Doing the numbers we get an interval (adjustet with the 136 hitrating base): [8.789% - 9.725%]
The total swings is a bit low thats why the interval is so wide.

Well either pets follow a different mechanic (or same mechanic with different constants) or our assumption about petattacks are wrong or your pet has a hidden +hit or +skill bonus

1) yes
2) horde so no
3) no boomkins so no
4) 99.9% no

I thought 8.6/27.6% was correct until this post:
http://elitistjerks.com/424269-post120.html

Basically people say that 360 ws + 308 hr + 5/5 precision = never miss for rogue:
19.5% (308 HR) + 5% + 0.4% (10 weapon skill) ~ 25%

What if hunters in TBC have diffrent miss rate from 2h warriors/pala and/or feral druids? I checked quickly this thread but could not find any WWS raid data confirming any theory.

As for dual-wield, I had 360 ws and ~22.8% (17.8+5) hit and results from WWS are:
VR: 626 attacks, 6 miss (0.96%)
Lurker: 781 attacks, 6 miss (0.77%)
Morogrim: 1096 attacks, 16 miss (1.46%)
Tried to pick fights with none to almost none adds. It shows that mi miss is around 24-25%. Now ok, there can be some error, some luck but with 28% miss it should be 3-4% hit from luck on those fights. Sorry but I could not believe in THAT much of luck.

Of course there can always be possibility that WWS is bugged somehow.

That is correct as far as we know.
The small little detail that always gets overlooked is the 360 skill.

A few post above Spoon derived two formulas based on the testing here.
Basemiss:
5+dualwield + (bossdefence - (350+weaponskill))*0.1 if (bossdefence - your weaponskill) <= 10)
5+dualwield + 10*0.1 + (bossdefence - (350+weaponskill) - 10)*0.6 if (bossdefence - your weaponskill) >= 10)

So for someone with only 350 weaponskill against a boss that translates to 28% for dualwielders and 9% for all others.

The numbers are not rock solid yet but pretty convincing

If you have 360 Weapon Skill equipped, then it is as though you are attacking a Level 71 mob when you are attacking Level 73 mobs. Which means you are facing an opponent with a base miss rate of 24.5%. So your results are perfectly in line with our working theory.

The ~28% base miss rate applies if your Weapon Skill is at 350, attacking a mob with a 365 Defense Skill.

Also, it is still theoretically possible that Hunters have a different combat calculation from other classes. But it seem pretty unlikely. So far, all the testing has indicated that Ranged physical DPS works exactly the same as Melee physical DPS (at least with respect to calculating hits and misses), and so that is our working assumption right now.

Also, you have to be very careful to not pollute data tests by including combat with adds. Bosses are level 73 and so have a base miss rate of ~28%. Adds on the other hand, will usually be Level 71 or 72, so they will only have a miss rate of 24.5% or 25%, respectively. If your test mixes boss fight with add fights, then you will compromise the integrity of the test.

Just to clarify, we still haven't really tested whether those first five point of Weapon Skill (i.e., from 350 to 355) reduce miss rate linearly (i.e., by a an equal .6% per Skill level).

I certainly think it is the more elegant formula. (And I actually hope it is right!)

But there is still this competing idea:

Which implies an abrupt and fairly large reduction in miss rate when going from Weapon Skill 354 to 355.

As I said before, I certainly emotionally favor Sp00n's formula over the Wowwiki formulation. But I don't want to assume it is accurate before we have tested the impact of incremental Weapon Skill between 350 and 355. Right now we don't actually have any data to favor one theory over the other.

Did a test of my own today. I will hopefully follow it up with a more pertinent one.

Blizzard has stated that bosses behave like +3, and we are all assuming this is still true. However, that information came out before TBC. Since there are no standard level 73 mobs to test, this means using a lower-level alt to check.

http://img.photobucket.com/albums/v3...MissProof1.jpg
http://img.photobucket.com/albums/v3...MissProof2.jpg

Those are two pictures of a test I ran with a level 52 hunter against a level 56 BL servant. Note that this is a +4 mob, and yes I'm aware we really wanted a +3, but I couldn't find an L55 and didn't want to level just so I could work on my weapon skill some more.

