Spell +Crit (effect of Int)

I've modifed the page again to include this information: http://forums.worldofwarcraft.com/thread.aspx?FN=wow-general&T=8532087&P=1

I've inferred from other posts by Tseric that every class should have 5% int per crit at that expected value, and then worked backwards to get the base crit %. I believe this is correct - but feel free to debate it here if you disagree. Not sure what to do with shaman/paladins for which Tseric had no info available.

--Mania 12:24, 31 May 2006 (GMT +8:00)

I've just modified the page to include the latest information from Tseric, which can be seen on http://forums.worldofwarcraft.com/thread.aspx?FN=wow-mage&T=1009382&P=1. I did not include a link to this forum post, as in a matter of weeks it'll just return a blank page (it won't make the blizzard archive). If anyone has any problems with the mods, let me know :)

The spellcrit formula on this page is wrong. I also assumed 100Int to be 1% Spellcrit up to now but this Thread including Blue Post #6 states that 59.5 Int = 1% Crit.

--Ymihere 07:10, 7 Dec 2005 (EST)

I know for a fact that shaman crit chance is not 20 int per crit. I have no idea where that number came from, but it is WAY off.

The number is in fact 39.5 or 40 or 40.5 (hard to tell exactly which it is).

But I did two tests of 1000 casts of healing wave (rank 1), each with different gear sets on as follows:

Test 1: 282 INT, 3% crit gear, 5% crit from talents --- 149/1000 crits = 14.9% crit rate

Test 2: 147 INT, 0% crit gear, 5% crit from talents --- 86/1000 crits = 8.6% crit rate

DIFFERENCE: 14.9-8.6-3 = 3.3 (282-147)/3.3 = 40.9 int per crit

Test 1: 14.9-8 = 6.9 282/6.9 = 40.86

Test 2: 8.6-5 = 3.6 147/3.6 = 40.83

Indeed, here is the quote from Tseric.

"The basic mechanic of INT to Crit% is an increase of 1% every 59.5 points for mages. A mage is generally expected to have around 286 points of INT at 60. This works out to about 5% crit on average for mages. It is possible to go higher, as Crit% does go up incrementally.

EDIT- The increase of 1%crit for 59.5 is for everyone, not just mages. However, mages tend to have more INT, thus my phrasing.

When asked if that meant there was no Base Crit %:

"Basically, yeah."

--Finnias 05:31, 20 Dec 2005 (EST)

Just a note, Tseric corrected himself later:

"First off, there is an expected number of INT for each level for players of different classes. For continuing examples I will refer to the mage. Again, each class has different values on them and therefore scale differently, as we shall see. " Details on spell crit chance. --Tbannister 11:12, 23 Jan 2006 (EST)

Another fine reason why spell crit &, and ranged crit % should be displayed, somewhere, anywhere. CJ 05:40, 20 Dec 2005 (EST)

Tseric has previous said unequivocably that "there is no base crit chance", So if he did indeed post the numbers on the page somewhere, I suspect he simply can't do math, and the corrected numbers are:

"Warlock 200 - 60.6 Druid 192 - 60 Shaman 160 - 59.2 Priest 250 - 59.5" are respectively 40, 39, 32, and 50 int/% crit. Also this page is terribly messy and needs a clean up, there is too much "discussion" on the formal page instead of the talk page. Citations should be collected at the bottom of the page, not inline and the horrible black on white formula bits needs to be made less painful to read. Those number would be be more inline with observed behaviour.

--Tbannister 13:59, 11 October 2006 (EDT)

This information was inferred from a post by Tseric, in which he revealed the expected amount of Intellect that Mages, Druids, Warlocks and Mages should have at 60, and their Intellect per Crit ratios. Knowing that at the expected amount you should have a 5% crit rate, the base crit rate can be worked out. If classes other then mages are not intended to have a 5% crit rate, this information will be incorrect.

For Paladins crit chance is still unknown, thus the question marks. The estimates shown though assume 0 base crit, which in light of the new information is probably wrong.

Tseric writes, "Here are some other numbers to that end: At level 60, these are expected numbers of INT and points per Crit%

Warlock 200 - 60.6 Druid 192 - 60 Shaman 160 - 59.2 Priest 250 - 59.5"



LumberLamer tested as a lvl 60 dwarf paladin. With 215 intellect and no crit items or talents, 566 flash of light rank 1 resulted in 35 critical heals (6.18%). Unequipped, with 76 intelligence, 20 of 576 spells were critical (3.47%). Extrapolating that would mean 0 intelligence would have 1.98% to crit, and each 51.92 INT would add 1% chance to crit.

