Chance to hit and its translation to crit %

[Gimped]

First off, forgive any glaring or gross ignorance of math and Warcraft. I have had a number of people tell me over the past few days that an extra 1% chance to hit is equal to an extra 1% chance to crit, but I don't see the connection.
Let's say, for example, I have a 15% chance to crit and 76% chance to hit. I subsequently acquire a bow that gives me +1% chance to hit. Would this not just result in 1% more hits (assuming infinite trials) - 77% chance to hit - with the same crit percentage of 15%?

This may be a silly question but it's late and I'm bad at math, so again forgive my feeble attempt at using numbers :happy34:

Edit: Just realized that perhaps they meant you would have 1% more total crits, but even then I thought you would only have 0.15% more crits based on the above example?

[Krollin]

Well there is a relationship between hitting and critting but its not what others have told you.

Chance to Hit% is quite simple, the higher it is the more often you will hit.

This does not have any direct effect on your Chance to Crit% however.

What it does do is improve your chances of being able to crit at all, if you don't hit you cannot crit, simple.

Example with 20% Crit chance.

25% Hit chance means 1 in 4 of your attacks will, on average, hit the target.
Each of those hits has a 20% chance to crit so...
1 in 20 attacks should produce a critical hit.

50% Chance to hit means 1 in 2 attacks will, on average, hit the target.
Each of those hits has a 20% chance to crit so...
1 in 10 attacks should produce a critical hit.

Doubling your Chance to Hit% has not affected your crit%, it remains the same. However your critical hit frequency has been increased due to you hitting more often.

Equation is

Crit% per attack = (Hit Chance/100) * (Crit Chance/100) * 100.
or (50/100) * (20/100) * 100 = 0.5 * 0.2 * 100 = 10% chance per attack.

[NotAgain]

If you have 1% extra chance to hit, those extra attacks that will hit will sometimes also crit, thus giving you more TOTAL crits, but not a higher crit %.

[Kaiylen]

So, the question boils down to: What's better? 1% to hit, or 1% to crit? My gut feeling says crit, since special attacks hit something like 95% of the time anyway, and auto-attack damage is just icing on the cake.

[Konrad]

So, the question boils down to: What's better? 1% to hit, or 1% to crit? My gut feeling says crit, since special attacks hit something like 95% of the time anyway, and auto-attack damage is just icing on the cake.

If you depend only on normal hits, it's 1:1 my opinion

[galzohar]

For normal attacks, chance to hit is quite better when dual wielding. Hitting 77% instead of 76% is almost a 1.33% increase in DPS, while an extra crit % is slightly less than 1% increase in DPS.
However, most of your damage is in your specials. When a special (with the exception of evis) misses, you lose very little energy and can attack again, so chance to hit has little effect on DPS of your specials (which do way more DPS than normal attacks AFAIK).
One last thing to note is that in PvP when performing stunlocks, you'll want to smack yourself on the head every time you miss, though even if you never miss the enemy can still parry/dodge you.
Bottom line is that the value of chance to hit is quite impossible to measure :(

[jtkrause]

With the formula above:
if you have 10% to crit each 1% hit will give you 0.1% crit.
if you have 20% to crit each 1% hit will give you 0.2% crit.
if you have 30% to crit each 1% hit will give you 0.3% crit.

Are you sure that's right? That doesn't make +hit look that great.

[Havoc Jack]

25% Hit chance means 1 in 4 of your attacks will, on average, hit the target.
Each of those hits has a 20% chance to crit so...
1 in 20 attacks should produce a critical hit.

50% Chance to hit means 1 in 2 attacks will, on average, hit the target.
Each of those hits has a 20% chance to crit so...
1 in 10 attacks should produce a critical hit.

Sorry, it doesn't work that way.

When the game rolls the outcome of a swing, it does it on a table, for example, from one to 100. With the numbers from the quote, a roll below 20 gives you a crit, a roll below 25 gives you a hit, and a roll above 25 gives you a miss. From a game design perspective, this makes more sense, as the game only has to roll once, instead of multiple times. (Remember the game also has to decide about dodges, blocks, parries, glancing blows, and that sort of thing).

+hit does not change yellow damage at all; skills are locked at 95% chance to hit. As evidence, try leveling up a new skill. If you havn't touched it before, nearly all of your swings will miss, and the few that get through will deal normal damage. But if you use a skill, the skill will almost always hit, and for as much damage as you'd expect it to.

Considering white damage only, +hit and +crit are exactly the same. Consider an individual swing, on which you can hit, miss, or crit. Your hit chance is (1-miss), your crit chance is C, and you hit for D damage. A crit deals 2D damage.

