Critical and Block v3.0

[jlegendwielder]

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...)

[Yuna]

valdus, thank you for this thread. i was so confused about the new crit and block system until i read your post. guess it's easier for me to understand mathematical formulas and charts than those explanations given on yt lol.

[ValdusWildheart]

Valdus...will you marry me?

LOL?

Absolutely love the graphs. What software are you using?

Excel for 2D, but I have an older version that isn't that great with surface graphs, so that I plugged in to Wolfram Alpha.

Is there any way you can graph the expected value of the damage %?
When 2 wizards have identical critical and block, as you mentioned, there is a 25% chance to outright block and a 75% chance to have a *1.25 boost, so the expected value would be: (1.25)*75% + (1)*25% = 1.1875, or an expected 18.75% damage increase.

So, here it is. On expected damage you have to factor in the additional probability of a critical that is blocked vs. unblocked, so you have 3 possible outcomes (and the examples, again assume equal scores for critical and block at level 100+ for modeling purposes -- or 75% critical chance, 25% block chance. For a 100 pt wand strike, you would have a 0.5625 chance of landing an unblocked critical and doing 1.25x damage, which would give you an expected value of 114).

Weighting the values by probabilities (note, I did not add in any of the max/min limiters -- I have Thanksgiving to prepare for! But it doesn't really change the shape and idea) and simplifying gives you:

Graphing gives you a very similar shape to the original damage graphs:

If helpful, I can paste in the table with the factors to multiply by if anyone is interested. You could use it like a tax table :D Note, that as @Ratbeard said, these values can be adjusted -- so they aren't forever values. But, as we've all learned in math class: it's the idea that counts, not the specific answer

And thus endeth the lesson.

[KingNothing]

Ew! Does someone have a moist towelette? I picked up the new critical/block system and it yacked math all over me. Gross!

[Patrick FairyStalker]

Beautiful! Just what I was looking for. I think that it makes it much clearer that block beyond 200-300 is definitely worth reaching for, but there are still diminishing returns (around the 400 range), which wasn't as clear in the first plot.

One last thing: would it be possible for you to put another expected damage graph, but with block rating on the x-axis and critical rating as the plotlines? I think this would give a pretty visually definitive answer to "how much critical should I stop at?"

EDIT: I multiplied everything out and your math checks out, as hideous as it looks

[Robobot1747]

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

[ValdusWildheart]

One last thing: would it be possible for you to put another expected damage graph, but with block rating on the x-axis and critical rating as the plotlines? I think this would give a pretty visually definitive answer to "how much critical should I stop at?"

Yes, but I may have to insist on that wedding now...

EDIT: I multiplied everything out and your math checks out, as hideous as it looks

Wow a marriage proposal AND sweet nothings? I'm speechless.

[Dylan Windwalker]

Just gonna put this in here....

[Patrick FairyStalker]

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.

Just gonna put this in here....

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

Yes, but I may have to insist on that wedding now...

It's official.

[RedValkyre99]

Just gonna put this in here....

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.