Bubblebee has also tested as a 60 dwarf paladin without crit gear and talent crit. With gear (235 intellect) on, 1000 flash of lights resulted in 77 crits. Without gear (75 intellect), 1000 flash of lights resulted in 48 crits. Additional tests w/ 153, 172, 210, and 270 intellect resulted in 6.2, 7, 6.3, and 7.5 crit respectively. Each crit test at a certain intellect was done with 1000 flash of lights. The best fit linear equation of the data suggests that 0 intellect equates to a 4% spell crit and approximately 72 intellect adds 1% spell crit.

Semaj used 1200 flash of lights with no gear and 1200 with full gear. His results suggest that 0 INT would = 0% crit rate and every 29.5 INT = 1% crit for paladins.


Aryxymaraki tested the ratio using 400 casts of HW with naked int, 400 casts with half-gear, and 400 casts with full gear. He arrived at 39.5 INT = 1% crit.

Quoted from this General Forum post by Tseric on May 31st, 2006

Not exactly, but the numbers tend to hover around that mark for many casters, at least. Obviously, for melee the numbers are somewhat irrelevant. Sorry that I don't have the exact numbers for Paladins, but the trend is illustrated. Here are some other numbers to that end:
At level 60, these are expected numbers of INT and points per Crit%
Warlock 200 - 60.6
Druid 192 - 60
Shaman 160 - 59.2
Priest 250 - 59.5

These is still a disconnect between the previously discussed 5% crit base and these numbers, but Blue information is always worth capturing.

Can Crits Miss ?

Seems to some misconceptions here about crit/miss interactions. They are separate tests - crit rate and hit rate do not affect each other. Further critical rate is the percentage of *hits* that crit, not the percentage of *attacks* that crit. So if you have a 60% chance to crit and a 50% chance to miss, that doesn't give you a -10% chance to score a normal hit. It gives you a 50% chance to miss, a 30% chance to crit and a 20% chance to hit.

--Danya 13:08, 4 Jan 2006 (GMT)

Danya please explain where you got your information from? The explanation from the Tank Points Mod says it's actually a single roll not a double roll as you suggest. And again, here's the blue post from the forums that says the same thing: Thundgot Post

--Tbannister 14:00, 4 Jan 2006 (EST)

Thungdot's post seems very contradictory - he states that crit chance includes misses, then in part 2 has crit and miss chances shown separately. I can't decide if he's saying there are two rolls (hence the two parts and crits including misses) or one (as given in his example).

My numbers are based on in-game observations FWIW.

--Danya 21:12, 26 Jan 2006 (GMT)

Part 1 of the blue post on +crit/+hit is perfectly clear. CRITS CAN MISS: "The way WoW calculates crit rate is over ALL attacks. Crit rate is not based on hits only." How can that possibly be misunderstood? Why would he use the phrasing "ALL attacks" and then go on to specify "not based on hits only" if he didn't mean "also misses"? Look at the sentence this way: "Crit rate is calculated over ALL attacks - not hits only". I don't believe this is a mangling of the original wording, and it certainly is much clearer.

BUT!: in part 2, crit rate is deducted from hit rate! This seems to indicate misses can't be crits... If you ask me, though, part 1 is a lot clearer than part 2...

To be honest, someone needs to drag a new answer out of this "motive" guy - OR - sit down and test your crit rate against something you have a noticeable miss chance against. Only way I can think of this being possible is by getting a friend on the other faction to join in (or use 2 accounts). One could also get some semi-decent results out of MC bosses, for example Magmadar and Golemagg (as a mage you are safe while fighting these, and they have enough HP to get off some frostbolts).

--Asherett 06:39, 29 March 2006 (EST)

What's the problem? Yes part 1 means that Crits can Miss.

Now, why does part2's deducting of crit rate from hit rate mean that "misses can't be crits"?

The fact that the statement "New miss chance - (Original miss%) - (toHit modifiers)" (just noticed he had a typo there, that first "-" should be a "=") doesn't mention crit at all doesn't in any way affect the fact that a Crit can Miss. In fact it is exactly stating that a Crit can Miss, because although Crits eat Hits, and Hits eat Misses, Crits eating Hits does not carry over into Crits eating Misses if the Crit chance is higher than the Hit chance. Thus indeed a Crit can Miss because it can hit a ceiling due to toCrit modifiers never affecting New miss chance.

Athan 14:46, 13 July 2006 (EDT)


read this if you think critical rate is the percentage of *hits* that crit.

The miss chance is capped at 60%? Can you explain where you got your information from?


Yes, please do, Tbannister. The last part in my original edit was actually a post on the official forums (from Eyonix, I think), that's why I ask. Don't take it personally, we only want to find out the truth ;) Stilpu 03:49, 5 Jan 2006 (EST)

I can't find my original reference for the avoidance cap at 60%, there's a mention of it in the notes from the Titan Panel Combat Bench addon.

