[Mechanic Primer] - Haste - How it works, and what that means. - Page 6

Akuman · 03/10/08, 5:10 PM

Sorry, double post.

Please delete if possible.

Akuman · 03/10/08, 5:17 PM

Well haste does have diminishing effects but it's pretty much linear until you get to around 500 haste.

That's what I got when I compared spell haste to casting time using the spell haste formula.
Those graphs are assuming a 3 second cast spell such as fireball.

Increasing or decreasing the cast time of the spell will not affect the amount at which haste is a diminishing value, however as you decrease the casting time you come closer and closer to the cap of 1.5 seconds (or 1 second in 2.4).

Daidalos · 03/10/08, 6:24 PM

Originally Posted by Prell

[recap] The effective cast time formula (c' = c / [1 + x/1577] ) exhibits gently diminishing returns on casting speed, because the next point of haste rating will decrease cast time less than the previous point.

The first 200 haste decreases cast time by the factor c'/c = 1/(1 + 200/1577) = .887, netting 1/.887 - 1 = 12.7% haste. The next 200 haste only gets us to the cast time multiplier .798, so it only causes a .887/.798 - 1 = 11.2% cast speed bonus over the first 200 haste. Some people feel cheated out of haste, and others might conclude that haste has diminishing returns on DPS.

Oops I see what he is saying now I thought he was saying that the second 200 haste wouldn't reduce the cast time by as much as the first 200 haste did. He was using percentages I was thinking absolute ms. Yes as far as dps gains go it does have dimishing returns.

Zodiac2049 · 03/16/08, 1:47 PM

Ok so I'm decently sure I know the answer but I'm going to as anyway: is the AP to dmg calculation made before or after calculating Haste into your melee attack speed. I ask this because if it would calculate haste first, that would mean it would make AP less effective as you get more haste. now I havent really spent time to look into it but going off judgement I would say AP to dmg is calculated first but I just want to clarify.

Thanks

Ticia · 03/16/08, 9:31 PM

Originally Posted by Zodiac2049

Ok so I'm decently sure I know the answer but I'm going to as anyway: is the AP to dmg calculation made before or after calculating Haste into your melee attack speed. I ask this because if it would calculate haste first, that would mean it would make AP less effective as you get more haste. now I havent really spent time to look into it but going off judgement I would say AP to dmg is calculated first but I just want to clarify.

Thanks

The AP to dmg calculations use the base speed of the weapon to determine how hard each swing hits (or the normalized speed for yellow attacks), so haste has no affect on the effects of AP. Your weapon will till hit just as hard, it will just hit more often than it would without the haste.

Malconstant · 04/30/08, 1:09 AM

There seems to be some confusion. It has been stated that the effect spell haste rating has on overall DPS is linear, and yet follow up responses seem to suggest a belief that there is a diminishing return in overall DPS. This is simply not the case. Even though there is a diminishing rate of decreased casting speed with spell haste rating, the increase in overall dps is constant, i.e. linear.

Consider, if the casting time of, say, a shadow bolt linearly decreased with haste rating, then a finite amount of haste rating would eventually drive the casting time down to 0 sec, which would result in dps approaching infinity. How much haste rating would result in an infinite dps? Precisely the cap, 1570. For this calculation, I am using the assumption that cast speed = 1 + (spell haste rating)/1570 , and that new casting time = (base casting time)/(cast speed). I then found the rate of decreasing casting time for spell haste rating = 0 (this is just the derivative of the new casting time as a function of spell haste rating), and followed that rate down to 0.

No one believes this model is accurate, it results in a possible infinite dps for finite haste rating, which would be an extraordinary failure on Blizzard's end. However, people do seem to believe that because the rate of casting time decrease is NOT linear, that the overall dps must ALSO be non-linear, and that is simply not the case. The impact spell haste has on dps may be calculated by:

New DPS = (Old DPS) (Old Cast Time)/(New Cast Time)

For example, consider the shadow bolt spam. Assuming one talents for the 2.5 base casting time, our (Old Cast Time) = 2.5 sec. Now suppose our lucky warlock has gathered enough spell haste rating to give a (New Cast Time) = 1.25 sec, never mind how much spell haste rating that requires (it's irrelevant for the given calculation). As you would expect, our New DPS = (Old DPS) (2.5)/(1.25) = (Old DPS) 2. So by halving our cast time, we have doubled our DPS. good. You can try out other numbers as I have if you need more convincing that this function is accurate (it is).