The hunter has 260 bow skill (non-troll), which is max for 52, and no hit rating at all. The pet is 51, and you'll notice some of the pet's specifics mentioned in the one screenshot as well -- "miss" also includes parry and dodge and stuff, though, so I'm not sure if anyone really cares.


However for the hunter safely shooting for afar, with 2000 autoshots taken, there were a total of 178 misses, or 8.9%. I would hope we can consider 2000 statistically significant, but stat was never one of my finer points and we are effectively looking for accuracy up to 3 digits, so maybe not. It did start closer to 8.7% and crept up to 9.0 in the last 500, and then fluctuated a little. 178/2000 is pretty darn close to 8.9%, though, so I'm going to label this the miss rate for a standard player against a +4.

The special attacks I wove in as mana permitted had a higher miss rate. They are not statistically significant, although if you incorporate them into the autoshot, we then have a 9.1% miss rate. Do with that what you will, but I am going to assume that we do not know for certain that specials operate the same as base attacks, so I'm going to stick to the 8.9 figure.

Now, with our current model(s) that we've been using, 8.9% is less than what we would expect for a +4, (as is 9.1,) and even less than Olgas is theorizing is the miss rate for bosses, which means one or more of a few things:
1) Lower-level targets have a different formula used than level 70. (Unlikely considering they'd use the pre-TBC model then, which also should be higher -- about 9.8%)
2) The boss miss rate is actually under 9%.
3) Bosses are not true +3's for the sake of physical attacks.

If you trust Olgas's tests, then I suspect #2 is false. Although (s)he hasn't done testing on exactly 9% +hit, Olgas has at least found that boss miss rate is higher than the old original 8.6%, and 9% is what I suspect will be the agreed-upon figure. If that much is true, and my test is reasonably accurate, then #3 very well might be correct.


If and when I do the test with a +3, I'll be sure to report back. 75+ minutes of autoshooting and hitting Mend Pet every 15 seconds is zzzz, though.

A possible alternative is, that they clamp the leveldifference at +3 level. So any mob >= 3 level counts as 365 defence.

Easy to test - get a warlock to summon a level 1 character to SMV and have a go at one of the channelers.

I would suggest a character with higher level than 30 or so.
There are a number of exceptions to mechanics if the character level is below a certain threshold.

Sigh, yes. Someone is going to have to remind me how to find my own confidence intervals. I'd settle for 90% and/or accurate to within a quarter percent rather than a tenth.

No, went pure BM to get to Serpent's Swiftness so the test would go by faster. I didn't want to pick up any talents or effects that could throw off the testing. There was absolutely no chance-to-hit modification on this character.

Even easier: get a level 1 hunter into Duskwood and shoot at Stitches while he fights the watchers. (Has to be a hunter or someone with a ranged attack since he has a short-range AE aura.)

Karmon, while it's true that a level 1 can hit a level 5 mob alright, I believe the primary exceptions for low-levels are with regard to PvP.

Remember, that we still have two competing theories for how the formula works when Defense Skill exceeds Weapon Skill by more than 10:

The "Sp00n/Karmon" formulation:
5 + 10*0.1 + (Def Skill - Weap Skill - 10)*0.6

And the "modified Wowwiki" formula:
5 + (Def Skill - Weap Skill)*.266667

We all like the Sp00n/Karmon formulation better because it is cleaner and yields a linear impact between Weapon Skill 350 and 355. But we have no actual data yet to prefer one formula over the other yet.

And, actually, if you apply the modified Wowwiki formula to this particular test against a +4 mob, you get an expected miss rate of 10.33% (instead of 12%) which is still outside the 95% confidence level of the test... but just barely now, since the high end is 10.15%.

Unfortunately, I've only been able to go on about a raid and a half over the last week. So, I've had very little opportunity to do this testing.

However, last night we did do a quick Gruul's run. And I was equipped with exactly 142 hit gear (9.00%).

728 hits, 168 crits, 0 misses

So, zero misses in 896 shots.