--Tbannister 14:07, 10 Jan 2006 (EST)

It doesn't have any credible source, so it is just a assumption. --Firefox

As I understand, it was determined through experimentation. If you can show that it doesn't happen, please do so.

--Tbannister 11:12, 23 Jan 2006 (EST)

That mean you can not provide any credible source.


Firefox, that link doesn't prove or disprove critical rates being the percentage of hits. If anything though it supports it since he was seeing below 40% of attacks critting, which suggests that his miss rate was affecting it. He doesn't state his miss rate which makes it more difficult to analyse, but if he has a say 80% hit rate (I'm assuming dual wield penalty is applying), then the expected number of crits would be 425. That's fairly close to his actual numbers...

--Danya 21:27, 26 Jan 2006 (GMT)

Did you read motive's post? He's a Blizzard Poster.

Firefox 22:20, 26 Jan 2006 (EST)

What lots of people are forgetting is that there are abilities which ASSURE a critical hit. They may your critical hit chance 100% for your next swing. Guess what, these swings can still miss. This seems to prove that an attack must hit before it can crit. I firmly believe that crit rate is based on your hit rate. If you hit 50% of the time, your crit rate is 50% lower than it is reported. But if you wanna test it then go attack a mob that is 10 levels over you and get your crit rate to 10-20%, having a priest heal you. Swing at it a few hundred swings and see if you crit 10-20% of your swings, or if 10-20% of your hits are crits (this will be the case). Also see if you notice that 60% miss rate cap, which you will notice is not actually real. -Shadar

This ability (I think you mean "Cold Blood") does not assure a critical hit. It increases the critical hit chance by 100% (read the tooltip). Your chance to miss and the dodge/parry chance of the opponent are unaffected by this. The normal hit chance is 100%-dodge-parry-miss-crit (the rest of all your attacks so far). Crits and normal hits are different events! So, if you increase your critical hit chance by 100%, you consume all your normal hit chance. That means that "Cold Shot" normally assures that all your normal hits turn to be crits. The crit chance is STILL based on ALL SWINGS but can NEVER ignore the miss chance and the dodge/parry chance of the opponent. If you test this on a 10 level higher mob, you have to take into account the better dodge/parry chance of the mob (2% better each) and your increased miss chance due to level difference (10 level usally means 94% miss with single or two-hand weapons, but will be capped at 60% here). Of course, your crit chance is also decreased because of the difference between the mob's defense and your weapon skill (2% here). The 60% miss rate cap only means the base miss chance because of level difference. The overall miss chance can be higher due to the better defence skill of the mob (again 2%). "MISS the mob" and "The mob DODGES" are different events and don't depend on each other. Finally you miss at (60+2)%, the oppenent dodges at (basedodge+2)%, he parries at (baseparry+2)%. You crit with (basecrit-2)%. All of your other swings (if left) are normal hits. I tested this and it fits so far. But you have to deal a million swings on the same type of mob to be quite sure of chances and possibilities. --Morrh 14:47, 13 Mar 2006 (CET)

But in the end, if you add 100% crit rate you are only adding a base of 95% dps (assuming a 5% base miss rate). If this is the case, 1% crit adds .95% dps, not 1% dps. On the other hand, 1% to hit increases your dps by 1% up to the point where you remove all chance to miss. If this is true, +hit gear provides a greater default bonus... before talents/procs are factored in. -Shadar

You can't compare the "cold blood" ability with +hit items. If you add a 1% crit to your gear, you increase the dps bei 1%, since 1% of all your attacks deal the double damage. But your hit chance is decreased by 1% then. If you add 1% hit, you deal also 1% more damage, since 1% of your attacks that would normally miss will hit now. The "cold shot" will only assure that all your hits become crits. It is not possible to calculate the +dps% of this fact. It depends on miss, dodge and parry as you stated in your example above. The basic is to understand that +crit will do -hit and +hit will do -miss. If one doesn't understand this rule, it's quite convenient to think that crit% is the chance of hits that crit rather than attacks that crit. --Morrh 14:09, 12 Apr 2006 (CET)



motive[blue] @rogue forum, Topic: BACKSTAB NERFED:

    • Wait, motive can you verify some theoretical numbers for me? (assuming ideal distributions)
    • 1) 1000 swings with a 50% chance to hit and a 50% chance to crit (against an equal level unarmored/no defense enemy) would result in
    • a) 500 crits, 500 misses (chance of regular hit = to hit - crit)
    • or
    • b) 500 crits, 250 hits, 250 misses (chance of regular hit calculated independently after crit roll)
    • or
    • c) 250 crits, 250 hits, 500 misses (chance of crit calculated independently after to-hit roll)
    • Sounds like you use option A as your calc, which is cool although not particularly intuitive.
  • Option a) is correct. But keep in mind that 50% hit AND 50% crit is not a possibility since in your example the % chance to miss stays the same. The way this works is that when your chance to crit increases, your chance to hit is consumed by that increase. So if I initially have a 25% chance to miss and a 50% chance to crit, then I have a 25% chance to hit. If I increase my crit chance to 55%, then my chance to hit (not crit) becomes 20%.