Assuming you're not dual wielding, miss=5%, and therefor hit=(1-.05)=0.95, or 95%. Any additional +hit from items adds directly to this number. Your chance to hit, then, is 95% minus your chance to crit, which is C. So a swing on average will deal damage equal to

(0.95+H-C)D+C*2D

Multiply through (0.95-C) by D, and we get

0.95D+HD-CD+2CD

Add together, and factor out the "D"

(0.95+H+C)D

Ok? So if we have a 5% chance to crit and no +hit, then "D" would be multiplied by 1. Add 1% hit, and D would be multiplied by 1.01. Take away that 1% hit and add 1% crit instead. D would be multiplied again by 1.01. Considering white damage only, +hit = +crit.

+crit is better when it comes to yellow damage. As I've stated, chance to hit doesn't affect yellow damage at all. But chance to crit does, so therefor yellow damage is benefitted more by chance to crit. Additionally, there are often talents which proc on a critical hit, which further increase dps from +crit, while ignoring +hit.

[towelrod]

I agree with you about the game only making one roll. It helps if you think about +1% hit really being -1% miss.

Crits are different. If you have 20% crit, then 20% of your SWINGS will crit, not 20% of your misses.

I'm not sure about the distinction between white and yellow damage, however. I was recently skilling up my polearm on my warrior, so I was just spamming hamstring/gouge every second. I missed pretty much all the time with both of those for a long time. Those aren't big yellow damage like MS, but they are still yellow damage (and certainly special attacks).

I think the difference is that special attacks are not penalized if you are dual wielding. But that's just a guess, I haven't done any research.

Another thing to think about is that a crit is usually worth more than 2x a hit. Crits have side effects: they trigger extra damage via deep wounds, or frenzy, or give extra combo points.

[Havoc Jack]

I'll check the yellow damage and miss thing next time I skill up a weapon. It's been a while since I did it in the first place.

As for your last paragraph, I know. Read my last paragraph.

[Caradok]

Havoc Jack is correct about the mechanics and it affects specials too. There is one roll and it is checked against a look-up table. That table has (for arguments sake) 100 entries, 1-100, 1-5 are misses, 6-95 are regular white damage hits and 96-100 are crits. This makes combat fast and minimises CPU time on the server/client.

+1% hit merely reduces your miss rate by 1%, so there is a maximum beneficial +hit% (5% for 1-H, 24% for dual wield, 6-9% for ranged assuming equal level opponents)
+1% crit swaps 1%hit chance for 1% crit chance and crit generally deasl 2x damage.

So both +1% hit and +1% crit give +1% to your total damage output or +dps/100*wpn spd per swing.

BUT - crit can be worth more than 2x damage (hunter using mortal shots has +30% crit damage) and some attacks can not crit, but can miss.

So not cut and dried.

[Krollin]

Yeap, Havoc Jack is correct.

I have since learnt a lot more about how attack rolls are resolved.

[Havoc Jack]

Whoops! forgot to report back in.

I tried leveling up a new skill, and my specials missed just as much as my normal hits did. As such I retract my statement that skills are unaffected by +hit.

Regarding the comparison of +hit and +crit, I've derived an exessively detailed formula (http://forums.worldofwar.net/showthread.php?t=373985) for it regarding druids and cat form. It can get complicated.

[Umi]

Without talents, 1% crit is generally equal to 1% crit.

Vs a normal mob, base stats is 5% miss, 90% hit, 5% crit.

The +1% "to hit" bonus converts 1% of miss into 1% of hit.

4% miss, 91% hit, 5% crit.

The +1% "to crit" bonus converts 1% of hits into 1% of crits.

5% miss, 89% hit, 6% crit.

This means assuming equal weapon skill vs defense, anything more than +5% hit is wasted, as there are no more miss results to convert to hits.

In theory getting more than +90% crit is also useless, but that pretty much never happens, and I doubt anybody would complain if it did =P

As far as the value of +hit% vs +crit%, it depends entirely upon talents really, as well as proc's on "hit"

100 white damage attacks, 5/90/5 (miss/hit/crit) with a base of 10 damage"

5 misses for 0 damage
90 hits for 900 damage
5 crits for 100 damage
Total damage = 1000

+5% hit (0/95/5)
0 misses for 0 damage
95 hits for 950 damage
5 crits for 100 damage
Total damage = 1050 (+5% dps)

+5% crit (5/85/10)
5 misses for 0 damage
85 hits for 850 damage
10 hits for 200 damage
Total damage = 1050 (+5% dps)

As you can see, in pure white damage, they are 100% equal, until you hit the +5% cap for miss.