Therefore the effect spell haste rating has on overall DPS is to just multiply the Old DPS by (Old Cast Time)/(New Cast Time), which itself is just (Old Cast Time)/{(Old Cast Time)/[1 + (Spell Haste Rating)/1570]}. And THAT function IS linear. That is to say, the marginal effect on DPS is constant, no matter how much haste rating you have (barring the unattainable 1570 cap). Of course the OVERALL effect on DPS depends on how much haste rating you have, it is only the CHANGE in DPS that we are concerned with here.

[edited for clarity: read embarrassing errors that were quickly noted by others]

François · 04/30/08, 6:32 AM

Originally Posted by Malconstant

There seems to be some confusion. It has been stated that the effect spell haste rating has on overall DPS is linear, and yet follow up responses seem to suggest a belief that there is a diminishing return in overall DPS. This is simply not the case. Even though there is a diminishing rate of decreased casting speed with spell haste rating, the increase in overall dps is constant, i.e. linear.

(...)

That in and of itself is unique to haste rating. The result is that haste rating scales with gear better than any other stat. For instance, once the lucky warlock has attained 2000 spell damage, the effect of gaining an additional 1 spell damage has a smaller effect on overall %DPS than when the warlock only had 1800 spell damage. For spell haste rating, however, even when the warlock has 1569 spell haste rating, the percentage increase in DPS from of gaining one more spell haste rating is equal to the percentage increase in DPS going from 18 to 19 spell haste rating, etc.. Of course, this does not mean that getting a large spell haste rating will always result in the most DPS, only that its effect on dps is linear.

There is nothing unique to haste effect, as haste has actually an affine effect on one-technic-spam average result, just like spell damage, attack power, critical rating, and even hit rating. The one stat that behaves differently is Armor penetration, because its contribution to dps is 1/(C - ArPen/b) instead of a clasical base + stat x coef.

Daidalos · 04/30/08, 1:10 PM

Originally Posted by Malconstant

There seems to be some confusion. It has been stated that the effect spell haste rating has on overall DPS is linear, and yet follow up responses seem to suggest a belief that there is a diminishing return in overall DPS. This is simply not the case. Even though there is a diminishing rate of decreased casting speed with spell haste rating, the increase in overall dps is constant, i.e. linear.

I think you have to be carefull what exactly people mean by linear vs diminishing. Yes haste gives the same amount of dps increase per rating linearly I think what people meant what as a PERCENT increase in dps it's diminishing. So yes there is bound to be some confusion, but really it boils down to which stat will give you the biggest increase in dps for your gear and situation. The semantics aren't really as important as long as people understand the impact on their dps from each stat.

Morwen · 04/30/08, 2:43 PM

Originally Posted by Daidalos

I think what people meant what as a PERCENT increase in dps it's diminishing.

The semantic relevance here, I think, is that if people have an expectation of this type of 'linear' then they're not thinking through the implications. If a stat gave a non-diminishing percent increase to dps, then it would be an exponentially increasing function and thus be utterly broken unless capped very quickly.

Daidalos · 04/30/08, 2:54 PM

Originally Posted by Morwen

The semantic relevance here, I think, is that if people have an expectation of this type of 'linear' then they're not thinking through the implications. If a stat gave a non-diminishing percent increase to dps, then it would be an exponentially increasing function and thus be utterly broken unless capped very quickly.

Yes the only non-diminishing stat I can thnk of is armor pen which is of course capped. Haste is a little more complicated for melee classes just due to thier mechanics for rage, combat potency, WF cooldown etc. Coming back to casters I think really the only thing to keep in mind in how each stat affects other stats in relative importance. Purely stacking haste at the cost of spell dmg and crit may or may not be worth it and all that depends on how much you have of each. I frequently see people asking how much haste they should have or what stats they should have before they start to stack haste as if there is a magic haste number everyone should get. Understand stat weighs and get whatever is the biggest upgrade is really the only advice you can give imo.

