Theorycrafting Time
You pull back the hammer on your gun, the hammer lands, the bullet flies. There are three things that can happen: Miss, Hit, or Crit.
How does it work?
Example: You are level 70, your enemy is level 70. You have 0% +Hit and 0% +Crit. Blizz has made the following mechanics standard:
Miss = 5%
Hit = 95%
Crit = 0%
Example: You are level 70, your enemy is level 70. You have 0% +Hit and 20% +Crit. Blizz has made the following mechanics standard:
Miss = 5%
Hit = 75%
Crit = 20%
Everyone OK so far? Good. Now, let’s freak you out. Everyone should agree that a 5% miss-rate means that for every 100 shots, we will Miss 5 times. But is this miss-rate calculated with a One-Roll or a Two-Roll System?
The One-Roll System
Imagine, if you will, a 100-sided dice. If you roll a 1-5 you Miss. If you roll a 6-80, you Hit. If you roll an 81-100, you Crit. One roll, everything settled, pretty simple.
The Two-Roll System
Imagine, if you will, a 100-sided dice. If you roll a 1-5, you Miss. If you roll a 6-100 you Hit. If you Hit, you roll the dice again. If you roll a 1-20 you Crit, if you roll a 21-100 you just Hit.
In both systems, the Miss/Hit/Crit percentages are applied but the mechanics are very different. Which system does Warcraft use? We’re not certain. The writer of the HunterGuide project has this to say:
“More recent observations suggest a 2 roll system is being used for special attacks: First a roll to see whether you hit or not, then another roll to determine if you crit or made a regular hit. The exact roll system used for Hunters is hard to determine. The results are, in the case of Hunter attacks, very similar. Melee attacks, which suffer from parries and dodges, and often a higher miss rate than our ranged attacks, have results differing much more. Currently, I assume a standard 1 roll system for all attacks for my calculations.”
He reports that data suggests a two-roll system is used, but then says his calculations assume a one-roll system. Peculiar to say the least. Does BRK have the data analsyis to confirm one of these systems is correct? Nope. But we can show you how they both work.
Watch the magic!
The One-Roll System and Crit
Back to our 5% Miss, 75% Hit, 20% Crit model, which we will call the 5/75/20 for simplicity.
If we shoot 1000 times, we should miss 50 shots, hit 750 shots, and crit 200 shots. Simple roll of the dice.
The Two-Roll System and Crit
If we shoot 1000 times, we should miss 50 shots and hit 950 shots. Of those 950 shots, we should crit 20% of the time. 20% of 950 shots is 190 shots. 190 is less than 200…
Under the Two-Roll System, a 20% Crit rating does not mathematically mean that we will crit 200 out of 1000 shots! OMG!
Take a moment to recover. Have a raspberry coffee.
What does this all mean? It means that under the Two-Roll System, your +Hit becomes even more critial than you think it is. How? Why?
Watch.
The One-Roll System and Hit
If our +Hit increases by 1%, our 5/75/20 is modified to 4/76/20. The number of crits we have does not increase, the frequency of crits does not increase. We Miss less often, thus we have more Hits. If we fire 1000 shots, we should see 40 misses, 760 hits, and 200 crits.
The Two-Roll System and Hit
If our +Hit increases by 1%, our miss-rate falls from 5% to 4%, so we should see 40 misses out of every 1000 shots. Our Hit-rate jumps from 95% to 96%. Since we crit 20% of our Hits, we shall have 20% of 960 shots be crits. 20% of 960 shots is 192 shots.
When we had a 0% +Hit we had 190 crits, but with a 1% +Hit, we had 192 crits…
Under the Two-Roll System, as we increase our +Hit, our crit percentage remains the same but the number of Crits increases!
This seems pretty d@mn important, doesn’t it. If we’re playing under the Two-Roll System, our +Hit has a much larger influence over our total-damage than it does under the One-Roll System. The problem is that we cannot find any blue-post or stastical analysis to prove which system is used in the miss/hit/crit calculations for us hunters. Nothing, nada, the empty-set.
