Having been sort of an advocate for +hit myself the past 2 years, I've recently become starting to wonder if it is really as good a stat as we believe it is.

The biggest problem I see about the +hit stat is:
a. It's still chance based. (Even a mage with 99% hitchance could get 5 resists in a row)
b. It's only applied to a rather small margin of 16%.

And the biggest reason I started to wonder is because, due to circumstances I ended up with a set of raidinggear that has very low +hitrating (3,5% without talents) (even though I've been trying to improve it).

Yet on the other hand I really don't feel like my DPS suffers from it, nor do the damagemeters. On bossfights I often top the DPSmeters (among the mages) even while some other mages have like 6% more hitchance than me (and slightly lower spelldamage.)


This made me believe that our simple: "X DPS (if 100% hit) * hit% = average DPS" theory doesn't fly, which is I believe still the biggest base of theorycrafting with hitchances, which led a grand majority of mages to believe that +hit reigns supreme over all other stats. Yet however if this would be true, then why did Blizzard make it one of the "cheapest" stats to get?


What I basically am thinking is that our mathematics for theorycrafting around %-based stats (like hit and crit), should be taken a step higher then just multiplying. Basically, we should have to apply heavy statistical chancebased mathematics. It has been a looong time since I've had statistical classes in university but there is 1 thing I do remember, and that is that certain marginal % chance-values in statistics can be neglected because of the chance that the actual results will vary from the "theoretical average" is very big. Or more simple said: There isn't a big difference between a 87% hitchance value on DPS or a 94% hitchance value. The difference is, due to the nature of chance, neglectible. Which would basically mean that +spelldamage (with a margin of play between 16% hitchance (bossmob resistchance) is still alot more reliable for DPS, instead of upgrading your stats with a chancebased stat (like hit or crit) instead.

Offcourse this is only just a bit of a vague theory which I'll have to back up with numbers, but this thought has been haunting my mind for a few weeks now so I'd thought I'd share the basic philosophy allready before I'd embark on a mathematically delicious journey in the world of statistics, and most likely there will be people more specialised then me in statistical-mathematics or chance-calculations then me, which could help clarify the "real" mathematics behind %-based stats.

It's simple math really, though. Increasing hit% will, on average, boost your damage by a specific known amount. However, due to itemization costs hit% is cheaper than crit%, so hit% is always more valuable than crit% until you are capped out.

One can make the argument for statistical reliability, however TBC fights tend to be resonably long and the number of spells cast in a raid is enough for many larger trends to play out. On one Gruul fight, you're looking at casting 80+ Fireballs/Scorches with a Fire build, and substantially more as a Frost or Arcane mage.

Over such a sample size, I think there would be quite an obvious end result of having, for instance, a 1% resist rate and a 16% resist rate.

The thing is that in statistics, to actually see the real difference of 15% appear between 1% resistchance and 16% resistchance, you'd have to have cast the theoritical amount of "infinite" spells.

Yes, the fights in TBC are averagely 8-10 minutes long. But, to refer to your example, 80 is nothing compared to "infinite". You might notice a slight difference, but the difference will never be exactly 15% (ofcourse).. but not only that, due to the range being 84% to 99% hitchance, the chance that you'll actually get to notice a difference far smaller then the 15% is very big. Because you've got in that range a much bigger chance to get a hit, then to not get a hit.

I'm not saying that you won't notice a difference, but the difference will very rarely be 15% or bigger, in fact, the chance that you won't notice a difference (or the mage with 85% hitchance getting more hits than the mage with 99%) is about the same as seeing an exact 15% difference in hits.

Edit: after rereadin, I seem to /fail at expressing what I exactly want to stay, so i'll try to explain it with an example.


For example do take a mage with 99% hitchance (mage A) and a mage with 84% hitchance (mage B)(although most mages have the +3% hitchance talent I suppose).


Now in pure theory you'd see the following:
End of the fight:
Mage A's DPS: 990. (1% resists)
Mage B's DPS: 840. (16% resists)
DPS difference: 150 (15%).

In reality you would most of the time get results more like this:
Mage A's DPS: 1000. (0% resisted)
Mage B's DPS: 900. (10% resisted)
DPS difference: 80 (10%).

There are certain formulas that could show which the average amount of mage B's resist% is the highest, I for now just made an excel file filled with ASELECT fields and spammed F9 a number of times, the result of resists popping out most was 10% resists. (On some occasions even 3% (or 18%).