    • As for attack skill vs defense skill, am I correct to assume that the formula is crit adjustment = (ATTACK SKILL - DEFENSE SKILL) * 0.04?
    • So if rogue with 325 dagger skill and 50% crit attacks an enemy with 300 defense, the rogue's effective crit is 51%, and attacking a warrior with 425 defense the effective crit is 46%?
  • Yes, this is correct, applying the formula to a rogue with 325 dagger skill vs. a target with 300 defense increases the rogue’s crit chance to 51%.
  • (325 – 300)*0.04 = +1%
  • Your second assumption is also correct, applying the formula to attacking a warrior that has 425 defense yields a -5% to crit rate, dropping this rogue’s crit chance vs. the warrior to 46%.
  • (325 – 425)*0.04 = -4%

    • As for the original poster, Blizz you might want to reverify the (ATTACK SKILL - DEFENSE SKILL)*0.04 formula, as if that suddenly become (0 - DEFENSE SKILL) * 0.04 while tweaking defense, it would explain the ~12% drop in crit percentage.
  • I can't make any assumptions about the original poster's data because the weapon skill and target defense ratings were not posted. As many people have stated above also though, probability distribution is not always perfect and there is still a chance that once can be "unlucky". It's not impossible to toss tails 50 times in a row, it's not impossible to only crit 40% of the time when the chance to do so is 50%

Avoidance cap


Tseric[blue] @warrior forum, Topic: 60% Avoidance cap?

    • I've heard this mentioned a couple of times, is this true in regards of tanking? What specifically is it referring to regarding our abilities?
  • I have not seen any information which would lead me to believe there is a cap of these abilities. The only limitation I can see would be in the amount of gear you could stack with bonuses for each ability.

    • [Obould]I tested this by gathering a group of 10 Kul Tiras mobs (levels 5 and 6) together and let them attack me for 20-25 minutes in my tank gear. I didn't use any abilities (I was AFK watching TV for most of the time). Upon returning, my life total was exactly the same as when I began. It was obvious from Scrolling Combat Text that every single attack was being dodged, blocked, parried, or missing.
    • [Lomr]
    • Block 25.70%
    • Parry 25.27%
    • Dodge 21.76%
    • Miss 20.10%
    • I think the discrepency in block is because i couldnt always keep the 7-8 mobs hitting me directly in front, and occasionally i'd have to reposition a new mob, however this testing clearly blows away a 60% or even 90% cap in damage mitigation. Basically the sky is the limit, and blizz will have to itemize properly to make sure 100% mitigation does not occur.
    • [Greysen]
    • Level 5 Wendigo
    • 2429 Attacks
    • 535 Missed (22.03%)
    • 576 Dodged (23.71%)
    • 716 Parried (29.48%)
    • 602 Blocked (24.78%)
Firefox 19:56, 29 March 2006 (EST)


The [Obould] [Lomr] & [Greysen]'s test are very interesting. But the level difference between the player and mob level may result in a wrong way. So I decided to do a test with a highter opponment to confirm it. I've choosed a Winterspring's bear, cause he is level 56, he has no special ability and no cast.

Context :

  • Winterspring 19 may 06
  • Mob "Marteleur Crocs acérés" level 56 vs "Caiden" level 60 / Def 397
  • My abilities for this test: dodge 25.38%, parry 15.88%, block 24.88%.

No buff, only healing potion +12hp/5sec

I aggro the mob in defensive stance, but I let him hit me, doing nothing. When I reach 2300 healpoints I cast my "fear" ability and heal myself with a bandage. The "fight" was run on 1000 attack and during approximately about 40 min.

Results :

    • [Caiden]
    • Level 56 "Marteleur Crocs acérés"
    • 1000 attacks
    • 259 mob hit 25.90%
    • 88 missed 8.80%
    • 283 dodged 28.30%
    • 172 parried 17.20%
    • 198 blocked 19.80%

So the 60% avoidance cap is effectively broken with 65.3% and 74.1% if included the miss rate.screen here

There are some differences between my abilities and theses stats. First, I believe the difference level of the mob has increased my dodge/parry capacity. For the block, after a bandage, my shield was everytime in my back, so I've spent a few second each time to take it ready in my hand.


Rogue Crits

I've experimented with Rogue Crits until I was about to cry blood, and as best I can reckon, the formula on this page is wrong.

The formula isn't [5+ AGL/29], it's simply [AGL/29]. The +5% comes from a Talent called Malice.