This is too small a sample size to draw any definitive conclusions from. I figure I probably need to see something like 5000 shots without a miss, before we can be comfortable about the 9% cap. But I wanted to share these preliminary results with you.

slightly offtopic .. but in order to help us "not-so-statistics-pros" in testing ....

could someone give me the numbers, how many samples are necessary to get a 95% confidence interval for
+/- 0.5% ... 1% range
+/- 0.1% ... 0.2% range
+/- 0.05% .. 0.1% range

Ashlan

A lot. Thousands of samples for +/- 1%, hundreds of thousands for +/1 0.1%. It depends on the actual proportion with the worst case at 50%.

While I was once able to work these out myself, I am lazy and prefer to use things like Confidence Interval for Proportions Calculator to do math for me.

For example, if we are looking for a value around 10% and want 95% confidence, we need:

3457 samples for +/- 1%
~14000 samples for +/- 0.5%
~350000 samples for +/- 0.1%

Almost
This site also offers Confidence Interval for for means. That is what we need for the testing here.

We sample the average number of misses divided by total swings. This is a guess for the mean of the distribution.
Now we need to know how sure we are, that this guess is near the true mean.
For that you need the confidence interval for means, not for proportions.

As for the original question:
You always can give a 95% confidence inteval, even with a small sample size. The catch is, the smaller the sample size is the wider the interval is.
Th real question should be: how many samples do I need so that the true mean is not more than X away off the observed mean (in 95% of the cases).

For the missrate tests here, if we allow the for 2% variation of the intervall bounds (e.g the true missrate will be between 7.5% and 9.5%) we need about 2000 samples.
If we only allow 1% of variation (e.g 8.5%,9.5%) we already need about 8000 samples.
The width of the intervall scales with the square root of the samplesizes, If you want to halve the interval you need to quadruple the sample size.

Yesterday I got a chance to raid Karazhan with 363 hitrating.
The bosses I did participate were Maid, Big bad Wolf, Nightbane, Kurator, Illhoof, Netherspite and Aran.

Out of 3140 autoattacks there were no misses.
That was with no +skill (neither items nor talents), dualwielding daggers, 5% precision and 363 hitrating.

With the earlier observation that there were misses with 362 hitrating this hints that
the missrate for dualwielders and only 350 weaponsskill is something between
27.95% and 28.02%
Of course the 3100 hits are a bit low. I try to repeat that next week so we get another sample of that size

OTOH Netherspite is a strange boss. I had only 5% glancings against him. We only attack him when the beams are there.

Netherspite also doesn't have the partial resists that every caster gets against mobs higher than his level. He seems to behave like a same-level mob.
Illhoof also doesn't receive partial resists from casters either, but his amount of glancing looks pretty normal. Maybe a bit lower than 25%, but it's not 5-10%.
Those two have pretty weird mechanics really, so be careful with data on them.

Hmm...

Even though we haven't aggregated enough evidence to be 100% sure yet, the collection of tests so far really do seem to be pointing to a 9.00% base miss rate (28% if dual wielding) against Level 73 mobs.

I think we still need to complete these tests -- and I intend to complete mine.

But I'm wondering if we can't run another test in parallel -- a test to determine whether the "Sp00n formula" or the "modified Wowwiki formula" is more accurate for determining the incremental value of each point of Weapon Skill between 350 and 355. I mean, now that we've narrowed down the bass miss rate on a 73 mob to a very narrow range, I think this might be possible.

For example, if someone were to do a test with exactly 354 Weapon Skill, their base miss rate against a Level 73 would be either:
(i) 6.60% (25.60%) under the Sp00n formula, or
(ii) 7.93% (26.93%) under the modified Wowwiki formula.

6.60% versus 7.93% is a pretty big difference -- indeed, it's a much bigger difference than the current range of uncertainty we have around the base miss rate. So this test should work, I think. And because we know that fractional Weapon Skills are simply dropped (thanks to testing by Dontmindme and Sp00n) we can confidently eliminate that variable as well.