Offcourse the above is with the assumption of the biggest possible hit% difference that mages can have. 1% and 16%. But when you'd take some more realistic "daily" numbers of raiding mages you would have to compare the statistical DPS difference between a mage (B) with 88% hitchance and a mage (A) with 93% hitchance (just random common numbers taken as example.)

If you'd applied a same sort of test with these numbers you would get stuff like this:

Pure theory:
Mage A: 930 DPS (7% resists)
Mage B: 880 DPS (12% resists)
Difference: 50 DPS (5%).

In reality you'll most of the time see results like this:
Mage A: 940 DPS (6% resists)
Mage B: 920 DPS (8% resists) (again this number derived from spamming pages of ASELECT in Excel).
Difference: 20 DPS (2%).

But this offcourse is with the assumption that both mages have the same amount of stats with the only difference being hit%. While in reality the mage with more hit% will often has somewhat less +spelldamage or crit. Thus then we can start to wonder how reliable it really is to sacrifice spelldamage for hit.

It sounds to me like you've spent one too many hours at the hookah bar, my friend. Come back from your astral journey.

Your spell hits the boss. Would it have hit anyway, without your +hit gear? Was that extra 3 hit rating socket bonus that made the difference, or was it the hit rating from your Spellstrike Hood? Maybe it would have crit, if not for that wretched hit gear you swapped in for the fight? Or got corrupted to packet loss, had not the crit flag been set to zero? Did God will your spell to hit the boss? Did Blizzard will it? Is Tigole watching you, right now, rolling on his almighty percentage tables to decide whether your next keystroke will be a typo?

It doesn't have to be as complicated as all that. You plug the numbers into the equation and you get your average damage on the other side. Hit makes your DPS more dependable, and crit/damage make it more spikey. That's all you really need to think about.

Unless I'm doing my math wrong, the statistical chances of being able to cast 80 nukes in a row without a resist with a 1% resist rate is around 45%. A similar statistical chance of a resist with a 16% resist rate occurs around the 18 cast mark.

Even in worst-cast scenarios, I would say the difference between 16% and 1% is extremely non-trivial. Furthermore, the value of hit and crit scale with damage as well--when you already have average Fireballs of 3.4k, it would take a hell of a lot of +dmg to compensate for evening resisting one Fireball over the course of 80.

1 point of +dmg adds roughly 2 damage to my average Fireball with my current figures. Over 80 Fireballs it would add 160 damage. Therefore, I would need 21.25 +damage to counter the effect of 1 single resist. You would need 272 +damage to counter the effect of the average ~13 resists you would get after casting 80 spells at a 16% resist rate.

You could say the same for crit.



Fact is, a resist cant crit, and isn't affected by spell damage. Hit is not overrated and never will be, not in the current system. For melee its questionable to a point, for casters, it is not. Stastically speaking, yes, there will be variations, but any amount of basic knowledge of statistics or probabilities or the game itself will argue not in your favor.

HOWEVER, one could calculate the value of spell damage or crit VERSUS hit, and say that even though 16% get resisted, those 84% that don't hit so hard, it makes up for the 16 resists.

However, given the item budget system and the fact that spell hit is thankfully so cheap, hit is still the most effecient method of doing more damage.


As well, playing into the variations in a fight is not good theorycrafting. One could say, "Well, I amassed 1400 fire damage, so my one fire blast would kill the mob before it reached me." Yes, but could you do it again? What if it resisted? Would you have enough mana to recast, or enough heal to survive the melee?

Arguements on this forum tend to be all encompassing. There is a reason that the preferred method of DPS theory is spreadsheets, and not single lines of text such as 16% x300dps.

After rereadin, I seem to /fail at expressing what I exactly want to stay, so i'll try to explain it with an example.


For example do take a mage with 99% hitchance (mage A) and a mage with 84% hitchance (mage B)(although most mages have the +3% hitchance talent I suppose).


Now in pure theory you'd see the following:
End of the fight:
Mage A's DPS: 990. (1% resists)
Mage B's DPS: 840. (16% resists)
DPS difference: 150 (15%).

In reality you would most of the time get results more like this:
Mage A's DPS: 1000. (0% resisted)
Mage B's DPS: 900. (10% resisted)
DPS difference: 80 (10%).

There are certain formulas that could show which the average amount of mage B's resist% is the highest, I for now just made an excel file filled with ASELECT fields and spammed F9 a number of times, the result of resists popping out most was 10% resists. (On some occasions even 3% (or 18%).