Here's my evidence:

I've got a 60 Rogue with 257 AGL, 5/5 Malice, and +11% crit from items.

According to the formula above, this should equate to a 29.86% crit rate:

[5+(257/29)]+5+11 = [5+8.86]+16 = 13.86 + 16 = 29.86.

BUT... my tooltip crit rate is ACTUALLY 24.84. Now, I'm certain that the 0.02% difference is just calculator slop, but the whopping 5% difference HAS to be because of the added 5 in the formula. I respecced recently, and when I did, I lost exactly 5% from Malice, and regained exactly 5% when I re-purchased it. I've rotated out all of my +crit gear, and lost EXACTLY how much was listed on the item (none of my +crit stuff has AGL on it).

So it HAS to be the formula that is messed up.

Where did this figure come from?

it should be Malice + calculation then. CJ 11:20, 17 Feb 2006 (EST)

Druid Spellcrits

I just finished a Undead Stratholme run. I was using the same gear the whole time, and together with buffs I had 276 int in total. My Healing Touches, various ranks, critted to 5.8% according to my damage meter, Recap. My Insighful Hood gained me a spellcrit chance bonus of 1%, so subtracting that I get 276 / 4.8 = 57.5 points of int per percent of spellcrit. Using the formula given in this article, I should have got critical hits on 276/30+1 = 10.2% of all Healing Touches, including the Insightful Hood bonus.

Which sucks. Loriel 23:59, 3 Mar 2006 (EST)

About +hit

I've modified some information about chance to hit. If you dont agree, please whine here =)

regards carve

Example of the Three Outcomes interpretation

Consider an orc with a knife, and that orc swings it at a dwarf who is sleeping (and cannot react defensively). There are exactly three possible things that can happen.

  1. He can stab the dwarf in the arm, and normally damage him.
  2. He can poke the dwarf in the eye, and critically damage him.
  3. He can miss entirely, causing no damage.

A crit cannot convert to a miss or hit: If his swing pokes the dwarf in the eye, there is no chance that the orc will miss entirely on that swing. There is also no chance that that swing will instead stab the dwarf in the arm.

A hit cannot convert to a miss or a crit: If his swing stabs the dwarf in the arm, there is no chance that the orc will miss entirely on that swing. There is also no chance that that swing will instead poke the dwarf in the eye.

A miss cannot convert to a hit or crit: If his swing misses entirely, there is no chance that the swing will instead stab the dwarf in the arm. There is also no chance that that swing will instead poke the dwarf in the eye.

(This should be easy to verify with some testing on a Mage/Shaman with Combustion/Elemental Mastery as they will guarantee a crit. Unless ofc Blizzard have made some type of hack with the possibilities for miss on those abilities.)

I removed the above section from the article, as I think that example is irrelevant, pointless and mathematically wrong. --Batox 06:09, 7 June 2006 (EDT)

Can anyone source the cap on +hit? I've got one person telling me it's 5%, another 6% (or 5.6), and another saying there is no cap. --Morbid-o 10:19, 19 July 2006 (EDT)

There is no cap. What they're talking about is anything except Dual-Wielding hits (base 76% hit chance), which all have base 95% hit chance. Therefore against same-level targets you only benefit from at most 5% hit.

Except people thinking +5% is enough are failing to take into account what happens when the target is higher level than you.

Firstly for players and mobs +3 levels you benefit from up to 5.6% due to your weapon skill vs. their defense skill, 0.04% per difference, 3 levels == 15 skill, 15 * 0.04 = +0.60% miss chance. The 6% is simply because +hit only comes in multiples of 1%. And note that in the case of players you will likely encounter warriors and possibly druids with significant +defense, so even though you have 300 weapon skill (maybe ~310 with the right items) they could easily have 350 or higher, depending on how PvP-tuned their gear is.

So that's the 5.6% and 6% figures you've quoted explained, but ...

...that's only the weapon skill vs defense adjustment. There's also an adjustment simply for level, which is +1 levels = -1% hit, +2 levels = -2% hit, and +3 levels = -13% (mobs or -9% (players).

So, "it depends what you're fighting, and how you fight it". At level 60 if you PvP primarily then you only need +5% hit, although you will still want more if you Dual-Wield. If you PvE in raids at all you can definitely benefite from more. --Athan 10:39, 19 July 2006 (EDT)

Ah, thanks. I should've been more clear, I understood most of that already. The 'simply by level' adjustment is what I didn't know about. Specifically, I was wondering at what point +hit was redundant for hunters (not a class I've played much with). From the above, I'm thinking that a PvE hunter would need 5% for the same level +hit, 13% for the +3 effective boss level, and then another .6% additionally to account for the difference in boss defense and hunter bow skill (assuming no modifiers)? Also, is the %hit modifier for level derived from experimental data?--Morbid-o 13:02, 19 July 2006 (EDT)

Unfortunately I've not seen a solid cite, either of Blizzard-provided info, or concrete experimental data, about the +1/2/13% miss chance on mobs levels above you. The rest is from Blizzard info though.