Why does the HunterGuide guy assume a One-Roll System? Our inital thought is that it’s an easier system, mathematically. No if-then statements to program saves work and makes more simple forumlas.
But is he right… and what if he’s wrong…
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30 Responses to “Theorycrafting Time”
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Most all of the theorycrafting I’ve read on tanking (that is Mob hits player) assumes a 1 roll system. I would have to assume it works the same for Player hits mob.
It sounds like you know most of this already, but this is from Gestalt’s Tankadin 101:
“Exhaustive testing and sly confirmations from Blizzard indicate that physical combat involves a one-roll system. All the possible outcomes for an attack are arranged on a table and assigned a range value, totalling 100. A random number is generated by the game and this number is compared to the table.
Miss
Dodge
Parry
Glancing Blow (only players and pets versus mobs)
Block
Critical
Crushing Blow (mobs only)
ordinary hit
Values on the table can slide off the bottom, not the top. Additionally, certain effects may directly reduce other values (for example, Defense will reduce the range of Critical, and increase the range of Miss). This is how the mitigation numbers can be true “absolute values”. If your block rate is 65% at the time of the attack, “Block” will have a value of 65% of the table. If there isn’t enough room for all 65% (for example, if your Miss, Dodge, and Parry already totalled 40%), the excess Block will “fall off” the table. Note that at that point Critical, Crushing, and Ordinary Hit have already been pushed off.”
Most everyone prescribes to the ‘one-roll theory’ and for good reason. The servers have lots to do, two rolls effectively doubles the workload for every strike.
And for those of you who would like some more reading:
http://www.wowwiki.com/Attack_table
/sigh I want Crushing Blows!!
Melee hits suck already, and before I get flamed, Melee happens if only until you can mash Misdirection or Disengage for us lowbies!!
/rant off
For some reason I thought that Blizzard has a 6% miss rate in the mechanics, where 1% of that miss rate cannot be mitigated. Am I wrong? Cause if I am, I can go back to the cheap stuff again…I dont mind Jack Daniels and have no problem putting up my Bookers for a night or three.
There’s some testing going on in the Elitist Jerks forums on the hit cap and how +weapon skill affects it, and I recall reading there that evidence is suggesting a two-roll system for (rogue) special attacks. Thread is at http://elitistjerks.com/f31/t11885-rogue_warrior_weapon_skill_adjustment_discussion/
So, it’s possible that normal attacks are 1-roll, specials are 2-roll.
Oh, and the 1% minimum miss rate, misfit, is for spells, not melee/ranged. Those can be brought down to 0% miss.
Interesting. For what it’s worth, hunters are ideally designed to test whether it’s 1-roll or 2-roll in an empirical fashion. You’ve already caught the critical element, all you need is the practicum. You’ll need Dr. Boom aka Dr. Target Dummy. You’ll also need a stats analyzer — SWStats or WWStats as desired.
Strip down to, well, naked shooting. Autoshoot for a long, long time to establish a baseline. You’re not really caring about damage, you want to confirm your base rate of crits approximates the alleged 5% baseline.
At this instant you should have a suspicion. By 1-roll you should see 50 misses, 50 crits and 900 hits out of every thousand shots. By 2-roll, however, you should be seeing 50 misses, 48 crits and 900 hits. Obviously large numbers WILL be required.
Test further with an increase to CRIT ONLY. As you already noted, 20% means you’re either around 190 or 200 crits out of 1000 shots. 50% crit gives an even clearer disparity - 500 vs 450 crits.
Of course, since we’re talking “random rolls” 1000 shots isn’t a large enough sample. Which is why I recommended a hunter. Set up the test, kick off autoshot, start a good movie, and remember to move the mouse every so often to stop the AFK…
Thanks, Indy, for throwing a wrench in my test (grin). Specials… hmmm….
a further wrench might be our shots that are treated as spells… but, unless you a a shot rotation macro wizard, it probably doesn’t matter. The duration of most fights will be short enough that the randomness of the roll will be more significant than then slight percentage changes.
So am I gathering this test will be merely testing a 1 or 2 roll system?
