Regarding this rage per second calculations, I did one myself last week and try to model a graph based on crit and haste needed. Assumptions were:
18.5 rage per second (2xBT, 1xRB, 2xHS incl theoretical 15% reduction due to free hits, no Slams), 4.5 attacks during a flurry proc (3 Autoattacks, 1.5 skills used in that timeframe, generous calculation), 10% raidhaste up, flurry uptime calculated in the formula itself.
Formula used was
18.5 = 6.5·1.5·(1.1·(1 + 0.25·(1 - (1 - y)^(4.5))))·(1 + x) (updated, was 17.5 before, mistake or at least I don't know any longer how I came up with that value)
(edit: I forgot the 4.8% crit supression on boss mobs...so haste needed is even higher)
Y axis is crit raidbuffed (yeah, I could tweak that to base crit I know), X axis is haste on gear.
A few sample values would be:
⎡ y = 0.3 x = 0.4377156393 ⎤
⎢ y = 0.35 x = 0.4208500887 ⎥
⎢ y = 0.4 x = 0.4082271243 ⎥
⎢ y = 0.45 x = 0.3989405995 ⎥
⎢ y = 0.5 x = 0.3922593301 ⎥
⎢ y = 0.55 x = 0.3875872826 ⎥
⎣ y = 0.6 x = 0.3844364236 ⎦
So basically, around 30 to 35 % haste on gear, rage generation should no longer be a limiting factor. I played around a little on the Beta servers with the premades they give you (they finally work on EU servers!) and even though they are completly fit out with heroic dungeon gear, they are nowhere near any interessting cap values (except expertise). You get around 16% crit unbuffed, 8% haste and 13% hit, reforging or gemming to hit does yield nearly no benefit, as the rating-conversions are that terrible, that I would guess we will not be able to reach the hitcap until 2nd or 3rd raid tier.
edit:
18.5 = 6.5·1.5·(1.1·(1 + 0.25·(1 - (1 - y + 0.048)^(4.5))))·(1 + x)
updated graph and table including crit suppression:
⎡ y = 0.3 x = 0.4589536702 ⎤
⎢ y = 0.35 x = 0.4369461670 ⎥
⎢ y = 0.4 x = 0.4202704127 ⎥
⎢ y = 0.45 x = 0.4077969777 ⎥
⎢ y = 0.5 x = 0.3986276928 ⎥
⎢ y = 0.55 x = 0.3920374422 ⎥
⎣ y = 0.6 x = 0.3874349663 ⎦
@ Voric
Edit: I just thought of something. I was hitting harder with RB when I was trying out stacking mastery. I do not know if I'm still hitting harder now that I'm not stacking mastery.
The damage RB does scales directly with mastery because it requires an enrage.
Unshackled Fury (Mastery) - Increases the benefit of abilities that cause or require you to be enraged by 25%. Each point of Mastery increases enrage effects by an additional 3.13%.
This is observable in the actual tooltip for RB as the % damage shown will change as your mastery does.
The damage RB does scales directly with mastery because it requires an enrage.
Unshackled Fury (Mastery) - Increases the benefit of abilities that cause or require you to be enraged by 25%. Each point of Mastery increases enrage effects by an additional 3.13%.
And exactly this is what might push the value of mastery up in later tiers of cataclysm raiding, because mastery will get progressivly better (similar to ArP) as RB does get a direct damage boost from the scaling of the ability AND a passive boost from the better enrage and death wish.
I would guess we will not be able to reach the hitcap until 2nd or 3rd raid tier.
Keeping in mind that blizzard plans to make bosses harder to hit and to crit each tier, it'll be interesting to see if we scale as well as other classes given that both of those effect our resource generation so much. Crit being mentioned only in relation to flurry uptime.
And exactly this is what might push the value of mastery up in later tiers of cataclysm raiding, because mastery will get progressivly better (similar to ArP) as RB does get a direct damage boost from the scaling of the ability AND a passive boost from the better enrage and death wish.
