I'm a glutton for punishment. Another research and source thread for Lhiveras mage mechanics FAQ and my own quoting use. This one started out with a dual purpose, prove a coefficient for Ice Lance, and prove the interactions of Ice Shards and Spellpower (aswell as the base mechanic of them both).

I did three datasets for this set of experiments. All were done wearing +552 frost damage, 259 crit rating and 400 int, casting on troggs and wolves in the dwarven starting area. Spec was tailored to avoid any talents that actually adjust damage output other than crits (No Arcane Instability, Arcane Potency, etc in the arcane tree).


First dataset, specced 5/5 Ice Shards.

Overall Results:

Non-Critical Strike Datapoints: 592
Minimum Recorded: 252
Maximum Recorded: 279
Average Recorded: 265.503378378378

Critical Strike Datapoints: 200
Minimum Recorded: 505
Maximum Recorded: 557
Average Recorded: 530.255

Calculating the gain of the critical strikes:

Minimum Values: (505 / 252) = 2.00396825396825
Maximum Values: (557 / 279) = 1.99641577060932
Average Values: (530.255 / 265.503378378378) = 1.99716856048556


This establishes that the Ice Shards bonus is being correctly tooltip-theorycrafted as a 200% crit. The math explination for how the talent works is that it generates a 100% bonus on the bonus spell damage.

Lets say that Ice Lance hits normally for 100 damage (to make the math easy). When you crit therefore it would be 150 damage, or in formula:

100 + (.5 * 100) = 150

Where .5 is the 50% increase in damage we are accustomed to having with spells. The 100% increase is a doubling of that bonus (100% increase is equivilent to saying X * 2.0 (where 1.0 would be no increase)), so now you have:

100 + ( (.5 * 2) * 100 ) = 200

Second dataset, specced 2/2 Spellpower.

Overall Results:

Non-Critical Strike Datapoints: 545
Minimum Recorded: 252
Maximum Recorded: 279
Average Recorded: 265.902752293578

Critical Strike Datapoints: 202
Minimum Recorded: 441
Maximum Recorded: 488
Average Recorded: 465.074257425743

Calculating the gain of the critical strikes:

Minimum Values: (441 / 252) = 1.75
Maximum Values: (488 / 279) = 1.74910394265233
Average Values: (465.074257425743 / 265.902752293578) = 1.74903890017755


This establishes that Spellpower bonus is also being correctly tooltip-theorycrafted as a 175% crit. The math explination for how the talent works is that it behaves exactly as ice shards, but only does a 50% increase.

Lets say that Ice Lance still hits normally for 100 damage. When you crit its 150 damage, and we know the formula

100 + (.5 * 100) = 150

Now we are adding 50% to that .5, before we were multiplying by 2.0, now we're multiplying by 1.5.

100 + ( (.5 * 1.5) * 100 ) = 175



Third dataset, specced 2/2 Spellpower and 5/5 Ice Shards.

Overall Results:

Non-Critical Strike Datapoints: 708
Minimum Recorded: 252
Maximum Recorded: 279
Average Recorded: 265.40395480226

Critical Strike Datapoints: 202
Minimum Recorded: 568
Maximum Recorded: 627
Average Recorded: 598.247524752475

Calculating the gain of the critical strikes:

Minimum Values: (568 / 252) = 2.25396825396825
Maximum Values: (627 / 279) = 2.24731182795699
Average Values: (598.247524752475 / 265.40395480226) = 2.25410177176222


This establishes that again, the two together is being correctly tooltip-theorycrafted as a 225% crit. The math is just that the two stack together aditively not multiplicatively.

If they were multiplicative, we would get the following:

100 + ( ( .5 * 2.0 * 1.5) * 100 ) = 250

Whereas if they are additive we get the following:

100 + ( ( .5 * (1 + (1 + .5) ) ) * 100 ) = 225




For the TL:DR crowd:

We were right, 5/5 Shards = 200% crits, 2/2 Spellpower = 175% crits, 5/5 Shards + 2/2 Spellpower = 225% crits.