Offcourse the above is with the assumption of the biggest possible hit% difference that mages can have. 1% and 16%. But when you'd take some more realistic "daily" numbers of raiding mages you would have to compare the statistical DPS difference between a mage (B) with 88% hitchance and a mage (A) with 93% hitchance (just random common numbers taken as example.)

If you'd applied a same sort of test with these numbers you would get stuff like this:

Pure theory:
Mage A: 930 DPS (7% resists)
Mage B: 880 DPS (12% resists)
Difference: 50 DPS (5%).

In reality you'll most of the time see results like this:
Mage A: 940 DPS (6% resists)
Mage B: 920 DPS (8% resists) (again this number derived from spamming pages of ASELECT in Excel).
Difference: 20 DPS (2%).

But this offcourse is with the assumption that both mages have the same amount of stats with the only difference being hit%. While in reality the mage with more hit% will often has somewhat less +spelldamage or crit. Thus then we can start to wonder how reliable it really is to sacrifice spelldamage for hit.

Axira, you should have some real, hard data ready to present before you pursue this any further. Subjective analysis has very little value for what we're talking about. This is like audiophile nonsense about speaker cables affecting tonality and crap like that.

Once you have real statistics available (large sample set, not cherry-picked, standard deviations calculated, p-value determined, yadda yadda), then we can talk about why we aren't seeing what we would expect from looking at hit chance in Armory. If there is a real discrepancy, it can probably be explained by group buffs or mob debuffs affecting chance to hit. Your testing may still be valuable, but until you have numbers to back it up you're just creating unnecessary uncertainty.

As a sidenote:

Even scenarios like this can happen between mage A (93% hitchance) and mage B (88% hitchance):

Mage A: 880 DPS (12% resists)
Mage B: 920 DPS (8% resists)
Difference: 40 DPS (4%).

Offcourse the chance for above scenario to happen is "low". But it can happen ofcourse, and it can happen more then people think, due to the fact that a window of 16% (in above scenario even only 5%) is rather small when it comes to statistical mathematics (reality).

I don't think i'm creating unnecessary uncertainty.
I'm merely trying to explain some very basic statistical theories about how %'s and chances should be calculated to get realistic values (on which you can depend/rely).

I've got problems with expressing myself with "simple" words, because we all know statistics isn't just a thing in which you can add up or multiply a few numbers to get the result of your calculations. That's why I'm trying to show certain not-so-uncommon examples.

What I'm really trying to say is that, and btw. you bring up a really good point there with raidbuffs etc. that even make the hit%-gap smaller, is that with a window of 16% hitchance to play with, the possibility to neglect hitrating without crippling your DPS with it is very likely.

Anecdotal evidence is often unscientific or pseudoscientific because various forms of cognitive bias may affect the collection or presentation of evidence. For instance, someone who claims to have had an encounter with a supernatural being or alien may present a very vivid story, but this is not falsifiable.

A common way anecdotal evidence becomes unscientific is through fallacious reasoning such as the post hoc fallacy, the human tendency to assume that if one event happens after another, then the first must be the cause of the second. Another fallacy involves inductive reasoning. For instance, if an anecdote illustrates a desired conclusion rather than a logical conclusion, it is considered a faulty or hasty generalization.

In science and logic, the "relative strength of an explanation" is based upon its ability to be tested, proven to be due to the stated cause, and verified under neutral conditions in a manner that other researchers will agree has been performed competently, and can check for themselves.

-http://en.wikipedia.org/wiki/Anecdotal_evidence

What you fail to realise is it can work the other way.

Given you have a 16% resisted rate, there is a distinct possibility of only having 12% of your spells resisted, but there is also the exact same chance that 20% of your spells will be resisted.

Okay here's some real hard data - if you want the (admittedly poorly presented) excel file I can put it up. Used a Poisson distribution to calculate chance of a certain number of resists given the following set of circumstances.