As stated will autoshot be the factor? Or do specials somehow change the formula? I am VERY curious about this is all, and have no patience to do the work involved, hey don’t give me dirty looks at least I was honest!
Rabid
Kirk : The test you designed only tests whether autoshot is 1-roll or 2-roll.
It doesn’t tell us whether Yellow damage/Specials are 1 or 2-rolls.
Just thought you shold have pointed that out
Hey thats what I said!
sorta
Grimbert - note my response to indy. As in, “oops” and “darnit”.
You’re right, actually.
And for what it’s worth (and having read through not just indy’s referenced thread but the threads referenced WITHIN that thread), it appears that:
For melee, white damage uses 1-roll and yellow damage uses 2-roll.
At this point ranged and spell are at best unconfirmed.
According to an article on Wowinsider, http://www.wowinsider.com/2007/03/24/attack-tables-and-you/, it’s a single roll system. It’s explained pretty clearly in that article, and at some point it actually says: “Eyonix said spells were on a single roll system like physical attacks”. Hope that helps!
Haven’t read it all yet, but didn’t like the start!
Honestly, the +crit implies “additional” crit, and you start talking about base crits. Let me try to explain better: it’s different to say that I have +20% crit and that I have 20% crit! The former may be referring to +crit *added* to my *base* crit by say, +crit gear… So it starts off in a confusing way, if I may say so…
As for the 1 or 2 dice-roll, I do believe that Blizzard being so picky about server performance would pick the fastest solution of 1 single random roll: random generators are usually slow if they strive to be considerably random, so 2 rolls for each strike seems a bit of a waste of resources when you have thousands of players per realm fighting thousands of mobs/players: that’s a huge bunch of randoms in itself already!
Someone - the problem with that assumption is that there are several KNOWN second rolls already. Example: shield block (warrior). Example: second resistance roll to non-binary spelldamage (and maybe to all spell effects - early break on sheep and shackle and so forth). And then there’s the rogue example (Bastiaan, this applies here as well) where the rogue did several thousand identical backstabs - enough to make ‘unlikely’ odds REALLY unlikely - and demonstrated that the backstab crits were second rolls. Which drew a hue and cry and some more people doing the same tests with nominally equal results.
If it’s any comfort for us theorycrafters trying to maintain trust in the legitimacy of Blue statements, Eyonix’s statement was before the expansion.
I don’t have a super hunter, and I’m not by any means an expert in theorycraft or anything, but…
I think (correct me if I’m wrong) that theres a simple mistake in there:
In a single roll system, when you and your oponent are both level 70, you got 20% crit, like you mentioned, it’s all good: 5% miss, 75% hit, 20% crit. Ok.
But on a two roll system, you assume it’s still 5/75/20, when it (IMO) should be like one % for the hit (5%/95%), and then another for crit (80%hit/20%crit).
Meaning, in the first roll, you see if you hit or not, then in the second you finally find out if you crit.
That is, out of 1000 shots, 50 are missing, 950 are hitting; and, out of these 950, 20% are going to crit.
“But hey, that’s what BRK said!”
I know, but BRK said 20% crit in a two roll system “should” be the same as 20% in one roll system, but it isn’t.
It is, in fact… but it’s just 20% of the shots you actually hit, in opposing to one roll system, where you crit 20% of every shot - including the misses.
All these math problems gives me a headache…
I just want to have fun and play the game! :-/
//Róhirrim
Nagrand EU
BRK, you are missing a crucial calculation. You need to compare 2-roll with +hit% to 2-roll with +crit% to get a fair comparison.
With a 2-roll, +1% hit will get you 192 crits out of 1000. But the numbers if you have +1% crit:
50 misses, 950 hit.
Of those 950 hits, 21% are crits. .21 x 950 = 199.
199 crits is better than 192. If those extra 7 crits are better than the extra 10 regular hits lost (and I assume they are, but I don’t want to do the math) then +1% crit is better than +1% hit.
hdtoreau, no, you miss a critical (sorry) factor.
If you get +1 crit instead of +1 hit, you miss 50 instead of 40 out of 100 times if it’s 2-roll.