The next important part of this testing was to establish a coefficient for Ice Lance, unimportant to the entire crit gain deal, since it doesnt matter what the base damage and crit damage are really, the relative level between the two was what mattered. Looking at all the samples I took over the course of this entire test.


Overall non-crit datapoints: 1845
Minimum: 252
Maximum: 279
Average: 265.583197831978


Expected base damage range of 173 - 200, and having worn +552 frost damage, solving for coefficients:
By Minimum: (252 - 173) / 552 = 0.143115942028986
By Minimum: (279 - 200) / 552 = 0.143115942028986
By Average: ( 265.583197831978 - ( ( 173 + 200 ) / 2 ) ) / 552 = 0.143266662739091


Looking at that number of aproximately .143, we can find a model that explains it in this:

( ( 1.5 / 3.5) / 3 ) = .1429

Since Ice Lance does tripple damage to frozen targets, and was intended for use on frozen targets, this model seems to be reasonable, that it would have the normal instant cast coefficient of (1.5 / 3.5) on frozen targets (where its damage is trippled), and then a reduced one on frozen targets.



An interesting side note I observed, and am curious if anyone else has seen (I'll do more testing on this tomorrow morning after work), was my crit rate over this entire escapade. Heres the data on it.



Overall observed critical strike chance over the three trials:
Non Critical Strikes: 1845
Critical Strikes: 604
Total Spells: (1845 + 604) = 2449
Observed Rate: (604 / ( 1845 + 604) ) = 0.246631278072683



Odd, considering the crit chance tooltip in my character panel says 17.64% crit rate, I measured 7% higher than that. Other statements about crit rates being off have usually been written off on the low sampling total of the research (usualy between 50-100 samples)... But this is 2449 samples showing a 7% drift vs expected.

Citing Lhiveras FAQ (http://forums.worldofwarcraft.com/thread.html?topicId=106738310) for 22.1 crit rating you get 1% crit, and every 1 int gives .013% crit. So checking the tooltip out:

259 / 22.1 = 11.7195
400 * .013 = 5.2

11.7195 + 5.2 = 16.9194


Something, doesnt add up here. 259 really is the total of the crit ratings on my gear I was wearing for the test. I can understand a .7% drift vs the tooltip for rounding in those numbers (the 22.1 and .013) and possibly a base 1% crit chance or something like that. But the 7% drift vs expected needs to be accounted for somewhere. I suspect, but cant prove yet (will take about 1000 castings on Dr Boom after work tonight) that level would seem to be involved in the crit formula. I'll post that data up when I get it. For now I'm going to start winding down for sleep. Any questions or typo-findings are welcome.



Oh, and for TL:DR again, Ice Lance has an instacast coefficient / 3, and crits are acting funny based on my testing, more to follow.

Good stuff. I suspect that level differences do have something to do with crit. I know that melee crit deviates on level differences, I wouldn't be surprised if spellcrit deviates as well.

Also, there is a 0.909% base chance to crit for a Mage. That's where your "gear tooltip" and your calculated crit rate deviated.

Doing a rough estimate on the error on your crit rate, you have a 24.66% +/- 1.003% crit rate so I am very curious to see how your crit rate stacks up on higher level mobs.

I suspected I was missing part of the crit chance formula, who needs sleep, I'm off to find that 7% on Dr Boom since I wont be able to sleep very well without having figured that part out too now.

And first 1000 castings on Dr boom turned up 171 crits, 829 noncrits, for a crit rate of 17.1% on the nose. .54 vs expected is much much better than 7%. Going to have to devise a good controlled environment to do this against a level 70 target for a similar sampling, I'm satiated for now though, sleep time.

the crit rate thing comes from you attacking extremely low level targets.