Muphrid · 04/30/08, 5:56 PM

Originally Posted by Morwen

The semantic relevance here, I think, is that if people have an expectation of this type of 'linear' then they're not thinking through the implications. If a stat gave a non-diminishing percent increase to dps, then it would be an exponentially increasing function and thus be utterly broken unless capped very quickly.

The only reason it would be "broken" is because most other stats don't work that way. If all stats worked on exponential curves, then it would be fine. And indeed, there would be significant advantages for the purposes of balancing if they did.

That in and of itself is unique to haste rating. The result is that haste rating scales with gear better than any other stat. For instance, once the lucky warlock has attained 2000 spell damage, the effect of gaining an additional 1 spell damage has a smaller effect on overall %DPS than when the warlock only had 1800 spell damage. For spell haste rating, however, even when the warlock has 1569 spell haste rating, the percentage increase in DPS from of gaining one more spell haste rating is equal to the percentage increase in DPS going from 18 to 19 spell haste rating, etc.. Of course, this does not mean that getting a large spell haste rating will always result in the most DPS, only that its effect on dps is linear.

I think you got a little turned around here, so I'm just going to clarify for those at home: the marginal DPS increase is the same regardless of how much haste you have. The relative (percentage) DPS increase diminishes as haste increases.

razi · 05/14/08, 1:25 PM

Here's diminishing returns in layman's terms:

If I have five apples and I buy one apple, I have increased my appleness by 1/5 = 20%.

If I have ten apples and I buy one apple, I have increased my appleness by 1/10 = 10%

This is what people are claiming equates to diminishing returns...

But the bottom-line is, I'm still getting ONE MORE TASTY APPLE.

Compared to say, 100 apples, getting one more apple doesn't seem that great, but you could have said the same thing when you had 99 apples, and the same thing when you had 98 apples... and as a result you would never have gotten to 100 apples. That's why despite *relative* diminishing returns, that isn't reason enough to stop stacking more and more of haste or mostly any other stat for that matter.

There are however other valid arguments in favor establishing a haste "cap" (primarily referring to Hunters).

Muphrid · 05/14/08, 4:06 PM

Originally Posted by razi

Here's diminishing returns in layman's terms:

If I have five apples and I buy one apple, I have increased my appleness by 1/5 = 20%.

If I have ten apples and I buy one apple, I have increased my appleness by 1/10 = 10%

This is what people are claiming equates to diminishing returns...

But the bottom-line is, I'm still getting ONE MORE TASTY APPLE.

Compared to say, 100 apples, getting one more apple doesn't seem that great, but you could have said the same thing when you had 99 apples, and the same thing when you had 98 apples... and as a result you would never have gotten to 100 apples. That's why despite *relative* diminishing returns, that isn't reason enough to stop stacking more and more of haste or mostly any other stat for that matter.

There are however other valid arguments in favor establishing a haste "cap" (primarily referring to Hunters).

The problem with your argument is that stats interact with each other in a way that your analogy doesn't describe. The raw DPS increase from haste is a function of your other stats, yes, and not of haste. 1 haste is going to be worth X DPS, all other things being equal. But 1 AP or 1 spell damage may be worth Y DPS, and Y is a function of haste. The reason to stop stacking a stat comes from the idea that stacking that stat will eventually make other stats more valuable. There is a mathematical point where, if you were just stacking haste, Y will increase to be greater than X.

There may not be a practical, achievable point, depending on the stat you're talking about (for example, if you're a caster and you're talking about crit, this will never happen--1 spell crit will never outweigh 1 spell haste at any practical gear level), but it is important to realize that the value of a DPS stat relative to other DPS stats decreases as you stack it, with the sole exception of armor penetration.

turbo_012 · 05/24/08, 11:13 AM

Haste and the Hunter

This is an example I'm following from the original post, to see if I understand it correctly and tell others, and see what others think of it.