Technically, instead of 5/75/20, 2-roll is 5/(95*.8)/(95*.2). Increase hit and it’s 4/(96*.8)/(96*.2). Increase crit and it’s 5/(95*.79)/(95*.21).
Kirk, I just read your blog (didn’t know you were Mr. Priestly Endeavours - like it very much!) on wanding and it looks like you are right about that being on a 2 roll system. Do you have any ideas about the difference between your results and the expected percentages being within error margins?
On an other note: how did that rogue determine the backstab percentages? Dr. Boom may not aggro from wanding/shooting, but he might not be so forgiving for melee.
Kirk;
I think we’re talking past each other, because the formulas you posted result in the same numbers I posted: +1% hit gives (96*.2 =) 19.2 crits out of 1000 while +1% crit gives (95*.21 =) 19.9 crits.
Where I was unclear was the comparison of the number of normal hits. I’ll try to clarify. With +1% hit we end up with:
40 misses (out of 1000)
768 normal hits (960*.8)
192 crits (960*.2)
With +1% crit we get:
50 misses (out of 1000)
750.5 hits
199.5 crits
My only point was that BRK was premature in declaring +hit% more important than +crit% — we need to know whether the damage done by
(768 normal + 192 crits) > (750.5 normal + 199.5 crits) …
…but that’s a calculation that I am unable to do, since this post is my first attempt at theorycrafting.
I always wondered why shackled mobs broke that sheet so quick!!!
/lurking and staring at the Math
Ah. Hdthoreau -
Occasional hits will be very large (top of range) and occasional crits very small (double bottom of range).
But over time, the averages coalesce to a single value, with the average crit being 2 times the average hit. So for theorycrafting melee and ranged combat, we can assign hits damage D, and crits damage 2D.
Therefore we get 768D + 2*192D = 1152D against 750.5D + 2*199.5D = 1149.5D. The difference is tiny but present nonetheless.
Excellent! Thanks, Kirk, BRK’s point is proved to my satisfaction. All things being equal, in this game of small benefits averaged over long times, +hit% has an edge over +crit%.
Just to throw some petrol on this fire :O
This may be true for white damage, but.
I was doing some EPL goodness, and I fired arcane shot at some mob, which crit.
Crit alert then read, Arcane Shot crits for ~500 damage(250 blocked). Now I dont think this is just yellow damage, and if it isnt, this means that block may have to be firgured in somewhere here, depening on the attack table used
(is block above or below a normal attack? if its below, then the hit cap may not be quite such a cap, as it would in fact lower than chance of the projectile being blocked).
And as to whoever said shots count as spells, well arcane shot certainly doesnt. It wil miss, but it wont be resisted.
Just wondering… Could a Two-Roll System with parameters: Miss = 5%, Hit = 75% and Crit = 20% not be replaced by a One-Roll System with parameters: Miss = 5%, Hit = 76% and Crit = 19%? Or am I missing something here? If I’m not then why would Blizzard make things hard to interpret by using the Two-Roll System.
O.O
o.O
Then is a Resist on Scorpid not a factor in the shot being a spell damage? I take it Scorpid is Nature then? Fiorgive my lowbie logic, but seeing my Scorpid be resisted on certain elementals I have learned not to use it.
Rabid & Catnip
With mortal shots this becomes:
+1% hit: 768D + 2.3 * 192D = 1209.6D
+1% crit: 750.5D + 2.3 * 199.5D = 1209.35D.
For a difference of 0.25D.
Also, I maintain that if you can’t find a statistically significant difference with tons of data at your disposal, then you shouldn’t care.
Thank You Kindly,
Corwyn
for Kafsha and Shaelee
If you have a Relentless Earthstorm Diamond in your helm, that’s another 3% damage to your criticals, so:
+1% hit: 768D + 2.33 * 192D = 1215.36D
+1% crit: 750.5D + 2.33 * 199.5D = 1215.335D
Wow, such a close difference. I guess it might depend on your “chance on hit” procs versus “chance on crit” procs in your gear as far as which stats to go for.