---

Q u o t e:
the crit rate thing comes from you attacking extremely low level targets.

---

This is a plausible explanation.

Zaldinar, do you find that your crit rate inflates roughly as http://www.wowwiki.com/Formulas:Combat_Ratings_System#Combat_Ratings_Formula describes? That is...

---

Q u o t e:

Level 1 to 60 (level 1-9 uses level=10):



base * (level - 8) / 52



Level 60 to 70:



base * 82 / (262 - 3 * level)



Level 70 to 100:



base * (level + 12) / 52

---

That is, based on this analysis, were you attacking a level 63 or so target?

---

Q u o t e:
the crit rate thing comes from you attacking extremely low level targets.

---

As confirmed by the round of ice-lancing Dr Boom. It just struck me as odd, the topic of inflated crit rates vs lower level targets doesn't come up often in mechanics threads, since most everything we care about is your level + 3.


Muphrid, I'm on day five of a six day set, hour 19 with a shift in the middle and a bunch of mindless running around killing level 1 and 2 targets, I'm a little lost. If I'm reading that correctly that solves to 22.0769 crit rating per 1% crit vice the 22.1 I took from Lhiveras thread.

So my base becomes 259 / (14*(70+12)/52) + 400 * .013 + .909 = 17.8407, which is now .2% over the Blizz tooltip. A margin I'd say can be generally ignored, since any sampling I've taken so far tends to lose accuracy in the third decimal place from point to point, so that margin for error could be considered acceptable.

Whats got me confused, that is, 63 target? The initial samplings were all on targets level 1 and 2 that generated the 7% extra crit chance. The confirmation of level being the factor was on Dr Boom, level 68. who generated a 17.1% crit rate measured over 1000 datapoints, I'm not entirely certain I trust him as a test bed for this though. I think level 70 targets and Arcane Explosion is probably the quickest and easiest way to accomplish a true test, since if we are to assume that the lower the target relative to yours the higher the crit rate vs whats expected, then at 70 I should be able to get a measured value thats within reasonable tolerance of the 17.(6 or 8)4 predicted over a large enough sampling. Now I just need to find some level 70 targets that are AoE friendly and farm them like mad while ensuring that my crit stats stay constant. I can even do that without respecing on live and make something off of it. Imagine, research, netting profit not connected to the results


Edit: oh, and this time, I really am going to bed. I'll be refreshing this page in six hours.

---

Q u o t e:
Muphrid, I'm on day five of a six day set, hour 19 with a shift in the middle and a bunch of mindless running around killing level 1 and 2 targets, I'm a little lost. If I'm reading that correctly that solves to 22.0769 crit rating per 1% crit vice the 22.1 I took from Lhiveras thread.

---

Which could easily be attributed to rounding. My impression is that this formula was derived from an extensive data collection addon, but 22.1 is still correct to 3 decimal places anyway.

---

Q u o t e:
Whats got me confused, that is, 63 target? The initial samplings were all on targets level 1 and 2 that generated the 7% extra crit chance.

---

I backsolved for the level that would generate a 7% gap from 17% by ratio. Clearly, then, the rating conversion has little to nothing to do with it, unless it only holds for the rating proper.

As much as I respect and cherish the people willing to do that datamining to prove what the rest of us glibbly shoot out as "facts", its REALLY gotta suck doing hours and hours of datamining to "prove what we already know".


Guess what I'm trying to say is, thanks for the datamining lol.

---

Q u o t e:
As much as I respect and cherish the people willing to do that datamining to prove what the rest of us glibbly shoot out as "facts", its REALLY gotta suck doing hours and hours of datamining to "prove what we already know".


Guess what I'm trying to say is, thanks for the datamining lol.

---

Testing != datamining.

i'm sorry

what is the point again? I'm lost >_<

The point of post 1 and 2: Establish documented research for the bonuses gained from Spellpower and Ice Shards. We all had an assumption of how they worked, now that assumption has been proved.