Mastery can't even catch up to the other stats on live when you have higher relative stat levels than you will likely ever see again. On top of that, there's even less emphasis on RB usage in Cata since Slam/Colossal Smash push back RB regularly. Mastery will never be even close to competitive in Cata without receiving a significant buff in some form.
Mastery can't even catch up to the other stats on live when you have higher relative stat levels than you will likely ever see again. On top of that, there's even less emphasis on RB usage in Cata since Slam/Colossal Smash push back RB regularly. Mastery will never be even close to competitive in Cata without receiving a significant buff in some form.
You are most likely correct on that, but I did also not say, that mastery will surpass the other stats in cata. I merely mentioned, that is scales exponentially (meaning exponentially better), and that stats like haste or crit do not. Nevertheless, as we will never ever reach such crit/haste/hit ratings anyway, mastery will always be inferior I guess, even if they push up the numbers of mastery a little bit. Simply put, mastery in this form sucks and if they boost the numbers, this will be extremly difficult to balance in PvP
You are most likely correct on that, but I did also not say, that mastery will surpass the other stats in cata. I merely mentioned, that is scales exponentially (meaning exponentially better), and that stats like haste or crit do not. Nevertheless, as we will never ever reach such crit/haste/hit ratings anyway, mastery will always be inferior I guess, even if they push up the numbers of mastery a little bit. Simply put, mastery in this form sucks and if they boost the numbers, this will be extremly difficult to balance in PvP
How do you figure mastery scales exponentially? To me it seems the exact opposite, that it gets worse the more of it you have. If your RB is at 125% damage, and you add another mastery point, you increase its damage to ~128%, an overall increase of ~2.4%. However, if your RB is at 150% damage and you add another mastery point to boost it to ~153%, that's an overall increase of ~2%. Add to that the fact that mastery doesn't affect all our abilities the way crit or str does, and it does not seem like a very impressive stat in its current state and will need some number tweaking.
How do you figure mastery scales exponentially? To me it seems the exact opposite, that it gets worse the more of it you have. If your RB is at 125% damage, and you add another mastery point, you increase its damage to ~128%, an overall increase of ~2.4%. However, if your RB is at 150% damage and you add another mastery point to boost it to ~153%, that's an overall increase of ~2%. Add to that the fact that mastery doesn't affect all our abilities the way crit or str does, and it does not seem like a very impressive stat in its current state and will need some number tweaking.
Mastery does effect all our abilities as long as we're enraged. What he meant by exponentially is that RB double dips the mastery when you're enraged. The issue there being how much the mastery increases the Enrage talent (and Deathwish) in comparison to other stats since it's so complex, needing crit, hit, and haste to keep that mastery buffed talent up. There's a lot of thresholds to determine.
On a related subject, sorry if it's been said before, you don't need a full point of mastery to receive a benefit, any rating number at all will increase your mastery percent by whatever 1% step it rounds down to. 1 whole mastery gives you 3.13% increased enrage effects but the game will work in 1% steps until it reaches 3.13% as you gain rating towards your next whole mastery point.
9.52 mastery would technically confer you 29.80% better enrage effects at 80 for example, but the game reports a 29% increase in enrage effects. I don't know if it does the other .8 behind the scenes or simply ignores it until it reaches the next % worth or rating.
It does scale exponentially in that there is an obvious exponential component to its scaling. That's misrepresenting reality though since the exponential factor is so trivially small that you would need an impossibly high amount of mastery before it had a noticeable impact. For all intents and purposes at the levels of mastery rating we'll see, it scales just as linearly as every other stat.
Some napkin math assuming maximum death wish and enrage uptimes and RB being 10% of your damage before mastery gives this rough equation for the relative percentage increase in DPS per point of mastery rating:
f(x)=(.9+.1*(1+.03125*(8+x/179.28)))*(1+.1208*(1+.03125*(8+x/179.28)))/((.9+.1*1.25)*(1+.1208*1.25))
The first part (.9+.1*(1+.03125*(8+x/179.28))) accounts for RB being 10% of your base damage without mastery and the other 90% of your damage being unaffected. The second part (1+.1208*(1+.03125*(8+x/179.28))) factors in the increase in your average damage modifier from DW and Enrage. The .1208 is from .1*(114/144) + .2*(30/144), being the average damage modifier of DW and Enrage with perfect uptimes without mastery. The last part ((.9+.1*1.25)*(1+.1208*1.25)) just divides by your damage at 0 mastery rating to give the relative gain.
