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]

Originally Posted by 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.

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]

Originally Posted by Krollin

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.