Using an attack speed of 2.8s (Crossbow of Relentless Strikes), I've composed of attack speed or haste cap situations.

I'm assuming all hunters have 15% speed increase from the ammo bag/quiver and the 20% speed increase from serpent's swiftness from the beast mastery talent tree. Next in line is quick shots from imp aspect of the hawk, which is 3%, and is casted randomly. Then the non-random buffs, rapid fire(40%) and for those Leather workers out there drums of battle(~5%). Here's the table. It's comparing weapon speed and steady shot casting speed. Added speed is auto-shot buffer(0.5s) plus lag(0.2s). And the table goes by "level", so each row is accumulated to the next.

Base speed weapon(2.8s) steady shot(1.5s) added speed(0.7s)
Bag(15%)
Talent(20%) 2.03 1.09 1.79
Quickshot(3%) 1.97 1.06 1.76
Rapid Fire(40%) 1.41 0.75 1.45
Drums of Battle(~5%) 1.34 0.72 1.42

As shown, comparing the auto-shot speed and the added speed of steady shot, after using Rapid Fire ability you'll most likely clip your shots because 1.45(SteadyShot) is greater then 1.41(AutoShot). Does this mean hunters can reach the practical cap with just these skills alone? And does this mean that if you get enough haste to lower the weapon speed and steady shot to match up (around 30% ~ 480Haste Rating), that you'll never have to use rapid fire, drums of battle, or any other haste abilites?

alienangel · 05/26/08, 5:53 PM

That 0.7 added speed due to lag and autoshot casting time is questionable IMO - aside from that fact that 200ms latency is (I hope) painfully high and not often encountered, when the PTR stat duping bug was on people stacked haste and were firing autoshots with far less than 0.5s delay (search Midnight's posts for the results) - so at the very least whatever the autoshot delay is is reduced by haste).

The main problem with haste on steadyshot isn't the effective cast time, it's the GCD, which stays constant at 1.5s for hunters. Hence after a certain amount of haste, you can start just doing more autoshots than steadyshots for increased DPS, to the extreme case of only autoshotting (we already periodically get enough haste to do 2:1 rotations for brief periods of time).

Othieus · 07/09/08, 7:01 PM

Hey guys, with spell haste how much time is cut off of a spell at 1% spell haste. Does it differ for each spell you cast? For example, is the time cut off of casting Fireball less then if you're casting Pyroblast? Or are they the same?

Daidalos · 07/11/08, 6:41 PM

Originally Posted by Othieus

Hey guys, with spell haste how much time is cut off of a spell at 1% spell haste. Does it differ for each spell you cast? For example, is the time cut off of casting Fireball less then if you're casting Pyroblast? Or are they the same?

The foruma for cast time and haste is:

new cast time = (old cast time) / [1 + (haste rating)/1576]

1% haste is 15.67 haste rating.

Plug in numbers to see the result. As you can see it depends on the cast time as to how much time is cut off.

Really you should have read the forum before asking this. If you didn't understand what was posted in the forum point out what exactly you didn't understand, not "hey how does haste work".

Almehym · 07/20/08, 11:58 PM

So it's generally accepted that the Drums of Battle are the best leatherworking drums for use in melee situations. My question is: how much appreciable raid dps does a drummer add by using said drums?

I can use a rogue spreadsheet to model the increase to my personal dps, but is there a sheet for enhancement shaman, feral druids, arms/fury warriors, and ret pallies? Is there some way to average all of these to see based on the less-than-optimal melee setup versus the optimal one what the average gain from one drummer is?

Raski · 03/12/09, 2:43 AM

Ive been working on a spreadsheet to look at how gear effects stats for my Death Knight, I quickly came across the Haste rating to weapon speed issue. Once I got to 283 haste rating I was noticing a deviation of about 6% from the expected change in speed. All my data is purely from melee tests and is limited by gear availability and low speeds (compared to spells).

With 32 data points on a spell with a long cast time, I can get a formula to fit the curve that will more than suffice for ligitimate currently existing gear.