Graph for the first 5,000 mastery rating:
Graph for up to 100,000 mastery rating when the exponential effect is actually apparent:
Are you sure this is correct? I thought rage generation was normalized and was something like 6.5*weapon speed per hit for MH weapon and less for OH weapons. If so then rage generation should not improve because of the speed of your weapon.
Rage generation does not increase due to weapon speed in a talentless vacuum, but flurry changes it all up. With the faster offhand churning away about 1.73x as many swings per unit of time given identical stats, you end up with more flurry (and enrage) uptime. Yes, your chance of procing flurry is based on your crit, but your chances of being enraged or under the effects of flurry at any given second increase with the speed you swing your weapons. This is mitigated somewhat by increased weapon speed consuming flurry charges faster, however, the important factor is the deadtime when your flurry is not active. 2 seconds w/o flurry is a lifetime, and with synched 2.6 speed weapons, you're likely to have delays of that length (or longer) more often which translates into delayed (lower) rage gain which can cause delayed abillity usage.
During my testing of SMF I personally didnt feel I had more rage to spend. The rage was generated more smoothly but not noticably more abundantly (to use wording from the original post). Does the lose in haste and crit from you stats pool due to wielding 1handers instead of 2handers really still put 1hand rage generation above 2handers? I certainly havent noticed it and personally feel the consistency of yellow ability usage is better on my TG spec.
Also flurry would increases the rate of rage generation by the same mechanism with both 1handers and 2handers. Although flurry downtime for TG may be greater that SMF in a direct comparison what is important is the effect of that downtime on rage generation, flurry may have a greater downtime in TG but that may well work out to be proportional to SMF in terms of actual rage generated.
Honestly, I can't speak for TG's rage generation at all. The concept was kinda cool the first time I heard about it, but honestly, I've never liked the way it felt compared to the old slow/fast one handers I grew up with. As a result, I've been mostly working on tweaking my SMF stats and playing around with different gear/gems/reforges/specs/rotational priorities. So if I chime in here, I'll usually be discussing something relating to SMF, and I see more special abillity usage using a fast (1.5-1.6 speed) off-hand versus a slow (2.6 speed) off-hand.
The loss of stats for SMF vs TG is still a hinderance to properly gearing the spec, particularly for reaching hit cap- our #1 rage increasing stat. With heroic cryptmaker, achieving 27% hit was easy, I could even maintain a good spread of haste and crit, but without much in the way of hit gear in the bank I still sit below cap as I refuse to trade strength for hit rating (gem selection). I also find myself needing to either stack crit or haste to achieve a similar value in that stat to what I was getting with my TG gearing (no haste/crit stacking or favoring one stat over the other).
The last few days it has been stated multiple times on the warrior forums that flurry uptime is higher with faster weapons (fast weapon speed or stacking haste). Lets look into this.
Flurry is triggered by crits (autoattacks or specials), and consumed by autoattacks only.
Given a fixed crit rate, we can follow from this that flurry uptime is a function of the ratio (total attacks)/(white swings).
This ratio grows larger the more specials you do relative to your white swings. Each additional swing on average produces less rage than an additional special ability would take for all 1h weapon speeds and most 2h speeds. This might be not true with 3.6 weapon speed and up (depending on hit probability and average special rage cost) but considering that not all additional rage can be converted into additional specials this should be true most of the time.
AE scenarios might be an exception though: in AE scenarios flurry uptime could scale positively with haste because of multiple additional hits resulting from more rage being converted into WWs or cleaves. Same goes to raging blow frequency on single target mobs. RB strikes with two weapons. This could tip the ratio in favor of flurry uptime with lower weapon speeds already.