Certainly there IS some such additional miss chance as I know that once a mob reaches +4 levels it gets much much harder to hit at all (probly something nasty like +25% miss or more then). I might be able to go parse my extensive logs and find data, if I limit it to MC bosses I know they're +3 levels for sure.

--Athan 15:04, 19 July 2006 (EDT)

Crit vs Blocking

Ok, so we're pretty sure that "+Hit eats Miss" and "+Crit eats Hit" (but +Crit won't overflow to eat Miss). Also Dodge and Parry can be treated as eating first Hit and then Crit, simply because they're both 100% damage mitigation.

Now, what about Block ? It's not necessarily 100% damage mitigation, so it applies *to* a melee swing that didn't miss, wasn't parried and wasn't dodged, rather than being instead of a hit/crit.

If you look on Formulas:Weapon Skill you'll see some discussion of Crit Cap due to Glancing Blows (which are always normal hits, not crits). In some of the examples there is so little normal Hit left that it would, if there was no blocking, all be turned into Crit. That page implies that a Block cannot be against a Crit, it will instead stop some of the Hit turning into Crit.

Is this correct? Does Block chance stop some of the Hit turning into Crit, instead reserving it for Block ? Or can a Critical hit indeed have some of its damage Blocked (heck, maybe all of it)?

My own (extensive) combat logs never show a single crit hit with any amount blocked, *BUT* my own Crit is only 28% (a bit higher with raid buffs) so I'd never be running out of pure Hit Chance anyway. I don't use Cold Blood, so can't easily test via that either. Anyone got any combat logs with "You crit <mob> for XXX (YY blocked)." in them ?

--Athan 15:05, 13 July 2006 (EDT)

Critical Hit chance effect on overall damage

The problem with this is what you're talking about when you say "+1% crit increases damage by 1%".

Let's think in terms of how much damage we do versus the pure weapon damage if we hit 100% of the time and 100% of those hits were just normal hits. Now, we know that 100% hit is possible (when not dual wielding). We also know that any crit chance eats up hit chance, and those hits that become crits are then double damage (modulo talents increasing this).

So the actual damage we will do per swing (and thus over time) is:

Damage = BaseDamage * HitChanceNotIncCrit + BaseDamage * 2 * CritChance
       = BaseDamage * (HitChanceNotIncCrit + 2 * CritChance)

Plugging in 100% hit (enough +hit% for 95% base), and 5% dodge (which can't ever be negated) this gives us:

Damage = BaseDamage * ((1.00 - 0.05 - 0.25) + 2 * 0.25)
       = BaseDamage * 1.20

So due to the dodge chance our 25% crit chance is actually only worth 20% extra damage.

Now, raise the crit chance by 1%

Damage = BaseDamage * ((1.00 - 0.05 - 0.26) + 2 * 0.26)
       = BaseDamage * 1.21

Now our 26% crit chance is actually woth 21% extra damage. That is indeed an increase of 1%. But that is only an increase of 1% to the INCREASE in damage we get from crit. The last editor is correct that this is actually only:

1.21 / 1.20 = 1.00833

i.e. 0.833% extra damage overall from +1% crit.

Now if we go to even more realistic:

  1. No base miss (+5% hit or more)
  2. 5% dodge
  3. 5% parry
  4. 5% block
  5. 25% crit
Damage = BaseDamage * ((1.00 - 0.05 - 0.05 - 0.05 - 0.25) + 2 * 0.25)
       = BaseDamage * 1.10
Damage = BaseDamage * ((1.00 - 0.05 - 0.05 - 0.05 - 0.26) + 2 * 0.26)
       = BaseDamage * 1.11
1.10 / 1.11 = 1.00909

So actually 0.0909% extra damage from +1% crit, i.e. the more you're not going to hit, the more +1% crit is worth.

I'll go edit that whole section to reflect this :).

--Athan 09:01, 18 July 2006 (EDT)

I don't doubt that a simple calculation for increase in damage from 1% crit is valid for white damage, but for rogues at least it is more complicated first because they are always dual wielding and second because a significant portion of their total damage is special attacks, which follow different rules. Here are a couple examples, using a rogue with a base crit rate of 25%, base hit rate of 9% (15% miss rate), attacking a level 60 target that has a 5% dodge rate (striking from behind). The numbers for a level 63 opponent would be similar as long as the rogue had 310 weapon skill (which he should) - these crit and hit rates put him nowhere near the crit cap and the only difference would be a 0.4% difference in hit, crit, and dodge rates (not insignificant, but I'm lazy).

