Yes, the model breaks down in the degenerate case as t = 0 (and, in particular, whenever Pd > 2Pf). However, the number of procs that this is true for is vanishingly small; for all real procs, where Pf > 2Pd, Pd/(Pf+.5Pd) is a superior estimate.

Regarding your critique of my model: that's actually factored in. Note that we're defining the length of a proc as "the time from this proc until the next proc, up to a maximum of 15 seconds". Hence, the removal of the overlap between the current proc and the preceding one is taken into account by the truncation of the preceding proc rather than needing to remove anything from the one we're analyzing.

So, for instance, lets say there are procs at T=-5, T = 0, T=10, and T=30. This means that Mongoose would actually be up from T=-5 to T=-25 and from T=30 to T=45. So, P_{-5}, the proc that occurs at T=-5, "owns" the uptime from T=-5 to T=0; the remainder of it's uptime is lost, because it has been overwritten at T=0 and hence that proc is over. P_0, the proc at T=0, similarly owns the 10 seconds of uptime from T=0 to T=10, before getting overwritten by P_10. P_10 then owns the uptime from T=10 to T=25, and P_25 owns the uptime from T=25 to T=40 (unless it gets overwritten by another proc itself, of course, but you get the idea). Hence, because were are defining the uptime of a proc to be "until it gets overwritten", the proc at T=0 by definition does not overlap any prior proc - because that proc is declared to end at T=0 when the proc we are investigating starts.

Note that this model, of course, has issues as well for Pf<1, because then p > 1 and clearly no proc can occur with probability more than one in any given second. So, if you want to be technical, it should really be 1-(1-min(1, 1/Pf))^Pd to fix that.

And of course, to be *totally* technical, one should not quantize to seconds, and instead define:

v = average numbers of hits per second
p = probability that a hit procs the effect
d = duration of the effect

and then set

Uptime = 1-(1-p)^vd (as opposed to the formula above, which is, effectively, 1-(1-pv)^d) which resolves this issue more elegantly; however, it can be easily shown for d of reasonable size (say, >= 10) these are very close to equivalent; for instance, in the case of mongoose with a 1.5 speed weapon, we have v = .667, d=.03, and v = 15; with the newest formula, this gives uptime of 26.26%, meaning that the value of this proc would be misestimated by less than one percent using either estimate in my previous post.

I think all we can do is agree to disagree. I don't see Pd/(Pf+0.5Pd) being a superior model as I'm pretty sure that the entire equation can be solved in a simple manner and the result is Pd/(Pf+Pd) which seems to work for all cases of duration and frequency. This formula does not breakdown as frequency goes to 0 and seems to be accurate in cases where frequency equals duration. Your equation seemingly has a flaw at some point, hence the issue with frequencies approaching 0.

I'm not sure where your formula is deviating. It might have something to do with the proc duration extending past your average proc time or the reduction of terms or the possibility of unlucky streaks of proc downtime which essentially extends the proc window and thus reduces the percent uptime. What I haven't seen is a refutation of the formula I derived other than the observation that it does not seem to agree with yours.

I believe I have approached the proc issue in a simple and direct manner and am looking for flaws in the logic of the derivation. I'm not trying to be critical nor argumentative. Just looking to see if there are any apparent oversights in the logic.

Is there a max haste rating? Is there a min attack speed? I heard that you can't get your weapon speed lower than 1 no matter what it says in your char screen. Please let me know and proof is nice if you have it.

Well, okay, lets go over your derivation again. Don't get me wrong, I'm not trying to attack you here; it's just that your conclusion a) contradicts significant amounts of existing theorycraft, and b) goes against my intuition. I admit it's a bit harder to demonstrate where your model differs from reality, but, for instance: Lets say Pd = 5, and Pf = 1. That is, on average, it procs once per second, and the buff lasts for 5 seconds. Does it seem reasonable to you that such a buff is only up 83% of the time? I confess that it seems to me that it should be up significantly more than that. And, for instance, we note that your model clearly must be missing *something*, since in this example if the attacks are occuring, say, once per second, it is *impossible* for the buff to drop, as the only way to average one proc a second when you attack once a second is to proc on every single attack - so the probably the the buff manages to drop is, well zero. Now, if you're attacking twice a second, then it *can* drop, as it only needs to proc on 50% of attacks so it can drop. However, in order for a 5 second buff to go down it would need to fail to proc 10 attacks in a row - a 1 in a 1000 shot, which I don't see causing 17% downtime.