Long story short: stacking haste or using faster weapons should result in lower flurry uptime. This should be true for all 1h weapons even considering that slam strikes with both hands. Only under the most freak circumstances (AE, slow weapons, rage shortage) haste could result in a higher flurry uptime though. On the other hand I'm not really motivated to look into detailed calculations.
Been testing all the stats since 4.0 hit, some clear conclusions I'd like to draw to:
Haste
While the affect of haste in rage regen is very positive, my own setup steers clear of it completely. People in above have come to the conclusion that at ~40% haste from gear (together with 10% raid buff and 25% flurry proc), rage usage is essentially optimized. There's enough rage to hit every meaningful attack, but at the same time any extra bit of rage gen (from extra haste) would not increase any yellow attacks. And mindful white hits only account for 30% of total damage. (My own calculations support the 40% haste cap finding)
Obvious problem is bloodlust, DBW haste proc, and even when there's mob aoe damage increasing our rage gen. When our rage is capped, all the extra points in haste are only getting 30% effectiveness (increasing white hits only). I am quite concerned how much haste is being put on the cata plate gear at the moment, which I believe is significantly worst for warriors than for rogues.
Personally I would recommend only 10% haste from gear and put all customizable stat points elsewhere.
Mastery
This stat does double dip for raging blow, and thus creates a minor exponential effect, so the benefit deminishes slower. My calculations show crit > mastery until crit > 61%. Below are my calculations for dps increase from mastery:
Assume: Enrage is up 79%, death wish is up 21%, raging blow is 10% of damage with 0 mastery, each pt in mastery increases enrage effects by 3.13%.
(1) DPS increase from Enrage = 3.13%*10%*79% / (1+ Mastery)
(2) DPS incresae from Death Wish = 3.13*20%*21% / (1+ Mastery)
(3) DPS increase from Raging Blow = 3.13*10%* (1+ Mastery) / (1 + Mastery)
(4) Total DPS increase = (1) + (2) + (3)
Note for Raging Blow: The double dip for raging blow is accounted for by enrage (1) and deathwish (2) increasing total damage (which includes raging blow already), and a further increase in the raging blow's 10% damage (3).
1) Did you take into account Flurry uptime when looking at relative crit Value? How about Deep Wounds? While we don't have it now, in Cata, when we can actually get meaningful levels of mastery relative to other stats, it will be available, and important to consider.
2) Assuming a 79% Enrage uptime is pretty unrealistic. Even looking at the top parses the highest I've seen is 65%, the norm is more like 55-60. This reduces the effect of Mastery slightly
3) As a point in favor of mastery, looking at a value lower than 25% might lower the threshold where Mastery becomes as useful as crit. For example, what kind of damage increase are we looking at going from the base 8 mastery to 9? That might be better than crit at an actually obtainable level of crit. Looking at things in 25% chunks is very imprecise. On the other hand you did come up with the 61% number, so you may well have been doing the math for every point and just shown those benchmarks.
1) Did you take into account Flurry uptime when looking at relative crit Value? How about Deep Wounds? While we don't have it now, in Cata, when we can actually get meaningful levels of mastery relative to other stats, it will be available, and important to consider.
2) Assuming a 79% Enrage uptime is pretty unrealistic. Even looking at the top parses the highest I've seen is 65%, the norm is more like 55-60. This reduces the effect of Mastery slightly
Relative crit value is based on today only, no deep wounds. Deep wounds would make crit value significantly higher (especially with blood frenzy/mangle raid buff). My guess is, including deep wounds, Crit > Mastery up to the softcap for white crits. Is it 75%? Need to double check.
I'm also assuming no additional benefit from flurry or enrage for crit. While these would increase crit's value, assuming crit>35%, any benefit from extra flurry/enrage would be marginal for 1% increase in crit. This is also a very conservative assumption for crit to prove the benefit of crit over mastery.