WhiteDmg = BaseDmg * (CritRate * 2 + (1 - CritRate - MissRate - DodgeRate)

SSDmg = BaseSSDmg * (CritRate * 2.3 + (1 - CritRate - DodgeRate)

BSDmg = BaseBSDmg * ((CritRate + .30)*2.3 + (1 - (CritRate + .3) - DodgeRate))

Sinister Strike and Backstab have a 0% MissRate since our rogue has over 6% to hit, or that would be in their equations too. Backstab's crit rate is increased by 30% from Improved Backstab. Both Sinister Strike and Backstab have their crit damage bonuses increased to 2.3 from Lethality. Our rogue's damage would be:

WhiteDmg = BaseDmg * (.25*2 + (1 - .25 - .15 - .05)) = BaseDmg * 1.05

SSDmg = BaseSSDmg * (.25*2.3 + (1 - .25 - .05)) = BaseSSDmg * 1.275

BSDmg = BaseBSDmg * (.55*2.3 + (1 - .55 - .05)) = BaseBSDmg * 1.665

Increase his crit rate by 1 and what do you get?

WhiteDmg = BaseDmg * (.26*2 + (1 - .26 - .15 - .05)) = BaseDmg * 1.06

SSDmg = BaseSSDmg * (.26*2.3 + (1 - .26 - .05)) = BaseSSDmg * 1.288

BSDmg = BaseBSDmg * (.56*2.3 + (1 - .56 - .05)) = BaseBSDmg * 1.678

How much of an increase is this?

WhiteDmg increase = 0.95%

SSDmg increase = 1.02%

BSDmg increase = 0.78%

Sinister Strike gets a bigger increase in damage than white damge does, due to Lethality. Backstab gets a lot less of an increase even with Lethality, because increasing your crit rate from 55% to 56% is a much small increase than from 25% to 26%.

How much of an increase in total damage does this translate into? This depends on how much of your damage comes from your special attack and how much comes from white damage, which will depend a lot on your talent build. Your Backstab damage can probably vary from 30% to 40% of your total damage while Sinister Strike is probably only 20-25%. So dagger rogues get hit double here - not only is their main attack less affected by an increase in crit rate, their main attack accounts for more of their damage. This means dagger rogues get less of an increase in damage than you would think by calculating their increase in white damage, while sword rogues get a little bit more of an increase than you would think.

Total increase:

Dagger rogue, 40% BS, 50% white, 10% misc (poisons, procs, etc): (.4*.78 + .5*.95 + .1) = 0.887%

Dagger rogue, 30% BS, 60% white, 10% misc (poisons, procs, etc): (.3*.78 + .6*.95 + .1) = 0.904%

Sword rogue, 20% SS, 70% white, 10% misc (poisons, procs, etc): (.2*1.02 + .7*.95 + .1) = 0.969%

If we had started with a better-equipped rogue with a 30% crit rate and 14% to hit (which is close to what I have), these numbers get worse:

WhiteDmg = BaseDmg * (.3*2 + (1 - .3 - .10 - .05)) = BaseDmg * 1.15

SSDmg = BaseSSDmg * (.3*2.3 + (1 - .3 - .05)) = BaseSSDmg * 1.34

BSDmg = BaseBSDmg * (.6*2.3 + (1 - .6 - .05)) = BaseBSDmg * 1.73

Add 1% crit:

WhiteDmg = BaseDmg * (.31*2 + (1 - .31 - .10 - .05)) = BaseDmg * 1.16

SSDmg = BaseSSDmg * (.31*2.3 + (1 - .31 - .05)) = BaseSSDmg * 1.353

BSDmg = BaseBSDmg * (.61*2.3 + (1 - .61 - .05)) = BaseBSDmg * 1.743

WhiteDmg increase = 0.87%

SSDmg increase = 0.97%

BSDmg increase = 0.75%

Total increase:

Dagger rogue, 40% BS, 50% white, 10% misc (poisons, procs, etc): (.4*.75 + .5*.87 + .1) = 0.835%

Dagger rogue, 30% BS, 60% white, 10% misc (poisons, procs, etc): (.3*.75 + .6*.87 + .1) = 0.847%

Sword rogue, 20% SS, 70% white, 10% misc (poisons, procs, etc): (.2*.97 + .7*.87 + .1) = 0.903%

Talk moved in from WoWWiki:Village pump

Cirt hit formula error?

I'm not really willing to "fixing things" that seem incorrect to me,that may be questionable with respect to authors intent of content. Thus, I'll post here and, hopefully, someone else can set me straight or fix the blow outlined error.