The two major factors are talents that boost "critical damage" as well as abilities that proc "on hit" or "on crit"

The warrior talent impale, for example, boosts the damage from crits, which improves the value of +crit%. The sword spec for warriors, which has a chance to proc an extra swing (but isn't based on crit) only cares if you hit or miss, regardless of crit. For sword spec +hit% is more valuable. Flurry, another warrior ability, triggers only on a crit, and once again increases the value of +crit%.

Really, the important thing is to look at which talents are based on you criting, and which are based on "a successful attack" as well as gear that has a proc based on "chance on hit"

Windfury, for example, will trigger for a shaman on a hit, but not a miss. It's 20% chance on hit.

5/90/5, and assume 1/5 (perfectly reliable 20%) procs on 100 hits

5 misses, 0 windfury proc's
90 hits, 18 windfury proc's
5 crits, 1 windfury proc
Total = 19% chance to proc windfury

0/95/5 (+5% hit)

0 misses, 0 procs
95 hits, 19 procs
5 crits, 1 proc
Total = 20% procs

with +5 crit, 5/85/10

0 misses, 0 procs
85 hits, 17 procs
10 crits, 2 procs
Total = 19% to proc

[ProteanBlue]

Sorry, it doesn't work that way.

When the game rolls the outcome of a swing, it does it on a table, for example, from one to 100. With the numbers from the quote, a roll below 20 gives you a crit, a roll below 25 gives you a hit, and a roll above 25 gives you a miss. From a game design perspective, this makes more sense, as the game only has to roll once, instead of multiple times. (Remember the game also has to decide about dodges, blocks, parries, glancing blows, and that sort of thing).

+hit does not change yellow damage at all; skills are locked at 95% chance to hit. As evidence, try leveling up a new skill. If you havn't touched it before, nearly all of your swings will miss, and the few that get through will deal normal damage. But if you use a skill, the skill will almost always hit, and for as much damage as you'd expect it to.

Considering white damage only, +hit and +crit are exactly the same. Consider an individual swing, on which you can hit, miss, or crit. Your hit chance is (1-miss), your crit chance is C, and you hit for D damage. A crit deals 2D damage.

Assuming you're not dual wielding, miss=5%, and therefor hit=(1-.05)=0.95, or 95%. Any additional +hit from items adds directly to this number. Your chance to hit, then, is 95% minus your chance to crit, which is C. So a swing on average will deal damage equal to

(0.95+H-C)D+C*2D

Multiply through (0.95-C) by D, and we get

0.95D+HD-CD+2CD

Add together, and factor out the "D"

(0.95+H+C)D

Ok? So if we have a 5% chance to crit and no +hit, then "D" would be multiplied by 1. Add 1% hit, and D would be multiplied by 1.01. Take away that 1% hit and add 1% crit instead. D would be multiplied again by 1.01. Considering white damage only, +hit = +crit.

+crit is better when it comes to yellow damage. As I've stated, chance to hit doesn't affect yellow damage at all. But chance to crit does, so therefor yellow damage is benefitted more by chance to crit. Additionally, there are often talents which proc on a critical hit, which further increase dps from +crit, while ignoring +hit.

This is on the right track but wrong on some very important points. Absolutely there is a single table that the game rolls once on per attack determination. However, a 20% crit chance does not equate to 1-20 or 80-100 on this table. If you have a 50% chance to hit then a 20% crit chance will be a 10 digit range etc... For example we'll say that you have a 90% chance to hit, 20% chance to crit. The range would be like so 1-10=miss, 11-82=hit, 83-100=crit. If you want to test it get any hunter you know. They probably have never trained throwing weapons in their life, or if they did they probably did not skill it up. Get a warrior to maintain agro on a mob but not kill it, have the hunter continuously throw weapons at the mob. Check his crit rate, there is your proof. Most 60 hunters will have like 20-30% crit and he will miss around 99% if his weapon skill is lower then like 75 against a 55ish mob. So in your table theory he would either miss or crit because there would be no room on the table for normal hits. However, in practice, his crit % of succesfull attacks will be exactly the same as his paperdoll crit % but his crit % of total attacks will be greatly diminished.

As far as yellow damage, I realize that there can be a greater then 5% miss chance on yellow damage because of weapon skills, you can spam wing clip or other yellow damage abilities with no weapon skill and you will only miss. However, I'm not sure if it does in fact follow the normal tables, there might be a boost of like 23% or w/e to counteract dual wielding, that wouldn't overshadow the penalties for extremely low weapon skill, but would certainly appear like a 100% chance to hit with a weapon skill = to the opponents defense skill. There also are some yellow damage abilities that specify that they can not be blocked, dodged or parried. While they still have the same miss chance as other attacks it appears as if it is lower due to the absence of dodges primarily, and with some classes parries.

