Critical and Block v3.0

[ValdusWildheart]

EDIT: Please note KI updated the formulas for PvP so while the concept is the same, the math is a bit different in the arena.

With the new critical and block system in Wizard101, it's difficult to get a precise answer on "what should my stats be?" With this revision, we're back to a relative statistic that varies based on your target's stats. Therefore, there is no specific number that can sum up your chance of critical and damage based on your wizard alone.

However, the developers gave us a general formula and some specific examples which allows us to derive what it is that is happening behind the scenes. I'll go through the mechanics, and give a tl;dr at the end for those who had to suppress a scream when they looked at the charts below. Please feel free to ask questions, I promise to try to be more succinct when answering (but this is a fairly complex mechanic now).


Base case: Opponent has zero block

The chance to critical is identical to level when an opponent has zero block. Chance to critical varies from 1% at level 1 to 95% at levels 95 and over.

• For level-based critical to kick in, you must have a critical rating of 1 (because anything times zero is zero).
• Example: A level 50 has a 50% chance to critical. A level 95+ will have a 95% chance to critical (it's currently capped there).
• The damage will be 2 times whatever the damage would have been without the critical

Typical case: Opponent has some (a lot of) block

The chance to critical will be modified based on a combination of your critical and the opponent's block.

• With identical scores for critical and block, a crit will have 3x the chance of occurring as a block.
• Example: At level 100+ equivalent scores will give the caster 75% chance to critical and defender 25% chance to block regardless of score (so, the same if each tall to 100 or 1,000). There will be a 25% boost in damage done if the crit lands.
• Example 2: At level 50, the chance is .50 of that same ratio, or 37.5% to critical and 12.5% to block with the same scores
• To get a situation where there is a 50% chance to crit and block, you need 3x the block rating of the opposing critical rating

Chart Madness (Everyone try not to cheer at once):

One of the interesting things about how this system works is it isn't linear. Therefore you get a LOT of gain at the lower ends, but then it gets much more difficult to increase your percentages as they get higher. I think this accomplishes what KI set out to do very well, which is to get us to make thoughtful trade-offs with our gear. What is the right level to stop chasing crit? It's a personal decision based on your specific goals.

To demonstrate this accelerating / decelerating trade-off I've posted the formula, the 3D graph, and a 2D graph of each affected stat. The royal blue line on each represents a score of 200 block vs. a range of critical on both charts.


Critical: Everyone's favorite stat, so let's start here. You can see right away from the formula, if someone has zero block that zeros out and your critical chance is just your level in percent. But starting on the lower left corner of the 3D chart, you can see a really steep increase where just a few crit points gets you a lot of chance vs. an opponent. Once you get to about 200 crit, it flattens out a lot (the red shaded area) regardless of your opponent's score (from 0 to 600 on the right hand side).

From the 2D graph, you can see the inflection point represented by the blue arrow. It's not a lot (Each line represents block in increments starting at 5 through 600). Those curves are steep and flatten quickly. Yes, it keeps increasing as you add critical but you'd have to go from ~400 to ~700 to add an additional 10% chance to crit vs. an opponent at 600 block. At 300 block, it's even flatter! You'd need to go from ~350 to 700 for that additional 10% chance.

Block: Similar to critical, you can see a little block goes a LONG way.

Damage is even more extreme. With block now modifying the damage done, you can see a rapid deceleration into the blue zone. From the 2D graph, you can see a larger change from block from 5 to 25 than from 500 to 600. The delta from 5 to 200 is much bigger than from 200 to 600.

Example: At level 100+ with a critical of 700 and and opponent with a block of 200, you'd have ~90% chance to critical, they would have ~10% chance to block, so it will very likely land. But it will only boost damage by a little over 50% based on their damage reduction.

TL;DR: Some block and critical goes a long way. A really high score at the expense of other stats probably won't do a lot for you unless you are chasing a very specific goal.

EDIT: For me, personally, I'm an 80/20 person and don't PvP. So I'm probably going to aim for about 200 block, and whatever critical results from getting good, balanced gear for questing. For farming, you should be able to fully critical all day pre Celestial / Halfang with just a tiny critical number if you're Level 100+ (but there seems to be some bugs currently, hopefully KI will iron those out).


Now, who missed my posts? LOL, what? Crickets????

[Zexion]

So... this means if you are level 100+ with literally 1 critical rating, you would have a 100% chance to critical in the early worlds?? o_o

Also, does this mean critical and block decay are nonexistent now?

Thanks for this post!