Originally Posted by Seerow
3) As a point in favor of mastery, looking at a value lower than 25% might lower the threshold where Mastery becomes as useful as crit. For example, what kind of damage increase are we looking at going from the base 8 mastery to 9? That might be better than crit at an actually obtainable level of crit. Looking at things in 25% chunks is very imprecise. On the other hand you did come up with the 61% number, so you may well have been doing the math for every point and just shown those benchmarks.
For clarification, 25% mastery refers to 25% increase to enrage (8 pts in mastery), which is baseline. I am trying to show at what crit level does the 1st point in mastery make sense.
While the affect of haste in rage regen is very positive, my own setup steers clear of it completely. People in above have come to the conclusion that at ~40% haste from gear (together with 10% raid buff and 25% flurry proc), rage usage is essentially optimized. [ ... ]
Obvious problem is bloodlust, DBW haste proc, and even when there's mob aoe damage increasing our rage gen. When our rage is capped, all the extra points in haste are only getting 30% effectiveness (increasing white hits only). I am quite concerned how much haste is being put on the cata plate gear at the moment, which I believe is significantly worst for warriors than for rogues.
Personally I would recommend only 10% haste from gear and put all customizable stat points elsewhere.
My gut feeling on this is that you're dramatically overestimating the rage generation from BL, haste procs, and AoE damage, as well as the penalties from softcapping rage generation. What you're talking about is dropping 30% haste-from-gear, because at some moments in a fight you'll have a 25% haste buff, and that just seems absurd. If only white swings benefit during Bloodlust (well, it would be a little more that white swings, as faster attacks increase Enrage uptime, which does impact the rest of our damage), that might not be a problem in itself if it means a large enough increase in damage for the rest of the fight due to a higher number of Heroic Strikes. Likewise, I'm doubtful that rage-from-damage will be so high as to take 30% off the haste we'd require to fully rage cap. I just don't think 10% haste is a realistic point for soft-capping on haste due to rage caps, and I'd like to see more information from level 85 stat levels and conversion rates before pronouncing so definitively that haste is going to be the absolute worst stat.
The other major concern is that I also think you're being unrealistic about Cataclysm gear. What we're seeing now is the first raiding tier's gear. If I had to guess, most warriors won't be hard hit capped starting off, and rage generation won't be quite as high as it is now. That doesn't mean that haste will be better than hit (hit is clearly better for rage generation), but it does mean that we could easily be sitting at maybe 14% hit, and from that it could be that the extra rage generated from haste is highly important and I wouldn't be surprised if it turned out that some level of haste is superior to mastery, or possibly even crit. I'm not saying it is, but that I wouldn't be shocked if that's how it turned out.
I guess my ultimate point is that the easy dismissal of haste is inappropriate at this time, even if a more rigorous and systematic dismissal of haste may well be the correct decision in the end.
Relative crit value is based on today only, no deep wounds. Deep wounds would make crit value significantly higher (especially with blood frenzy/mangle raid buff). My guess is, including deep wounds, Crit > Mastery up to the softcap for white crits. Is it 75%? Need to double check.
I also did some calculations for the value of Mastery, and I came up with similar results at around 0.5 - 0.6% per point (but had no DPS values for other stats calculated so far).
With your calculations in mind, it seems safe to say, that in Cataclysm raid-entry level gear, mastery should be neglected as much as possible in favor for hit and crit I think. As far as my premade looks, hit and crit values are abyssmal (10-11% hit on gear, 9% crit on gear) and with the addition of Deep Wounds, crit will gain a lot more effect than it has currently on live.
On my run last night, running at around 45% crit (unbuffed) my heroic strike crit rate was 71.3% with 2 points in incite. Flurry uptime on H Saurfang (2:51min) was 95.9%--world of logs showing 97.9% active time, and 92.1% uptime on H Festergut (3:17)--98.5% active.
I can't shake the feeling that 3/31/2 theorycraft came from the thought that we'd be using slam. 3 points in incite will also allow a slightly lower crit rate with the same flurry uptime.
After testing; the crit bonus of incite is added to your current crit rate, at 66% I crit 100% of my incite procs tested on over 100 heroic strikes. The proc rate of incite is also 33/66/100. 2 points basically adds 15% crit to HS, 3 points adds 25% roughly.