So, fundamentally: for Pf small but nonzero, your model seems to underestimate uptime; plus, the fact that it has no consideration of rate of attacks (which clearly does matter) indicates that it's somewhat lacking as well.

So, with that as a plausibility argument that there seems to be a flaw in the model - lets see if we can figure out what it might be. (Yes, the Pd/(Pf+.5Pd) model clearly has flaws as well; but it's clearly stated as an approximation for the case where Pf > Pd so it doesn't surprise me at all that it's wrong for Pf near 0. You'll note that the full model doesn't have this problem).

Now, the point of contention seems to be overlap, which I think we all have a fair idea what overlap is *supposed* to mean, but lets look for a minute at how it actually is modeling. It seems to be defined by the following equation from your post:

Up = Pd/Pf*(1-Ov)

So, overlap is the proportion of uptime that is lost to overlapping procs. Okay, sure.

Now, I think the place you get into trouble is with the assumption

Now, there's no real argument that %overlap is *related* to %uptime... but saying that they have to be equal doesn't strike me as clear at all. So lets examine this assumption in a little more detail.

Uptime is the precentage of the time that the buff is up; hence, if we have an event that happens at any point of time with equal probability, it clearly occurs during the time the buff is uptime percent of the time. So, if we were computing, for instance, what portion of sword spec procs occur during mongoose, the answer would just be uptime% of them. And, similarly, the number of mongoose *procs* that occur during exiting uptime period is clearly uptime% of them - but how much actual uptime loss is there (as that's what overlap measures)? Well, since the proc is equally likely to occur at any point during an existing uptime period, on average, only half of the uptime of that proc is wasted. Hence, uptime% of procs lose half their uptime; hence, overlap should only be uptime/2.

Fundamentally, the point here is that as a buff with *duration*, the intuition that uptime = overlap doesn't hold; if we were talking about, say, two different instant procs (SS and WF, say) occuring with probabilities p and q, the probably that both happen on one attack (that they "overlap") is the pq you'd expect. And the number of *procs* that occur during uptime also is what you expect. But the amount of proc uptime lost - which is what we defined overlap to be - has no reason to be the same, and, in fact, should be about half the uptime of the buff, not the full uptime. So I would argue that the equation we're leading to is uptime = Pd/Pf*(1-Uptime/2), which gives the Uptime = Pd/(Pf+0.5/Pd) result that I asserted previously.

Now, as you have pointed out, this approximation clearly has some problems; it doesn't behave correctly in the limit, and I freely admit it's an approximation. So where did we go wrong?

Well, overlap is the loss of uptime to overlapping procs, and we made the assumption that we lose half the uptime of a proc that occurs during an existing uptime period. Well, this isn't actually quite true. It's true that a proc can occur at any point in time during an existing proc with equal probability... but it's *not* true that it's necessarily the *first* proc. And if there has already been a proc during the current uptime period, the current uptime period is no longer 15 seconds long, so the amount of uptime lost is, on average, longer.

Hence, what we're looking for is the average time of the *first* proc during an uptime period, which is *not* uniformly distributed in the proc uptime; the probability it occurs at a given time is the probability that it occurs at that time... times the probability that it hasn't happened previously. Hence, the *first* proc is more likely to occur in the beginning portion of the uptime of an existing buff than it is towards the end - the probability isn't uniform, so the loss of uptime is not necessarily half, on average. Hence, one must inspect *this* probability distribution, which gets into things like attack frequency and the like, and the more sophisticated derivation I proposed earlier.