[Patrick FairyStalker]

Valdus...will you marry me?

I know you put a lot of work into this, but is there any way you can graph the expected value of the damage %? Right now you separate the "out-right block" case and the "non-blocked damage multiplier" case.

You almost definitely understand basic probability, but in-case you don't:
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.
If you do a base 100 damage spell many/infinite times, you can expect an average of 100*1.1875 = 118.75 damage.

Correct me if I'm wrong, but the formula would be:
(1+Damage%)*(Critical%) + (1)*(Block%), that is:

Or more aesthetically:
blah blah algebra blah into:



(This formula would give 1.1875, subtract 1 for the expected 0.1875 or 18.75% boost)
I did some basic calculations and as C -> infinity, E[damage] -> 2.0; as B -> infinity, E[damage] -> 1.0, as expected.

I think this would give a better idea of whether investing more in block or critical is better.

Absolutely love the graphs. What software are you using?

[KieranCaster]

Dang bro. This game IS rocket science. We're those space-time graphs?

As I've said before,

The most critical thing for me is to know if you want Fries with that burger.

Regards,
FSU Grads

[Dylan Windwalker]

I think I'll just crawl back to blissful ignorance about the critical system.... Ewwwww Math, what a strange creature.....

[ValdusWildheart]

So... this means if you are level 100+ with literally 1 critical rating, you would have a 100% chance to critical in the early worlds?? o_o

Yup. [EDIT, by yes, I mean no. Please see @Eric Stormbringer's and @Ratbeard's comments below. I didn't see the bit where they had a min and max limit/cap on the values. So 95% max chance of critical. The shape of the charts stays the same, just flattens at 95% instead of 100.]

Also, does this mean critical and block decay are nonexistent now?

Yup.

Almost every bit of v2.0 is now scrapped, including that awful threshold and decay. Frankly, this is what they should have moved to once they decided they didn't like the original critical and block. I think it's a really elegant solution. I'm a fan.



@Patrick FairyStalker - I see what you're saying. Good idea. I'll see if I can rustle something up tomorrow!

[Willowdreamer]

Excellent information, thank you! I must say that I am enjoying the Critical/Block I'm experiencing in Karamelle on my Life Wizard compared to earlier worlds like Mirage and Empyrea where every enemy seemed to block every critical attack.

[Eric Stormbringer]

Great post Valdus. Quick minor correction- The Devs have stated that critical is hard-capped at 95% so against a 0 block opponent you have a 95% chance to crit max(instead of 100%)

[Happy Fun Ball]

They still need to fix that glitch where it looks like an enemy doesn't block, but it actually does.

[Ratbeard]

Almost every bit of v2.0 is now scrapped, including that awful threshold and decay. Frankly, this is what they should have moved to once they decided they didn't like the original critical and block. I think it's a really elegant solution. I'm a fan.

Nice work.
I am glad you like it. I am not 100% satisfied because of certain deficiencies the system is showing, but I think this "tool" gives us most of what we need to tweak to taste:

Base Chance is a configurable parameter. Perhaps (level/2)% is a better fit (meaning capped characters would now have a base max of 70%). I am leaning this direction because players are unused to critting so much, but this might simply be a case of players needing more time to understand what the s
Min and Max chance is a configurable parameter. We just changed the min clamp from 5% to 0% to quickly address the "Lost Souls are critting!?" issue. This was due to a misunderstanding on my part of when in the calculation the clamp was performed. Since the only way to have 0% is to have 0 stat, and since that mostly affects mobs, I don't think we'll need to revisit this.

Block Scalar is a configurable parameter. The Block scalar is the "3" in the denominator under Block. Reducing this scalar increases the value of Block, which means less critting and more blocking. We might reduce this scalar in an upcoming patch. I don't mind players critting more in PvE, but some folks have said it "feels weird" to crit so much, so we might adjust. Or we might wait for you to get accustomed to the new feel.

Crit Scalar is a configurable parameter. That's the "3" in the denominator on the crit multiplier. Reducing this value means that crit counts for more, and the damage mult will go up. We might tweak this, too, based on player feedback.

These parameters are all configurable by Design, with no additional code required. We can not change these config files without a build - so we can't change them willy-nilly - but it does mean that we can be responsive to player feedback without requiring new code. Speaking from the Design side, I'm super happy about that - and you should expect to see more along those lines since it is a major part of my design philosophy.

Last but not least (although for some of you, perhaps this is the most important thing and should be mentioned first...) these parameters are configurable separately for PvE and PvP so we can tailor each experience to the tastes of those specific players.