Last edited by Wax On Danielsohn : 10/28/10 at 3:49 AM.
My gut feeling on this is that you're dramatically overestimating the rage generation from BL, haste procs, and AoE damage, as well as the penalties from softcapping rage generation.
As a forenote, all math done is for 4.0.1. At the end of this post I will give some of my thoughts for Cata. Thebitterfig is right in that there is probably an equilibrium for having haste between 10-40%... I will add that this equilibrium is highly "encounter/mechanics driven". I will try to elaborate my argument regarding haste by breaking down the components. Please note that when I talk about "efficiency", this does not include normal deminishing returns from having more and more haste, the final dps increase % should be the multiple of both factors.
Bloodlust
I believe the way to look at haste with bloodlust is to assume bloodlust would be used for any fight where min/max'ing dps matters. Lets thus assume a typical fight (5min) with 40secs of bloodlust, which comes down to 13% w/ bloodlust and 87% w/o bloodlust. Lets also assume again if haste from gear + bloodlust exceeds 40%, haste only benefits white hits and is 30% effective. Simple math gives us (87% + 13%*30%) = 91% effectiveness when haste from gear is between 10% and 40%. To summarize:
Haste Proc
Haste procs work similarly to bloodlust, reducing the benefit of gearing haste by another percentage (primarily in the 11-39% haste zone).
Incoming Damage
The benefit of this is higher than I originally expected. Whenever we take damage, we generate more rage/sec, effectively reducing the haste cap (40%). From prior posts, we see that 40% haste is equivalent to 3.3rage/sec.
Hit/Exp capped, 0 Haste, raid buffed, our rage gen is 15.2 rage/sec
Max Rage usage (capped by cooldowns) is 18.5 rage/sec
40% haste from gear makes up the difference of 3.3 rage/sec
So what does 1rage/sec mean? 1rage/sec = 30rage/30secs = 60 rage/min, and also means rage gen from 12.2% haste. (That's a lot of haste for so little rage!! 1 extra heroic strike every 1/2 minute!!) While I don't have any addon that tracks rage gen, my experience tells me I easily genearate 30rage every half min from incoming damage in most raid encounters, if not more. My expectation for cata is raid damage will continue given blizz is giving dps larger health pools, plus healers would be pretty bored if it's just tank healing. (if someone has a way to track rage generated from hits vs environmental damage in raids, happy to test)
With 30rage/30sec from incoming damage: (very likely case)
Haste cap is reduced to 28%
0-27%: 91% efficiency
(12-27%: 86.7% w/ DBW)
28+%: 30% efficiency
With 100rage/30sec from incoming damage: (extreme case, but not completely unlikely)
Haste cap is reduced to 0%
1+%: 30% efficiency
Putting it all together
I completely agree that hit, expertise is superior to haste/crit/mastery. For crit vs haste analysis, assuming bloodlust in a 5min fight and including normal deminishing returns for crit and haste, here are the tables: (remember from stat point perspective, 1% crit = 1.4% haste)
Where there is low to no raid damage, Haste benefit is clearly better than crit. However, it must also be noted that should there be incoming damage, the swing in haste's benefit is significant. This is what I mean by haste gearing is extremely encounter/mechanic driven. Where you want to place your bet is entirely up to personal choice. Considering how raids have evolved from vanilla, I don't expect raid damage to decrease (healers would be extremely bored). Some may want to customize gear between haste/crit in between encounters, personally I won't, unless my raid hits a giant wall, which these days is most likely from complex boss mechanics rather than my personal dps.
Thus I will be allocating my stats where I have certainty would increase dps in all cases, and leave extra buffer for incoming damage/bloodlust to increase my dps further. My recommendation remains, get as much gear with +hit or +exp, reforge all haste into hit/exp then crit, and not gem haste.
My personal testing experience showed that I did 10.5k on dummies with haste>crit built, but only 11.5k in raid.
When I switched to crit>haste built I did 9.5k on dummies, but did 13k+ in raids. Both were virtually hit/exp capped.