On an unrelated note:

There may be a minimum, but it's certainly not 1; I know for a fact I've had my OH hitting around .7 (as confirmed by viewing combat logs, not trusting the character screen) and I've had the character sheet report it as low as .17. So if the character screen is wrong, I can't swear there's no minimum, but I can confirm it's not 1 second. And if the character screen is right... if there's a minimum, it's totally irrelevant is it's only achievable with 2 Unholy Frenzies from Hyjal + Bloodlust/Herosim + SnD + Blade Flurry + Haste Pots + Drums + Dragonspine proc... or something similar.

That would be your opinion, and most of us would disagree with it for several reasons. First off you can't proc combat potency on a miss, considering there is no cooldown on Combat Potency, the more you hit the more procs you get, second, things like Mongoose, Executioner, Dragonspine, and Madness all Proc on hit, they can't proc if you miss, more hits leads to more procs (even if you aren't combat spec'ed).

Now looking at your gear, you could easily add 40 hit rating to your gear, and swap to 0/20/41 instead of 20/0/41 and significantly increase you damage. However, I find the people who try to justify spec'ing shadowstep for raiding and try to justify agility over dodge due to increased survivability tend to be a lost cause, because they don't understand that there are about 3-4 fights in the game where you need to dodge, and the additional 1% or so dodge you are getting from that additional 40 Agility instead of 40 Hit, isn't going to save you when you screw up and pull aggro.

This is the same argument that people were using to try use to justify spec'ing shadowstep for raiding (which coincidently you have done), because while it did less damage you could survive screwing up. As a rogue your job, and your only job, is to do as much DPS as possible based on your gear and the fight, anything that prevents that is a failure in your role as a rogue, there is nothing random that will kill you that could not be prevented by playing better, so there is no real justification for ever spec'ing anything other then Combat as a raiding rogue as long as you are trying to progress.


The real difference between hit and Agi is that hit is going to give you more DPS and it is going to be more consistent, with more consistent cycles thanks to more CP Procs and more hit based procs. Dodge is nice when it works, but it isn't something you ever want to rely on, if you pull aggro, you have already screwed up, if you plan on not screwing up, then you don't need to spec to survive the screw up.

There is no maximum haste rating that you every have to worry about hitting, while there might be a theoretical cap at 100%, that would be 1580 haste rating, which really isn't obtainable.

As far as weapon speed below 1 that is one of those stupid myths that I am pretty sure is covered multiple places on this forum. Think about it, Blizzard put 1.3 and 1.4 speed weapons in game, Slice and Dice causes you to hit 30% faster, Heroism causes you to hit 30% faster, 2 Piece T6 causes you to hit 5% faster, Dragonspine, Abacus, BS Maces, and Haste Pots all cause you to hit faster.

While I could provide combat logs to show this, I am at work currently, and don't have access to my logs, but you can test it by taking you 1.4 speed offhand, and attacking mob, hitting S&D, then popping a haste pot or getting a shaman to pop heroism or popping Abacus. Look at the combat log, you will see off hand hits less then 1 second apart.

In the future, try searching before posting.

I want to thank everyone immensely who has contributed to this thread.

As I posted in the DPS spreadsheet thread, I am very new to theorycrafting on this level, and have solo-researched for a week or two before replying, since that is what I EJ likes to inspire before coming here for questions.

If I may, I have a question or two I have not found the answers to doing searches:

Could someone politely tell me if I have the jist of Amor Penetration gear? ArP value increases the more you have of it, but Vulajin has said there's nothing special about ArP in terms of it's EP weight, so you just sub in items with this value as they come if they are better pieces.

[Bladeangel's Money Belt] is the first item I have encountered with this stat, and will be replacing [Girdle of Treachery]. The rest of my gear is similar: badge and Kara gear. I'm aware the more on hit procs you have, the higher +hit's value rises, and I have double mongoose and Hourglass. Both sheets show an increase in dps for me, but I am not sure if the sheets weigh +hit higher for me since I have those procs or not.

