Haste vs Expertise hardcap?
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Haste vs Expertise hardcap?
Hi,
assumed we have 7,5% hit and 7,5% exp and therefore, have reached spell hit cap and melee hit cap, and our melee attacks can't be dodged anymore:
Could it be possible that haste gives more Shield of the Righteous uptime now than exp?
Jugdement always hits and gains nothing from expertise, so the only HP generator exp influences is CS (+Grand Crusader procs).
But haste improves BOTH, CS and Judgement, by the same rate each, that exp improves CS.
My conclusion is, haste>exp(after expsoftcap), but that differs from the mainstream opinion (getting exphardcap).
Am I overlooking something?
assumed we have 7,5% hit and 7,5% exp and therefore, have reached spell hit cap and melee hit cap, and our melee attacks can't be dodged anymore:
Could it be possible that haste gives more Shield of the Righteous uptime now than exp?
Jugdement always hits and gains nothing from expertise, so the only HP generator exp influences is CS (+Grand Crusader procs).
But haste improves BOTH, CS and Judgement, by the same rate each, that exp improves CS.
My conclusion is, haste>exp(after expsoftcap), but that differs from the mainstream opinion (getting exphardcap).
Am I overlooking something?
 GreyedExpectations
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Re: Haste vs Expertise hardcap?
Edit: was bad info
Last edited by daishan on Mon Nov 26, 2012 11:57 am, edited 1 time in total.
Daishan of <Nidor Amo Nex>
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daishan  Maintankadonor
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Re: Haste vs Expertise hardcap?
Hm, I'm pretty sure Judgement always hits. Just tested it, with some pieces of armor taken off, 60 Judgements, 60 hits on the boss training dummy. My chance to get parried is 7,5% and my chance to get dodged is 4,33% (i took some peices of armor off).The chance of this happening would be below a tenth of a percent ((1(0,075+0,0433))^60=0,000523902472), if Judgement was on the melee table.
 GreyedExpectations
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Re: Haste vs Expertise hardcap?
Judgement cannot be parried, but can be judged, making your chance for that run 7.02%.

Nooska  Posts: 1355
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Re: Haste vs Expertise hardcap?
Nooska wrote:Judgement cannot be parried, but can be judged, making your chance for that run 7.02%.
"can be judged?"
Judgment cannot be dodged or parried, it can only miss. Expertise does absolutely nothing for Judgment.
Expertise is still better than haste for HPG, however. Proof:
Assume that your base (with 0% miss and 0% haste) HP generation rate is B. Your actual HPG rate is then:
A = B*(1m)*(1+h)
where m is your chance to miss (really the sum of miss+dodge+parry, for this let's assume you're already at 7.5% hit and 7.5% expertise so we're only concerned with parry) and h is your decimal haste (i.e. 10%=0.10).
Adding 1% expertise is the same as turning m into m0.01, or:
Am = B*(1m+0.01)*(1+h) = B*(1m)*(1+h) + 0.01*B*(1+h) = A + 0.01*B*(1+h)
Adding 1% haste turns h into h+0.01, giving:
Ah = B*(1m)*(1+h+0.01) = A + 0.01*B*(1m)
Since (1+h) will always be larger than (1m), you'll always get more HPG out of expertise than haste.
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theckhd  Moderator
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Re: Haste vs Expertise hardcap?
Ahhh, of course. It's an absolute "percentage point" increase, applying it to the smaller coefficient is of course a higher increase overall. I should have thought this through before assuming stuff.
Thank you very much for explaining.
Edit: Actually, your m influenced the complete B, even though a part of B, the Judgement part is not influenced by it. The whole B is influenced by haste, though. So I think your calculations might be incorrect (please read my latest post)
Thank you very much for explaining.
Edit: Actually, your m influenced the complete B, even though a part of B, the Judgement part is not influenced by it. The whole B is influenced by haste, though. So I think your calculations might be incorrect (please read my latest post)
Last edited by GreyedExpectations on Mon Nov 26, 2012 2:50 pm, edited 1 time in total.
 GreyedExpectations
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Re: Haste vs Expertise hardcap?
*cough* Judged = dodged  wasn't it dodgeable at some point during the beta then?, or am I mixing it up with something completely different?

Nooska  Posts: 1355
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Re: Haste vs Expertise hardcap?
Assume that your base (with 0% miss and 0% haste) HP generation rate is B. Your actual HPG rate is then:
A = B*(1m)*(1+h)
Doesn't this only cover the HPG rate of Crusader Strike? What about the HPG rate of Judgement which is not influenced by m? The factor (1m) only applies to the part of B which is generated by CS.
If I do the same for Crusader Strike and Judgement I get this:
Assume we have 7.5% hit and 7.5% expertise. Let J be the base HP generation of Judgement and C the base HP generation of Crusader Strike.