Here are a few tests we could do:
1. A Rogue with +4 Weapon Skill and 325 hit rating (20.61%). If the Rogue sees any misses, the Sp00n formulation can't be right. If they're able to eliminate misses, the Sp00n formulation almost has to be right.
2. A Pally or Warrior with +4 Weapon Skill (thru Talents or gear) and 105 hit rating (6.65%). Again, if the Pally or Warrior sees any misses, the Sp00n formulation can't be right, but if they eliminate misses, the Sp00n formula almost has to be right.

I wish I could do these tests myself, but I don't have any gear or talents to get to +4 Weapon Skill.

I have Aged Core Leather Gloves, Maladath and could get the Belt out of Dire Maul on my Rogue. These are pretty low values of Weapon Skill each, so if I can help you testing somehow, just tell me.

I gathered some data now.
Since I can hardly convince my raid leaders to let me equip a dagger main hand while being hemo specced (especially when it is such a fine dagger like [Finkle's Skinner]), I was running some AV matches tonight.
I thought I'd remember that Drek'Thar was flagged with the boss tag, and actually he was. Additionally Captain Galvangar is also flagged as a boss, which theoretically doubled my chances to gather some data (and in reality sometimes was my only testing field due to the alliance was having one of their 'better' days today...).

There seem to be no regular level 73 mobs in Outlands. Anymore at least, according to wowhead, there were some in BEM, but I couldn't find them and believe that since the implementation of Ogrilar the mob population have been redesigned in exactly these areas.
Other options would have been Temerus, but he wasn't spawned when I checked, and Anachronos, who would have 3 hitted me, so I vanished after Evasion and 2 hits.

So, doing PvP to help PvE theorycrafting, finally something different. O.O


The data seems to directly contradict my preferred formula (damn! I liked it! Really! ).

I was running (again) with my [Shoulderpads of the Stranger]. The 10 skill rating result in ~2.54 skill, which is cut down to 2 as we've shown before.
Therefore those 2 weapon skill points should have reduced the chance to miss by 1.2%, if it was 0.6% per skill point until you've reached 5 of them.
I couldn't gather enough hit rating to test with dual wield, so I simply equipped a dagger in my main hand and nothing in my off hand (I double checked to be sure that my off hand doesn't attack and doesn't increase my miss chance, and it doesn't).
Under these circumstances, the miss chance should have been 7.8% against a boss level mob.
Interestingly 7.8% match *exactly* into 123 hit rating.

I respecced to have 0 points in WEx and 0 points in precision and equipped my shoulders together with 123 hit rating.
The result:

Captain Galvangar
79 white attacks [24% Glancing Blows]
0 misses

Drek'Thar
61 white attacks [26.23% Glancing Blows]
1 miss

1 miss. However, I was a bit suspicious because 7.8% were exactly 123 hit rating, and maybe this wasn't enough to really prevent any misses (who knows). Therefore I respecced again and took all 5 points in precision (but again 0 in WEx). Now I would need only 2.8% additional hit rating, or 44.15 = 45 hit rating to never miss. Enough to eliminate the above assumption.
By the way, equipping exactly 45 hit rating was NOT so easy. But I succeeded, and the results again:

Captain Galvangar
63 white attacks [14.29% Glancing Blows]
3 misses
1 Hemo miss

Drek'Thar
201 white attacks [29.35% Glancing Blows]
0 misses
1 Hemo miss


So this is quite clear now. Even misses with my special attack.


I didn't feel like testing out the modified WoWWiki formula this time, or find out when I wouldn't miss anymore. Too tedious.
Does anybody have any idea where you'd find a level 73 or boss level mob that you could easily test on without the help of others?

Hum, don't suppose it's possible that you have DW miss rates even when single wielding?

No, that's what I've tested beforehand. Having no weapon in your off hand resulted in 0 misses against a terokkar mob, and having no weapon in the main hand I did see a ton of misses.

I remember that quite some time ago you would need to equip an off hand item (non weapon) in your off hand to actually stop it from attacking, but that has been fixed since obviously.


And a tiny update, with 54 hit rating I didn't see any misses so far (according to Olgas' proposed formula I'd need 54.667 to never miss). Of course I only have 244 attacks, and that was over the course of 3 AV games...
Really need some better way to test this.