While I very much respect Hanos' opinion (and despite his tone tarnishing his message sometimes, he really does have the experience and results to back it up), I do want to state that hit/agi gems are definitely very usable for all red/yellow slots, as it somewhat balances the fine balance between Agi being your top stat (slightly) in interrupted fights and hit being your top stat (slightly) in stationary fights.

That being said, in a lot of cases, especially at the T6 level, Lionseyes will be easy to get, Pyrestones perhaps somewhat less easy, and Spinels should be damn near impossible (if your raid leader is even remotely sensible in this regard), so sometimes scarcity of gems can play an issue in this as well.

The spreadsheet gurus seem to be in a bit of a mathematical tussle at the moment, so I'll give you a simple answer:

Try removing the Mongoose enchants from your weapons, then recalculate your AEP on the talents page. That should give you the answer you're looking for.

I didn’t want to make a thread seeing how I’m a noob on the forums. I’ve been lurking the forums for about six months now and reading up here and there but I’ve never fully gotten passed page thirteen of this thread I must confuse. So excuse me if this question has been asked but how does expertise affect you in raids?

I have gotten the Shoulderpads of the Stranger when I started raiding with my new guild. Now looking at things like shadowpanter.net they have it actually rated higher then that of the Deathmantle Shoulderpads.

Well I had just gotten my Tier 5 shoulders and feels like I had just wasted DKP on a item that I didn’t really need

How is it that Shoulderpads of the Stranger > then Deathmantle Shoulderpads?

FYI my rogue with Shoulderpads has 311hit, 174X AP, 25ish Crit and 12 expertises. If I use the Deathmantale Shoulderpads I have 32Xhit, 173XAP, 24ish crit and 10 expertise rating.

I mean shouldn’t your attacks not be dodged/parried if you’re behind your target in raids? Since the tank should have agro and faced away from the raid at all times
So confused and a little help/insight to this subject would be great.

You can't be blocked or parried from behind the mob. But dodges still happen. So that expertise, in the end, works like giving you more hit. 3.94 Expertise Rating = 1 Expertise = 0.25% less dodge/parry. So assuming there's no other expertise rating pieces on you, you get an effective 2 expertise out of those shoulders (2.54 to be exact but it's floored down). So that's another 0.5% less dodge. Equivalent to 0.5% more hit (~7.9 hit ratings worth of it).

Piece for piece I think Stranger is better. But if you get 4pc T5 you can swap in those for the bonus.

Glinting Pyrestone/Noble Topaz is an excellent gem, and I have personally used them extensively and still have more in my gear then the spreadsheets recommend, and they are a nice balance between fully buffed and unbuffed as well as keeping you from wasting itemization points when not fighting a boss. I was giving him a hard time for arguing for pure Agi gems and favoring them for the added dodge. If you use all Agi gems, you will gain 1-2% more dodge, which means instead of getting splatted on the first swing, you get spatted on the second (1 time in 50 when you pull aggro on a boss... and if a guild keeps you around long enough to pull aggro on a boss 50 times, min-maxing isn't your biggest concern).. There are even some specs and gear levels where Agi is better. The idea wasn't completely wrong, just the reasoning.

Spreadsheets are a tool, but you need to understand the ideas. Let's look at the 2 belts:

Both have 58 AP, so that is a wash
BA has 25 Agi while GoT has 18, so BA is at +7 Agi
BA has 21 Crit while GoT has 0, so BA is at +21 Crit
BA has 77 Armor Penetration, GoT has 0, so BA is at +77 -Armor

BA has 1 Socket, GoT has 2

Assuming you use Glinting Noble Topaz, you get 4 Hit and 4 Agi on BA and 8 Hit and 11 Agi on GoT
Which is +7 Agi +4 Hit for GoT

What this means is if you ignore Stamina, the difference between the two is +21 Crit Rating and -77 Armor vs 4 Hit Rating.

Bladeangle's Money Belt is always going to be better.

Thank you very much for that assessment. What I meant to consider was the global argument of armor penetration vs. hit at my gear level and I used a terrible example. But I understand the concepts a little more.

