplier for Lv101+ is the same as Lv100.)


[very technical detail]
When calculating the Critical Damage boost, the game takes your actual Critical and actual Block.

One of my notable test cases was for a 2738-DMG Judgement.
The caster had "3 Critical Rating" (actually 2.79, from Critical Hitter), while the enemy had exactly 3 Block Rating.
Instead of the critical landing for the 3422 DMG (3 Crit / 3 Block), it landed for 3385 DMG (2.79 Crit / 3 Block).

This difference is so small when you have decent Critical / Block, but I decided to note it here for completeness.


I do wonder how this applies to spells that are not single-target ― is your chance to Critical those kinds of spells a direct multiplier from your Level?
(Block is self-explanatory.)

Once again, well done on the post!

[ValdusWildheart]

The game might use the caster's level only as a determining factor for the chance to Critical or Block.

Yes, level does factor into it -- but only for critical. That ratio you have is reduced by level. These charts are for level 100 but you have to multiply by the caster's level to get the ultimate ratio. So e.g., with the same critical your chance to roll a crit is 75% at level 100, 37.5% at level 50, and 7.5% at level 10. Level doesn't affect the block score, but the crit/block ratios are dependent on one another.

One of my notable test cases was for a 2738-DMG Judgement.
The caster had "3 Critical Rating" (actually 2.79, from Critical Hitter), while the enemy had exactly 3 Block Rating.
Instead of the critical landing for the 3422 DMG (3 Crit / 3 Block), it landed for 3385 DMG (2.79 Crit / 3 Block).

I'm wondering if those crit scores were from a pet? If so, you'd have to make sure the stats developed on the pet were exactly equal as well (i.e., agility, will, and power all the same scores). What's displayed in the wizard stat page is rounded and could account for the difference.

I do wonder how this applies to spells that are not single-target ― is your chance to Critical those kinds of spells a direct multiplier from your Level?

It applies to both AoE and single target spells, although with an AoE each target may have their own block which will result in a different damage amount. There does seem to be a bug right now where critical block indicators are not showing.

Good questions, and glad you liked the post!

[jlegendwielder]

All my Ex's Live in Texas.


Regards,
George Strait

Thang is, ol George? He aint got no exs!

Lessen you were speakin all personal like which case I hope all yorn live in Comfort.

[Cody Nightblade]

I'm wondering if those crit scores were from a pet? If so, you'd have to make sure the stats developed on the pet were exactly equal as well (i.e., agility, will, and power all the same scores). What's displayed in the wizard stat page is rounded and could account for the difference.

Yes, I deduced that the reason the Critical Boost wasn't a clean 25% was simply because of the fact that the Critical Hitter gave 2.79 Critical Rating, instead of a flat 3 Critical Rating.

It applies to both AoE and single target spells, although with an AoE each target may have their own block which will result in a different damage amount. There does seem to be a bug right now where critical block indicators are not showing.

Ah, okay, but I do wonder for the chance to Critical non-single-target spells...
e.g.:
Lv100 Attacker has 300 Critical, uses Sandstorm.
1st Enemy has 300 Block.
2nd Enemy has 150 Block.

What would the chance of Critical for the Sandstorm be? 75%, 86%, 100%, or something else...?

Also, I'm pretty sure the Critical Block indicator only fails to show if the attack is not single-target.


Also, I've noted that for some reason, PvE enemies do not seem to Critical at all.....
(Not a single Critical from the Death Ghultures I farmed recently, even though I should have had a few occurrences of them.)
I wonder if the "enemy level" is 0....