In Base chance to crit in Melee The author uses a "template" style forumla for the basis of all following example formulas as follows:

Damage = BaseDamage * HitChanceNotIncCrit + BaseDamage * 2 * CritChance
       = BaseDamage * (HitChanceNotIncCrit + 2 * CritChance)

Example formula using the "template" from this article:

Damage = BaseDamage * ((1.00 - 0.05 - 0.25) + 2 * 0.25)
       = BaseDamage * 1.20

If you look at the template and resulting "valued" formula, you can see that the template has an extra value and operation involved as in.

Damage = BaseDamage * HitChanceNotIncCrit + BaseDamage * 2 * CritChance
       = BaseDamage * (HitChanceNotIncCrit + 2 * CritChance)

As I said, there may be some purpose or reason for having BaseDamage in there and not utilized in the resulting formuals but I see no purpose behind having this extra operation in the definition -- it would invalidate results if it were used as published.

In my opinion the formula should probably read as follows, based upon resulting formuals:

HitChanceNotIncCrit = (HitChance - DodgeChance - CritChance)
Damage = BaseDamage * HitChanceNotIncCrit + 2 * CritChance = BaseDamage * (HitChanceNotIncCrit + 2 * CritChance)

The addition of a formula HitChanceNotIncCrit allows for more understandable viewing of the resulting formulas.

Eleazaros 16:33, 2 September 2006 (EDT)

Well your thinking is basically the same. However, your formula is a bit erroneous. HitChanceNotIncCrit should be:

HitChanceNotIncCrit = 100% - DodgeChance - ParryChance - BlockChance - CritChance

But again, this is very basic and should be assumed by any readers. HitChance is obviously already the chance that it'll hit, which takes into account any type of evasion chance.

Secondly, there is most definitely a use for BaseDamage * 2 * CritChance. You screw up the fomula otherwise.

Damage = BaseDamage * HitChanceNotIncCrit + 2 * CritChance
       = BaseDamage * (HitChanceNotIncCrit + 2 * CritChance)

This is horridly bad. Note the parentheses. Do you remember your algebra? The two lines don't even equal eachother. The second BaseDamage is melded into the first one since:

Damage = BaseDamage * (HitChance + 2* CritChance) = BaseDamage*HitChance + BaseDamage*2*CritChance.

Also, if you think about it, 2 * CritChance by itself has no use at all in calculating damage. It's just the chance to do a crit, not how much damage you'll do with that crit.

Pzychotix 19:22, 2 September 2006 (EDT)

Well, I didnt want to say it... but to correctly "merge" probability values, you multiply or divide them, and you also will need the actual chance for your hit, not the chance you're not hitting. So it would be...

HitChanceNotIncCrit = (1-DodgeChance) * (1-ParryChance) * (1-BlockChance) * (1-whateverotherchancesyoumightfind)

and I dont really think that the crit chance should be in this value

-watchout 18:59, 4 September 2006 (EDT)

Oh dear, someone really doesn't have their head around this.

From the top.

The 'total' damage you will do is your normal hit damage plus your crit hit damage. For this we're still ignoring things like Glancing Blows.

Now, your chance to get a normal hit is:

NormalHitChance = 100% - MissChance - TargetDodgeChance - TargetBlockChance - TargetParryChance - AttackerCritChance

i.e. it's what's left over when all the other possibilities (ignoring Glancing Blows for now) are taken into account. Note also that TargetBlockChance and TargetParryChance are often ignored on the assumption we're attacking from behind.

So, our damage from normal hits is:

NormalHitsDamage = BaseDamageofWeapon * NormalHitChance
                 = BaseDamageofWeapon * (1.00 - MissChance - TargetDodgeChance - TargetBlockChance - TargetParryChance - AttackerCritChance)

Yes, I did a switch from 100% to 1.00 notation there.

Now work out the damage from a Crit 'hit'. In WoW Blizzard simply made this double the normal hit damage (if there are no talents or other abilities specifically increasing crit damage):

CritHitsDamage = BaseDamageofWeapon * 2 * CritHitChance

That's where the "* 2" comes from.

Now add it together:

TotalHitDamage = BaseDamageofWeapon * NormalHitChance + BaseDamageofWeapon * 2 * CritHitChance

Which, given BaseDamageofWeapon is a common factor either side of the + sign can be re-written as:

TotalHitDamage = BaseDamageofWeapon * (NormalHitChance + 2 * CritHitChance)

You can of course then start factoring in any Crit damage modifiers:

TotalHitDamage = BaseDamageofWeapon * (NormalHitChance + 2 * CritHitChance * CritDamageModifiers)

Clearer now ?

Athan 10:11, 13 September 2006 (EDT)

Beaza's Changes

Reverted the numbers to 1.12 until BC is released since values are subject to change.

--Beaza 18:15, 30 November 2006 (PST)
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