I'd love to do this but the sheet sort of goes bonkers on me when I push that button. Thanks for the recommendation though.

To make a long story short. I found the basic issue with that formula. That formula is true for the case of all real numbers where procs can occur at any time but the integral nature of the problem causes increasing inaccuracy where time between attacks approaches the proc duration.

Now, that said, I see one issue with the current implementation of your formula which is skewing it high. You are using hit frequency where one needs attack frequency (or in other words integral time between attacks - probably estimated as an average to simplify the equation which is true for basic offhand attacks by not so true for main hand). The difference between hit frequency and attack frequency needs to be factored into the proc rate as opposed to extending the attack frequency which you currently are doing. The equation you have proposed is only accurate when the hit rate equals the attack rate or in other words, one never misses.

So, using your example above but change d=4 (for simpler math) p=1 with 1 hit per sec and 1 sec per hit making v=1 .
Uptime = 1-(1-p)^vd correctly gives 1-(1-1)^4*1=1

But the problem is with the average hit rate. Let's say somehow one misses/is dodged 50% of the time. Now, you get the same formula when you have 2 attacks per second missing 50% of the time. Your average hit is still 1 per second which using the above formula still gives d=4 p=1 v=1
Uptime = 1-(1-p)^vd correctly gives 1-(1-1)^4*1=1

But if you propagate the hit rate to the proc rate you instead have the much more accurate d=4 p=1*0.5=0.5 v=2
Uptime = 1-(1-0.5)^4*2=1-(0.5)^8=1-0.015625=0.984365 for a 98.4% uptime demonstrating that there is a chance to miss.

I think I've found my issue with your formula. If one uses raw # of attacks with attacks per time propagating the miss rate into the proc rate, then I agree with your formulation. (I just derived the same thing a different way.)

There still is the issue regarding attack frequency not truly hitting the marks (instant attacks, sword spec procs skew this) , but it should be close enough and should certainly be accurate for offhand attacks (neglecting Shiv, etc)

I'm currently working on redoing parts of the Gear Selection section. Specifically, I'd like to reduce the number of builds for which EP weights are listed. By doing so, I can instead expand the chart to show EP values for different gear levels (I plan to have a set of values for tier 4, tier 5, and tier 6 each) so that it's clear how some stats vary in value as gear improves.

Which builds should I be considering "representative" for the raiding rogue population? Obviously swords should be there, and probably at least one Hemo variant, but beyond that I can't decide.

For better or worse, Mutilate is still pretty popular.

(10 points to Shaker)

I'd say the top 6 builds these days are probably something like:

Combat Swords (16/41 + 4)
Combat Hybrid (16/45 Fist/Sword or Mace/Sword)
TSH-Swords (11/28/22 or thereabouts)
TSH-Other (11/21/29)
Combat Daggers (15/41/5)
Mutilate (41/20/0)

There are certainly some other builds that get used (11/9/41, 43/0/18, 30/28/3, etc.) but they're defenitely rarer and pretty clearly inferior, so I'd leave them out for now.

In terms of pruning that list of 6 further: I'd expect Combat Swords and Combat Hybrid to be pretty similar, so you likely don't need both; I'd probably include both TSH options as they will likely have fairly different stat weightings; and Combat Daggers should probably stay as well, as, for better or worse, there's a lot of dagger rogues out there. As for Mutilate... while it is a decent build and it is fairly common, I don't have a lot of confidence that we know the stat weightings for it with the same accuracy, so I'm somewhat inclined to leave it off for now.

Right... upon contemplation, that's probably the better way of formulating it. So instead of the above definitions, we define

v = average numbers of attacks per second
p = probability that an attack procs the effect
d = duration of the effect

Note that the probability of an attack proccing equals the probability that an attack hits time the probability that the hit procs the effect, which is what you were saying, and at this point the formula

Up = 1-(1-p)^vd

should be correct.

However, in the name of scientific curiosity: I decided to test this. I wrote a simple program to simulate indefenite autoattacking with a single weapon, no procs that effect attack rate, etc., with the above parameters tunable.