5:1 Fireball:Scorch cast sequence
200 ms latency
Each rotation takes 17.7 seconds, give or take for all 6 casts
Given an 8 minute fight you would get approximately 163 casts - lets knock this down to 144 due to movement/other random elements of the encounter (and it's easily divisible by 6)

120 Fireballs
24 Scorches

In all the following situations the chance of a resist on a fireball will be 5/6, and scorch 1/6

Scenario 1: 950 Fire Damage, 30% fire Crit, 16% spell hit
Average Fireball: 3124.41
Average Scorch: 1385.413

Resists | Probability
0 .2369
1 .341176
2 .245647
3 .11791
4 .042448
5 .012225
6+ .003666

So now to put all this together (in my math i went all the way down to the chance that EVERY spell will be resisted which is 2.7x10-228 in case you were wondering)
The expected damage lost due to resists is 4081.791 loss of 8.5dps


Scenario 2: 950 Fire Damage, 38% fire Crit, 4% spell hit (elemental precision + random hit rating somewhere)
Average Fireball: 3301.541
Average Scorch: 1461.791

The resists probability is MUCH wider on this one so I wont list all many values, but the highest probability is 18 resists with a 9.23% chance
Expected damage lost due to resists is 56064.834 loss of 116.8dps

Nope, don't worry.. be prepared to be spammed with charts and graphics to proove what I've been saying. I thought I'd merely give some people a headstart if they'd wish to assist me in such statistical research. I'm at work atm, but I'll be working on creating tons of data this afternoon.

And offcourse I'll change my opinion if what I find as results didn't match with what I expected.


Edit:
Very nice calculations Mulva, the probability of resists combined with the stats of different mages is what I'm looking for indeed.
However the example you've given again is between the 2 extremes. 4% and 16%.
I'm quite sure if you'd compare it between perhaps 10% and 14% that the probabilities will be _very_ similar.

True, that is in a pure mathematical sense, but the fact is that due to the window being between the 84% and 99% value. It's alot more likely to get more hits. The likelyhood of "more" hits then theoretically expected (in mathematics) scales up the further the chance% is away from 50%. (And lower the further it is below 50%).

If for example the window was 50% then yes, the likelihood of getting a number of resists above 50% would be the same as getting a number of resists below 50%. However in the case of mage-mechanics we're talking about a window between 84% and 99% which totally shifts results in the favor of usually getting more hits and less resists than expected.

This is a bit OT yes and often results in flamewars, since there's no real "evidence" on the matter.


I personally assume, and I think most theorycrafting mages do, that crits can be resisted. (And are decided before the actual hitroll). Because the same mechanic is true for meleemechanics (crits being rolled before hits/misses are rolled), and there are statements by Blizzard on that matter.

I remember back in the day when spell penetration was first released that they had White and Yellow resis messages - white meant a "missed" spell akin to a melee miss (affected by spell hit) - yellow meant a "resis" due to the targets resistance (affected by spell penetration). This made total sense.

They then removed one of them so there was only one resis type - yet they claim that +hit and spell penetration are both necessary for reducing resistances while not providing the actual mechanics about spell misses/resistances.

While melee hit and mob hit mechanics are very well known with hit/crit/dodge/crushing/block/parry etc.

/boggle

I've never heard anything like this and it seems like wishful thinking. Can you elaborate or link to a discussion/explanation that expands upon or at least echoes this statement.

If the chance of an event is 85%, it seems ridiculous to me that 90% is a far more common outcome then 80% over any given meaningful set of trials.

Okay well I did more math, and using 950 damage, 30% crit, 13% hit as a baseline and using the 12.6 hit = 22.1 crit (since that's how much rating = 1% at 70) as equivalencies to get the other combinations of hit and crit I got the following:

Could it be that you have been playing around with DPS formulae involving %hit and %crit, checked to see how a 1% crit increase affected overall DPS and compared it to a 1% hit increase, then drew a wrong conclusion?

Because (assuming a one-roll-system,) with %crit below a certain threshold and %hit above some other threshold (both thresholds dependent on both %crit and %hit), a single %crit is more valuable in terms of DPS than a single %hit is, and becomes more and more valuable for lower values of %crit and/or higher values for %hit. Of course, 1% extra hit is easier to obtain than 1% extra crit.

I may be completely out of my league here, I remember squat about my statistic days but I cannot understand your arguments. What you seem to say is that, since fights offer limited number of casts, the DPS difference between a 16% hit mage and a 3%hit mage (all other things being equal, wich I agree is most likely not the case) is not 13% on average ?
I agree that on some of the fights the 3% hit mage could get lucky and achieve the same level resist than the 16% hit mage, but he could also get unlucky no ?
I know statistics and probabilities are a tricky subject where common sense can be swept aside in front of mathematical evidence but you will have a hard time convincing me of the logic of your assertion...i