Investigating Critical Hit Chance

Does anyone know the formula for what your critical rating is? There have been some changes in the last year, and after searching the web, I've come up a little short. I'm not the best internet searcher (and not the worst).

I did find these informative articles on Duelist:
http://www.duelist101.com/news/site-news/wizard101-critical-calculator/
http://www.duelist101.com/news/battle-points-critical-formula-revealed/

Unfortunately, these articles are old. I did check against them; but in the case of the calculator, it couldn't handle having jewel sockets, and doing their math against my pieces didn't add up. I'm sure it did 3 years ago, but now, things have changed enough that this formula is broken.

Here are some helpful pictures to illustrate my confusion as to what critical rating means as a percentage.

Here's my necromancer, with a little Christmas coloring for the holiday season. You can't see the wand hovering over the life symbol, but that's what's going on. All of my critical numbers other than Death are 171, because the Dragoon's Capitano Hat and Luphilim's Grim Footguards give universal critical rating. At level 114, with a critical rating of 171, I have a 1% chance to critical. Oof!

So how does 348 figure? Will it be a hair over double the percentage for the others? Let's see.

Well, that's a lot more than 2% or 3%, but I don't much know why. I checked on Alexander, who currently is only level 111 but has a higher critical rating and percentage.

Alexander's Critical Rating is 654, and he has a whopping 79% chance to critical. Those other scores of 231 are from universal critical numbers, and their critical percentage is a measly 7%.

None of this lends itself to figuring out how critical percentage relates to one's critical rating. The old formula from the links above point to adding each piece's critical percentage separately and coming up with a figure. If you were a high level character, this would be bad news for any critical jewels, as the minimum number you needed to get a 2% bonus at level 111 or above would be 38 critical. And since the floor for any piece was a guaranteed 1%, you could just equip the most basic critical jewels. They would have the same percent chance as your most potent jewels.

As I mentioned above, that's NOT how it works.

To test this out, I unequipped my athame from Alexander. It's the one with a pair of critical jewels and nothing else to add to the critical rating. By the old rules, it should only lower my percent chance by 2. But it lowered it by 5 percent! I then unequipped everything, and put the athame back on. My percent chance went from 0 to 1.

Looking above at John, for all of his non-Death critical ratings, they were all capped at 1 percent, but he had two pieces with universal critical ratings. By the rules of 2013's formula, I should have a minimum of 2%.

So, I did some trial and error. It doesn't give a formula, but it does allow for some helpful approximations.

A word of caution: it was late when I was playing around with equipping and unequipping and writing down scores. I may have written down numbers from one character and entered them for the other. Your level makes a difference with your critical rating. I was able to get the same critical rating number for both John and Alexander, but they both displayed different percentage chances (Alexander was 1% higher). The reason is that your chance degrades as you level up. There have been a number of people complaining about leveling from 110 to 120, because it meant their critical hit and block chances would go down as they did. In order to compensate, they would have to find a way to increase their critical ratings, but newer and better gear pieces are hard to come by.

So, here are the numbers I have for John, my level 114 Necromancer.

Critical Rating / Critical Hit Percentage
171 / 1%
180 / 1%
215 / 3%
241 / 7%
276 / 12%
348 / 20%

That's just a few numbers, so here's a few more from Alexander, my level 111 Pyromancer.

Critical Rating / Critical Hit Percentage / Calculated Divisor using 654 Max Rating
182 / 1%
186 / 2% / 6.078
189 / 2% / 6.039
196 / 3% / 6.026
198 / 3% / 6
202 / 3% / 5.947
223 / 6% / 5.904
231 / 7% / 5.875
239 / 7% / 5.764
240 / 7% / 5.75
262 / 11% / 5.765
333 / 19% / 5.35
366 / 25% / 5.333
433 / 34% / 4.911
472 / 42% / 4.919
548 / 57% / 4.818
654 / 79%

After getting these points, I tried to figure out a general guess as how many points would be needed to raise a percentage. If 262 gave an 11% critical chance, and 198 gave a 3% chance, I tried to figure what the difference would be. Subtracting 198 from 262 gave a score difference of 64. The percent rise was 8%, so dividing 64 critical rating by 8, I see that on average, raising critical rating by 8 should raise a character's percent chance to critical by 1.

You can't just pick 2 points on a set of numbers and call it a formula though. I did various numbers in the above fashion and got number ranges between 7 and 8 (almost always with remainders). This gets messy as I keep picking different points give different divisors. I did eventually pick one number to base against... which explains that third column.

Observations

- Somewhere between ratings 182 and 186, Alexander finally climbs out of the minimum critical percentage.
- At 10 critical rating points more, he increases another percent chance to critical.
- The jumps are gradual in the beginning, and may look big higher up, but that's because I have less close data points. I suspect they too are gradual.
- I played around with numbers for a formula, but they were weren't working, so I used 654 as a baseline to figure out how the divisors looked.
- The divisor is an estimation of how many critical rating points would need to be added to increase a critical percent chance. So if I'm at critical rating 198 and my critical percent chance is 2%, for every 6 critical rating I add, I would go up 1% until I reached 654 and would have a 79%.
- The divisor is changing, becoming smaller as the critical rating gets higher. Simply adding a number doesn't work.


Upshot

Without a lot of numbers, and being very rusty at higher math, I couldn't ascertain a formula. What is generally true is that you need to bust a threshold of critical rating before your percent to critically hit increases, and that threshold is near 200 critical rating. It takes 6 or 7 points of critical rating beyond that to raise your critical hit percentage by 1. As you approach 300 critical rating, you need slightly less points to further raise your critical hit percentage. At least that I can see. I may just have been arriving at the divisor in the entirely wrong way. I think it's clearer to see that you need quite a bit of critical to approach a hundred percent, and that you will need even more every time you level.