Data set 1:
v = 1.0
p = .02 (1 proc per 50 seconds, all attacks hitting)
d = 15

Predicted: 1-(1-.02)^15 = .2614
Trial 1: .2609
Trial 2: .2618
Trial 3: .2620

Data set 2:
v = 1.0
p = .018 (1 proc per 50 seconds, 90% hit rate)
d = 15

Note that this is a reasonable model of OH Mongoose for most rogues.

Predicted: 1-(1-.018)^15 = .2385
Trial 1: .2386
Trial 2: .2384
Trial 3: .2396

Data set 3:
v = 2.0
p = .009 (1 proc per 50 seconds, 90% hit rate)
d = 15

Predicted: 1-(1-.009)^30 = .2376
Trial 1: .2385
Trial 2: .2379
Trial 3: .2362

And, just to try something well outside the normal range, lets see what happens if we're attacking 10 times a second with a buff that procs 10% of the time and lasts for 5 seconds:

Data set 4:
v = 10.0
p = .1
d = 5

Predicted: 1-(1-.1)^50 = .9948
Trial 1: .9949
Trial 2: .9946
Trial 3: .9947

So, off the top of my head: this formula seems to match pretty well with theory under the assumption that attacks are more or less evenly spaced. Next step: check how well it works in a MH situation, where the attacks do not come at a uniform rate but can cluster and burst and whatever due to Sword Spec, Windfury, yellow attacks, etc. I suspect it'll run pretty close, though there will likely be at least some deviation.

The maths on Mongoose uptime probably belong in Roguecraft 201, not 101 :P

If you're planning on adding in MH, and determing the uptime when you have both weapons, you really don't need to do much more work as long as you continue to think in the same way. While the probability distributions for Sword Spec and Windfury are going to be heavily related to when the auto-attacks with each weapon, you can't make any determination where the Instants are going to fall in there. All you know is that they're going to come at most once a second and be on average every ~4 seconds for SS (the dps spreadsheet does calculate this exact value). That average value is all we need to work with though.

We get the probability that mongoose is up at any time as 1 - P(MH auto attack did not proc in last 15 seconds) * P(offhand did not) * P(Windfury did not) * P(Sword Spec did not) * P(instants did not). Each of these can be calculated just as Aldriana mentioned, without needing to worry about exactly how the attacks fell the last 15 seconds. Just knowing how many on average have occurred is exactly what we care about, as long as the chance of each hitting is constant.

We're still led to the circular problem of the cycle determining the attacks per time period and thus the proc uptime, but the proc uptime (since it gives haste) might have an effect the best cycle. That's one problem that I have absolutely no idea how to solve other than just saying it's close enough and you should always be modifying your cycles due to your luck in the recent past.

edit: I went back to the post on DP and somehow I completely missed Left's post the first time - presumably because I was typing up my own ramblings on Markov chains. While it was basically a perfect analysis if all that mattered is average stack uptime (it isn't, but it's probably close enough), I'm still going to maintain that you're overestimating the uptime of DP because from my experience it always drops off after the 4th tick without being refreshed - even if that was only 9.1 seconds ago. 10.5 is a much better estimate than 12 of time required since last refrech for the stack to drop, given that the refresh time is uniformly distributed with respect to time since last tick, which is always 3n seconds after the first application, for some n.

It's possible that I'm wrong with respect to how this works and I was just hallucinating or dreaming about when I saw a stack dissapear right as it ticked that clearly had more than a second left and a 1-stack appear immediately afterwards. I don't say that completely facetiously either - I've had plenty of dreams where strange things happen in WoW.

That's funny, I was going to remark that I was happy to see some interesting posts in this thread instead of all the 'rate my gear' crap >_>

While I agree with you there, some of the mathematics is beyond what most of the people I play WoW with would understand. While it's fairly simple probability theory to me, "simple" is a relative word when you're a graduate mathematics student taking classes in 2 different areas of statistics and probability this term. I tend to gloss over some of it myself because thinking is harder than skimming.