The main point of post 3: Establish documented research on the coefficient of Icelance.

Incidental point of post 3: Established an observed differential in crit rates vs expected on level 1 and 2 targets, which was confirmed to be a level difference generated situation by casting on Dr Boom and not observing the same gap in crit rates.

YOR MATHS SKARE ME!!!1

Posting this for a friend (Lucai), who can't post.

---

Q u o t e:
What if instead of a 2-roll system, blizzard just simulates a 2-roll system? They make a table just like you would expect for a 1-roll system but include hit chance when calculating crit chance. For example (modifying your Perl code for a 1-roll system):

$hitchance = 0.83;
$critchance = 0.3 * $hitchance;

$roll = &rand();
if($roll < $critchance){
print "Crit";
} else if ($roll > 0.99 || $roll > $hitchance) {
print "Resist";
} else {
print "Hit";
}

So while at 99% hit getting more hit wouldn't increase your hit rate but it still would increase your crit rate. Which could explain higher crit rates against lower level mobs.

I did a small experiment to test this theory (although I didn't run the experiment long enough to determine whether or not this is a viable theory).

On the PTR casting Arcane Missiles against Dr. Boom (level 68) using my level 70 undead mage (specced http://www.wowhead.com/?talent=obLVf0fzxhzb) with 455 int (counting Arcane Mind and Arcane intellect), 247 crit, 18 hit, +3% crit from Arcane Instability and +3% crit from Molten Armor. Which gave me 0.909 + 247 * 13 / 287 + 455 / 80 + 6 = 23.78% crit (matched exactly with the tooltip) and 18 *13 / 164 = 99.43% hit (again matched exactly with the tooltip).

Crits: 229
Noncrit Hits: 760
Resists: 11
Expected Crit Rate (using simulated 2-roll system): 23.64%
Observed Crit Rate: 22.9%

I then put 5 talent points into Arcane Focus (http://www.wowhead.com/?talent=oiLVf0fzxhzb) and redid the test:

Crits: 247
Noncrit Hits: 742
Resists: 11
Expected Crit Rate (using simulated 2-roll system): 26.02%
Observed Crit Rate: 24.7%

While I realize that 1000 data points for each isn't nearly enough to validate my theory I think there is enough evidence to trigger more research. Unfortunately I don't have the time or patience to collect enough data.

-Lucai

---

I knew this was a necro when I saw Irontygress.

/mourn

---

Q u o t e:
I knew this was a necro when I saw Irontygress.

/mourn

---

---

Q u o t e:
What if instead of a 2-roll system, blizzard just simulates a 2-roll system? They make a table just like you would expect for a 1-roll system but include hit chance when calculating crit chance. For example (modifying your Perl code for a 1-roll system):

$hitchance = 0.83;
$critchance = 0.3 * $hitchance;

$roll = &rand();
if($roll < $critchance){
print "Crit";
} else if ($roll > 0.99 || $roll > $hitchance) {
print "Resist";
} else {
print "Hit";
}

So while at 99% hit getting more hit wouldn't increase your hit rate but it still would increase your crit rate. Which could explain higher crit rates against lower level mobs.

---

An interesting theory. Whipping up a quick simulator (http://chemiserouge.bounceme.net/content/wowmage/lucai.pl) to brute out the result of it:

Over 100000000 iterations saw:
Hits: 58108167 / 100000000 = 0.58108167
Crits: 24894965 / 100000000 = 0.24894965
Resists: 16996868 / 100000000 = 0.16996868

So with a base 30% crit chance and 17% miss chance, you really net a 24.89% crit chance (.3 * .83 = .249, not too shabby eh?) This gives us a loss of 5.1% crit that should roll into hit, which under a classic one roll would in this case have 1.0 - (.17 + .3) = .53 of the sampling, which is consistent with what the brute observed.