Thoughts for Cata
I've had a chance to think through this some more. There are 2 major points I can think of. I would have to post more details/tables once cata hits. Not a beta tester and would like to test assumptions first.
Inner Rage: This significantly ups the value of haste beyond the haste cap. Currently extra rage is purely wasted, inner rage can convert extra rage at another 30% efficiency. 30% = 15% extra damage / 50% extra rage. As you can imagine, this nearly doubles haste efficiency after cap from 30% to 60%, slightly less if we are unable to convert every point of rage > 100 efficiently, which we won't. I will need to think about the best rotation/priority to make this as efficient as possible.
Deep Wounds: This ups the value of crit significantly, how much I can't nail down, rough guess is 1.5x. Need to see numbers including mechanics like colossal smash, etc.
Final Thought on Rage gen
Everything I've done so far is based on a key assumption, extra rage generated and yellow damage is linear. It really isn't. We all know tha RB>BT>HS from damage/rage. Thus the extra rage generated by haste gets hit with another deminishing return. (Just like how I said 12% haste only yielded 1 HS every 30 secs earlier) I've yet to figure out how to model this effect, will think about it some more. This problem does not affect Str, Crit, which increases % for all attacks.
Thus I still recommend minimal haste at this juncture (4.0.1), and my raiding numbers back this theory.
It does scale exponentially in that there is an obvious exponential component to its scaling.
[...]
f(x)=(.9+.1*(1+.03125*(8+x/179.28)))*(1+.1208*(1+.03125*(8+x/179.28)))/((.9+.1*1.25)*(1+.1208*1.25))
Well, that's definitely non-linear, but that's really not exponential scaling. In fact, it's a quadratic scaling (or a double-dipping stat), and this is more close to linear scaling than exponential scaling.
In order to have an exponential scaling, you must have f(x) >= exp(a*x) / b(x) , where b(x) is at most a polynomial function of x.
In practice, the functions of the type f(x) = a / (b-x) also exhibit an exponential scaling at some scales.
A quick list of exponentially scaling stats (I might have forgotten some) is :
- armor penetration, both in the 2.0 and 3.0 mechanism. The dps with regards to Arp was of the type of a / (b-x), with a limited cap on x (at b-a for 2.0, with a smaller value at 3.0).
- avoidance stats pre diminishing returns (which was integrated precisely for this reason). The real scaling effect is easy to understand with unhittable characters : you TTL can even go to infinity... The Time to Live was also of the a/(b-x) type, but x was not capped before b.
In practice, exponential scaling is really really hard to balance, and reflects usually a design flaw. You can realize that :
1/ both cases have been removed by Blizzard ;
2/ In both cases, the results were really high when you stacked that value, and when stacking was available, people did it;
3/ Low values of the stat were really not interesting in fact. You needed to really stack it to benefit the effect.
- armor penetration, both in the 2.0 and 3.0 mechanism. The dps with regards to Arp was of the type of a / (b-x), with a limited cap on x (at b-a for 2.0, with a smaller value at 3.0).
Just to add to this:
physical dmg scaling could be written as 3/(3-x) in Lich King where 0<= x <= 1, x being the Armor Penetration fraction.
At 100% armor penetration you did 50% more damage relative to 0% armor penetration.
TLDR: if your crit chance (not character sheet, but actual against 83 bosses) is lower than 47.18%, take 3/3 Incite. If it's higher, take 3/3 War Academy. Two important provisos are below.
I modeled 3/31/2 vs. 2/31/3.
On any given HS, one of three things can happen: a regular (i.e. earned) crit, an incite (i.e. freebie) crit, or a regular hit.
Let BC = baseline crit be your probability of critting the boss before the Incite bonus.
Let #I = # incite ranks be, well, guess.