J is not influenced by m, because as you confirmed earlier, Judgement can not be parried or dodged, and we have reached the hit cap, so we are only concerned about parry. So assume for the moment m=0,075 (because we have only 7.5% exp) and h=0. C is increased by factor 1.2 to include Grand Crusader.
Our actual HPG rate A is then: A = C*(1m)*(1+h)*1.2 + J*(1+h) = C*(10.075)*1*1.2 + J*1 = 1.11C+1J
So 1.11C+1J is our HPG rate with 7,5%hit, 7,5%expertise and 0%haste.
So here comes the important part:
Now, if we increase expertise by 3 percent points (1020 rating), thus lower m by 0.03 we get the following:
Ae = (C*(1m+0.03)*(1+h)*1.2) + (J*(1+h)) = (C*(10.045)*1*1.2) + (J*1) = 1.146C+1J
If we instead increase haste by the same amount of rating (=2,4%), thus increasing h to 0.024 we get this:
Ah = (C*(1m)*(1+h)*1.2) + (J*(1+h)) = (C*(10.075)*1.024*1.2) + (J*1.024) = 1.13664C+1.024J
==> Ah = 1.13664C+1.024J
==> Ae = 1.146C+1J
Which is higher? J = 1 HP every 6 seconds. C = 1HP every 4.5 seconds. C = 13.3333333 per minute and J = 10 per minute.
Ah= 1.13664*13.3333333 + 1.024*10 = 25.3952
Ae= 1.146*13.33333+10 = 25.2799962
==>Ae < Ah ???
Another Example (+2550 rating: +7.5% exp(hardcap) vs +6% haste): (keep in mind, this is only the rating and expertise which goes beyond the standard of the first calculation)
Ae = 1.2C+1J = 25.999996HP per minute
Ah = C*(10.075)*1.2*1.06+1.06J = 1.1766C + 1.06J = 26.28800HP per minute
==> Ah>Ae
Another Example (+170 rating: +0.5%exp vs 0.4%haste):
Ae = C*(10.075+0.005)*1.2+J=1.116C+1J=24.88 HP per minute
Ah = C*(10.075)*1.2*1.004+1.004J = 1.1544C + 1.004J = 24.8992 HP per minute
==> Ah>Ae
EDIT: Gab rightfully corrected that haste needs 25% more rating than expertise for 1 percent point increase.
Last edited by GreyedExpectations on Mon Nov 26, 2012 5:14 pm, edited 4 times in total.
 GreyedExpectations
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Re: Haste vs Expertise hardcap?
Not sure (I'm bad at math) but are you taking into account in your 3% examples that:
1% haste = 425 rating so 3% haste = 1275 rating
and
1% expertise = 340 rating so 3% = 1020 rating
Thus making expertise the supperior choice for HPG?
1% haste = 425 rating so 3% haste = 1275 rating
and
1% expertise = 340 rating so 3% = 1020 rating
Thus making expertise the supperior choice for HPG?

Gab  Posts: 690
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Re: Haste vs Expertise hardcap?
You are correct, thanks! I forgot that. But it's still not enough difference to change the result, at least not with a 3% example. I corrected it and added other examples (exp hardcap vs 6% haste and 0.5%exp vs 0.4%haste) which show the same results.
Assumed my calculation was correct, which I don't know (I hope that theck will have another look) and haste yields more HPG per minute on average, expertise might still be better because exp hardcap means we can only ever have a certain timewindow without SHoRBuff, while the hasteapproach is not "luckproof". Also, I don't know if ShotR can be parried and if it still gives the buff when parried.
Assumed my calculation was correct, which I don't know (I hope that theck will have another look) and haste yields more HPG per minute on average, expertise might still be better because exp hardcap means we can only ever have a certain timewindow without SHoRBuff, while the hasteapproach is not "luckproof". Also, I don't know if ShotR can be parried and if it still gives the buff when parried.
Last edited by GreyedExpectations on Tue Nov 27, 2012 11:19 am, edited 1 time in total.
 GreyedExpectations
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Re: Haste vs Expertise hardcap?
ShoR can be parried / dodged, but still gives the buff.
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Worldie  Global Mod
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Re: Haste vs Expertise hardcap?
I actually wrote up a long reply to this yesterday, but the forum went down before I got to post it. Hopefully it's still saved on my desktop, so I'll try and repost when I get home.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
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theckhd  Moderator
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Re: Haste vs Expertise hardcap?
Hm... you're right, I wasn't being rigorous enough there. It would be accurate for hit rating, but for expertise CS and J should really be treated independently. However, if we're going to go to that level of rigor, we need to do so more accurately than you did.
First, Judgement isn't 1 HP every 6 seconds, it's rotationally constrained to 1 HP every 6.75 seconds.