A very interesting theory. One that would be hard to prove given the deviations in crit rate on targets based on level (http://forums.worldofwarcraft.com/thread.html?topicId=108219860), or mayhapse, might justify them.

---

Q u o t e:
I did a small experiment to test this theory (although I didn't run the experiment long enough to determine whether or not this is a viable theory).

On the PTR casting Arcane Missiles against Dr. Boom (level 68) using my level 70 undead mage (specced http://www.wowhead.com/?talent=obLVf0fzxhzb) with 455 int (counting Arcane Mind and Arcane intellect), 247 crit, 18 hit, +3% crit from Arcane Instability and +3% crit from Molten Armor. Which gave me 0.909 + 247 * 13 / 287 + 455 / 80 + 6 = 23.78% crit (matched exactly with the tooltip) and 18 *13 / 164 = 99.43% hit (again matched exactly with the tooltip).

Crits: 229
Noncrit Hits: 760
Resists: 11
Expected Crit Rate (using simulated 2-roll system): 23.64%
Observed Crit Rate: 22.9%

I then put 5 talent points into Arcane Focus (http://www.wowhead.com/?talent=oiLVf0fzxhzb) and redid the test:

Crits: 247
Noncrit Hits: 742
Resists: 11
Expected Crit Rate (using simulated 2-roll system): 26.02%
Observed Crit Rate: 24.7%

While I realize that 1000 data points for each isn't nearly enough to validate my theory I think there is enough evidence to trigger more research. Unfortunately I don't have the time or patience to collect enough data.

---

You're right, 1000 datapoints isn't anywhere close to enough in such a brute force experiment. And actually, my one roll/two roll thread (http://forums.worldofwarcraft.com/thread.html?topicId=443186981) may have given your theory some weight:

---

Q u o t e:
Datapoints taken: 200
Resists: 186
Hits: 11
Crits: 3

Expected Resist Rate: .04 + .9 = .94
Observed Resist Rate: 186 / 200 = .93
Delta: .94 - .93 = .01

Expected Crits by One Roll: 200 * .06 = 12
Expected Crits by Two Roll: 200 * .06 * .1484 = 1.7808
Observed Crits: 3
Delta from One Roll: 12 - 3 = 9
Delta from Two Roll: 3 - 1.7808 = 1.2192

---

Now, adding in your simulated two roll expectations:

Expected Crits by Simulated Two Roll: 200 * (.3 * .06) = 3.6
Delta from Simulated Two Roll: 3 - 3.6 = .6



The problem with your experiment is you're shooting at Dr Boom, level 68, by released numbers you have a 98% chance to hit him at base (http://forums.worldofwarcraft.com/thread.html?topicId=10271182), with 18 hit rating you've already capped yourself at 99.4268% (as you observed). So changing your hit rating with Arcane Focus shouldn't change your results based on the system you propose. Looking into your system we'd expect with your base 23.78% crit chance and capped +hit that under your system for 1000 samples you'd have:

1000 * (.2378 * .99) = 235.4220 crits
1000 * (.01) = 10 resists
1000 * ( (1.0 - (.2378 * .99) ) - .01) = 754.5780 Hits

I'm confused how your second sampling with the Arcane Focus raised your crit rating using your system, you're already hard capped, so it won't gain you anything. The differential you observed looks like the result of the randomizer.

This would seem to tend to lend to my conjecture (which was actually given some credit in an EJ forum posting about the 6% hit for frost from EP, I cant find the link right now though for some reason, its somewhere in one of my threads) that crit decays against higher level targets, but would not explain why it inflates vs lower level targets, unless crit chance is not modified by a capped +hit, but by a raw +hit...

So in your case, your crit chance becomes:

.2378 * (.994268 + .1) = .2602

Which explains where you were going with that.



I'm actually very very interested in this theory now. I'm going to do some test environment sketches and see if I can come up with a good way to show this in action.


Edit: Forgot to link a referenced thread