There are also the factors of talents that raise crit damage, or proc off of crits or have some effect based on crits. Naturally, this makes crits very desireable in many situations. These effects are probably reason enough to make +crit% almost always greater then +hit%, but the factor of a soft cap on hit% seals it for sure.

In conclusion, %hit raises your dps in an amount greater then 1% until you reach 100% (or whatever the cap is for hit% probably like 99.50 or something) and then it has no effect. For example if you have 95% chance to hit and you get +1% to hit you will now be 96% to hit. Your dps will be 1/95th higher. That fraction equates to .0105 which is 1.05% thrilling I know, but just to give you an idea. Now, to determine exactly how much +%hit you need to get in order to reach 100% is the challenge. On players 25defense is equal to 1% to hit, meaning you'd need 1% to hit for every 5 lvls a player is above you assuming they have max defense for their lvl and you have max weapon skill for your level. However, on non-player characters, aka mobs, there is some kind of a parabolic scale to miss chance. You may have noticed it, but trying to hit a mob that's red to you is nearly impossible, even if the mobs is less then 10 lvls higher then you. Against a player that might only be a change of 2% but on a mob it's closer to 50-70%. So in raiding and pve environments +%to hit is far more important then in pvp environments. For pvp you will probably never need more then +5% to hit from items and talents, unless you are dual wielding.

Ok absolutely last thing to mention on hit%. Hit% is effected by your weapon skill vs the targets defense skill. Because of a weird determination of game mechanics, this makes weapon skill highly more desireable on mobs then +%hit. For example if you have a mob 3 lvls higher then you his defense will be 15 higher then your weapon skill. Now on terms of %hit there is some cumulative formula, and I would guess it is between about 8-10% miss in addition to your base. Whereas on a player it would be less then 1% miss. However, the mobs defense skill is unchaned as opposed to the player, it just calculates the miss chance parabollically rather then linear. So while you might need +15% hit (10% from skill difference 5% base) to hit the mob you would only need +6% hit to hit the player. But for both you would need exactly 15 weapon skill +5% hit. Now for the player you could remove the 5% base hit with 140 weapon skill. I'm not 100% sure on the mob, but I think that lower defense (lower level) mobs suffer from a penalty correlating to the higher parabolic benefit they get at higher lvls. For example I imagine that a mob that is grey to you would probably be close to 99-100% chance to hit. Since this would be about 10 lvls, that's approximately 50 defense difference, but rather then 2% to hit it becomes 4% maybe even higher.

For visual reference of the phenomena that I'm describing I'm going to make a hypothetical chart. It will visualize the idea, but the numbers will be fictitious. Hopefully reasonable, but in no way 100% accurate.

Difference in:
Level..........Defense......+%miss
-3.............-15............ -1.5%
-2.............-10............ -.75%
-1.............-5.............. -.25%
0...............0............... 0%
1...............5............... .75%
2...............10............. 2.25%
3...............15............. 6%
4...............20............. 11%
5...............25............. 18%
6...............30............. 27%
7...............35............. 39%
8...............40............. 51%
9...............45............. 67%
10.............50............. 85%

The point is that it can be more beneficial to get +weapon skill to overcome miss% vs very high lvl mobs. If you have a mob 10 lvls higher then you and you have +15 weapon skill then that mob would drop from 85% miss to 39% miss. However if you have a mob of equal lvl then +15 weapon skill will probably only reduce your base miss chance by like 1-2%. Again the actual results will vary but I tried to be reasonable based on percieved miss chances etc... Also, it should be noted that weapon skill and defense also effect dodge, parry, crit, and glancing blow chances. 5% hit will only effect the hit % while +weapon skill will also reduce the mobs chances to dodge, parry, reduce crits, and glancing blow. However, I have no idea if the mob and players defense effects these in the same way from defense or if a mob gets a parabollic advantage as with +hit%. I would assume that the mob gets a parabollic advantage. An extremely easy way to test what I'm demonstrating is to attack a lvl 1 critter in any of the end game instances and see that your crit chance is like 99%. This is due to their 5 defense vs your 300 weapon skill. Then attack a lvl 1 player and you will see that your crit chance is high, but not 100%, probably 12% higher then normal. Probably be easier to test on like a lvl 30 mob and a lvl 30 player, then the player will survive longer so you don't have to take as much time between hits and you can get a good idea of the visual % to crit/hit etc...

Anyway, I hope this clarifies things, but I gotta go to formation now.