Second, you get 1% expertise for 340 expertise rating, but it takes 425 haste rating to give you 1% haste.
So, rigorously then:
A = C*(1  m + dm)*(1+h+dh)*1.2 + J*(1+h+dh)
where
C is your CS rate (1/4.5=0.2222)
J is your J rate (1/6.75=0.1481)
m and h are decimal dodge/parry and haste values (assuming 7.5% hit  the earlier version is enough to prove hit>haste)
dm and dh are added expertise or haste.
Expanding this and ignoring secondorder terms (i.e. dh*dm), we get:
A = 1.2*C*(1m)*(1+h) + J*(1+h) + 1.2*C*(1+h)*dm + (1.2*C*(1m)+J)*dh
What we're really comparing are those last two terms: Ae=1.2*C*(1+h)*dm and Ah=(1.2*C*(1m)+J)*dh. But we want to do so in terms of rating r, and since dm=r/340 and dh=r/425, we can write:
Ae=(1.2*C*(1+h)/340)*r
Ah=((1.2*C*(1m)+J)/425)*r
For h=0, m=0.075, we get
Ae = (7.8431e4)*r
Ah = (9.2897e4)*r
So at 0% haste and exp softcap, haste is about 18% better for HPG than expertise. Conversely, it takes about 18.44% haste before expertise catches up to haste.
So yes, haste is actually better for holy power generation than expertise. That doesn't really matter though, since the advice to hardcap expertise isn't based on raw HPG or SotR uptime. It was based on damage smoothing, and in those simulations the hit/exp capped gear set outperformed the softcapped gear set that stacked haste.
The difference wasn't huge, but it was also a stochastic simulation (i.e. get as much SotR uptime as possible). In practice, a good player is banking and using HP intelligently, and the certainty that your next generator will hit has even more value there. Nothing sucks more than missing a Crusader Strike and dying to the next melee attack because you couldn't refresh SotR.
First, Judgement isn't 1 HP every 6 seconds, it's rotationally constrained to 1 HP every 6.75 seconds.
Second, you get 1% expertise for 340 expertise rating, but it takes 425 haste rating to give you 1% haste.
So, rigorously then:
A = C*(1  m + dm)*(1+h+dh)*1.2 + J*(1+h+dh)
where
C is your CS rate (1/4.5=0.2222)
J is your J rate (1/6.75=0.1481)
m and h are decimal dodge/parry and haste values (assuming 7.5% hit  the earlier version is enough to prove hit>haste)
dm and dh are added expertise or haste.
Expanding this and ignoring secondorder terms (i.e. dh*dm), we get:
A = 1.2*C*(1m)*(1+h) + J*(1+h) + 1.2*C*(1+h)*dm + (1.2*C*(1m)+J)*dh
What we're really comparing are those last two terms: Ae=1.2*C*(1+h)*dm and Ah=(1.2*C*(1m)+J)*dh. But we want to do so in terms of rating r, and since dm=r/340 and dh=r/425, we can write:
Ae=(1.2*C*(1+h)/340)*r
Ah=((1.2*C*(1m)+J)/425)*r
For h=0, m=0.075, we get
Ae = (7.8431e4)*r
Ah = (9.2897e4)*r
So at 0% haste and exp softcap, haste is about 18% better for HPG than expertise. Conversely, it takes about 18.44% haste before expertise catches up to haste.
So yes, haste is actually better for holy power generation than expertise. That doesn't really matter though, since the advice to hardcap expertise isn't based on raw HPG or SotR uptime. It was based on damage smoothing, and in those simulations the hit/exp capped gear set outperformed the softcapped gear set that stacked haste.
The difference wasn't huge, but it was also a stochastic simulation (i.e. get as much SotR uptime as possible). In practice, a good player is banking and using HP intelligently, and the certainty that your next generator will hit has even more value there. Nothing sucks more than missing a Crusader Strike and dying to the next melee attack because you couldn't refresh SotR.
Last edited by theckhd on Thu Nov 29, 2012 8:14 am, edited 1 time in total.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Call to Arms 5.x, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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theckhd  Moderator
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Re: Haste vs Expertise hardcap?
Ok, thank you for explaining. Everything's clear now.
I believe you mean expertise instead of mastery.
dm and dh are added mastery or haste
I believe you mean expertise instead of mastery.
 GreyedExpectations
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Re: Haste vs Expertise hardcap?
Yep, typo from generally using "dm" and "m" for mastery. In this case I used them for a generic "miss." Not the clearest notation, I guess, but it got the point across. I'll edit the other post for clarity.
"Theck, Bringer of Numbers and Pounding Headaches," courtesy of GrehnSkipjack.
MATLAB 5.x, Call to Arms 5.x, Talent Spec & Glyph Guide 5.x, Blog: Sacred Duty
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