Let Pr(x) be "probability of x happening on this HS"
Let Pr'(x) be "probability of x happening on the previous HS"
Pr(reg crit) = Pr(last attack wasn't a HS crit that proc'd Incite) * Pr(critting without the Incite buff)
= [ Pr'(hit) + Pr'(incite crit) + { Pr'(reg crit) * (1 - #I / 3) } ] * [ BC + 0.05 * #I ]
Pr(incite crit) = Pr'(reg crit) * ( #I / 3)
Pr(hit) = 1 - Pr(reg crit) - Pr(incite crit)
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Take a second to think intuitively about how your probability to crit changes from your first HS, to your second, to your third and beyond. Your first HS is the one least likely to crit, because you have a 0% chance of having the Incite buff up. Your second HS is the one most likely to crit, because you had a 0% chance of having the Incite buff up on the previous HS and thus a 0% chance of being ineligible to have Incite up for this HS. For the third HS and beyond, your probability of critting similarly oscillates up and down, but decays towards some center. (Again, think about it intuitively - your 100'th heroic strike should have the same crit chance as your 101'th.)
We can simulate it in Excel by just picking initial conditions, plugging the above formulas into three columns for "reg crit," "incite crit," and "hit," and autofilling multiple rows as our hit table asymptotically approaches some center. (The oscillations get smaller than 0.01% after about eight heroic strikes, in case you were wondering.) As an example, I have 32.19% crit (on my character sheet, not against level 83 bosses). 2/3 Incite boosts my long-run HS crit chance to 54.88%; 3/3 Incite boosts it to 64.12%.
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Now to answer the actual question: do I want 3/3 War Academy and 2/3 Incite, or 2/3 and 3/3 instead?
-I'm going to ignore War Academy's effect on Slam and Cleave. Correcting for this would favor War Academy.
-I'm going to ignore the 3% crit damage meta and Incite's boost to Flurry uptime. Correcting for these would favor Incite.
Boosting War Academy from 2/3 to 3/3 is a pretty straightforward 1.15 / 1.10 - 1 = 4.5454...% damage increase for HS.
The effectiveness of boosting Incite from 2/3 to 3/3 depends on your base crit chance. (Intuitively, boosting crit chance from 20 to 25% is nice; boosting it from 60% to 65% is less nice, proportionally; boosting it from 100% to 105% is useless.) At SOME baseline crit chance, the Incite boost is an equivalent damage gain to the War Academy boost. To find that chance, we just use Excel to compute (1 + 3/3 Incite HS crit chance) / (1 + 2/3 Incite HS crit chance) and solve for the base crit chance at which the proportional gain is also 4.54%, the same as for War Academy 2/3 -> 3/3. That percentage turns out to be 47.18%.
Thus - qualifying our answer with the two provisos above re: stuff we're ignoring - if your actual crit chance (not character sheet crit chance, but actual crit chance against a level 83 boss before talents) is less than 47.18%, 3/3 Incite is the way to go. If it's higher, War Academy is the better option.
Last edited by Kethas : 11/02/10 at 11:47 PM.
Reason: Added comment re: ignoring 3% crit damage meta
You say that you prefer crit over haste since the amount of crit you have will increase DPS much more then haste when warriors take a lot of damage and just a little less if they don't. On the other hand, haste is more consistant to DPS increase since it is not affected by extra rage generation.
Question: Would you not agree that a major benefit of a warrior is being able to deliver consistant DPS due to our high movement in raid situation abilities such as intercept / heroic fury and intervenne? These abilities cause us to have less down time on a lot of fights, so we deliver more consistant DPS numbers then most of the other melee classes through various styles of fights. Do you believe that the benefit that crit has over haste in some fights would be overall enough to out weigh this fact since afterall, what a raid leader often wants is someone that can always be toping the meters, not someone who will only be able in some fights even if in those fights he is greatly out DPSing everyone else?
10/25/10, 1:30 AM
I merely mentioned, that is scales exponentially (meaning exponentially better), and that stats like haste or crit do not. Nevertheless, as we will never ever reach such crit/haste/hit ratings anyway, mastery will always be inferior I guess, even if they push up the numbers of mastery a little bit. Simply put, mastery in this form sucks and if they boost the numbers, this will be extremly difficult to balance in PvP
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