If anyone can help me with actual data or advice on how to see the effect of haste on spell times I would be very interested, especially from Akuman who seems to have already predicted the continuation of a haste curve. I am subscribed to this forum so please respond here with any help you can provide. Thanks for all the hard work everyone has already done.

chaos615 · 03/19/09, 9:12 PM

One thing I noticed on the damage meters is auto attack will deal the highest single target dps on a melee class, I also noticed that achieving a perfect 1 to 1 haste to critical strike ratio will, in mathematical theory, out perform any other ratio.

I.E. Character sheet lists players auto attack damage at 300dps, with 100% hit chance. The player can gear him self to allow 40 percentage points towards haste and or critical strike chance.

Dps * haste * crit = Average dps dealt
Haste should be multiplied before critical because haste directly effects the dps on the character sheet but doesnt really matter because both the values are equal to on another, so as long they are multiplied by each other it will work.

Haste * crit gives you the multiplier of both combined.

10% haste * 30% crit is 1.1 * 1.3 = 1.43 multiplier to dps
5% * 35% = 1.4175% multiplier to dps

This shows a 1.25% difference in ratio = to 1.25% crit chance or haste percent

20% * 20% = 1.44 multiplier

The numbers are nearly negligible once you get over 10% haste.

Haste cant hold as much of a value up to crit chance because haste rating as no influence, that I can tell, on skills.
So all skills receive the bonus from crit but not haste. Skill dps * crit chance = average dps of that skill.

adding in attack power is different, what the equivalence in attack power, 1% haste or crit, based off of how much 'dps attack power' you have.
Weapon is the titan steel steel destroyer at 186.6 dps and 3000 attack power = 214.28 dps
186.6 + 214.28 = 400.88 dps * 14 = 5612.39999999999 AP
186.6 dps * 14 = 2612.4 attack power + 3000 = 5612.4 AP

400.88 dps * .01(1% crit) = 4.0088 dps
Thus 1% haste or crit chance is equivalent to 56 Attack power with a 186.6 dps weapon and 3000 attack power.
So sacrificing 100 attack power for 1.5% crit chance will not improve your average dps of your auto attack.

However, Most skills dont receive the the full benefit of attack power and only 25% of attack power is used, in which case for that skill dps was in this case dropped down 2 dps worth of attack power, to multiply the average skill dps by 1.5%.

For kicks Ill attempt to do a intermediate calculator to calculate the attack power value of crit.
1000 / 14 = 71.42 dps * .01 = .7142 dps * 14 = 10 attack power
1100 / 14 = 78.57 dps * .01 = .7857 dps * 14 = 11 attack power
1200 / 14 = 85.71 dps * .01 = .8571 dps * 14 = 12 attack power

To make it simple the dps worth of each crit, will be set in increments of 100 AP
100 AP = roughly .07145 dps of crit. (that's not the perfect average but close enough)

The formula is...
weapon dps * 14 + Attack power = Total attack power.
Total attack power / 100 = y * .07145 = x dps * 14 = attack power value of 1% crit

Test Run
My sword of a thousand truths = 392 dps and I have 7600 AP

392 * 14 + 7600 = 13088
13088 / 100 * .07145 * 14 = 130.9...1% crit is equal to 131 attack power

The big question is what is the perfect ratio between haste, crit and attack power for maximum dps.
I don't know if players can even manage to make auto attack a greater portion of there dps. I know rogue could specced combat with slice and dice in BC.

I f i were to give a crude summery, in my opinion on how to equip a dps class it would be...
Ratio lay out is (Haste to crit) I don't know how to include Total attack power in to the ratio..
Its hard to give exact figures because the higher ap get the more crit and haste you want, but if you sacrifice attack power for crit and haste, the maximum effectiveness of crit and haste goes down. And you end up with more of whats worth less.

Skill dependent players 1 to 3 ratio
Auto attack Players 1 to 1 ratio

Always shoot for attack power because it effects auto attack and skill damage, Every 100 attack power increases your the effectiveness of every 1% crit buy the equivalent to .07145 dps!

I dont know why i didnt think of this sooner, but if Crit chance can be related to the players attack power in some way, then it would only make sense that 1% crit is always a certain percentage of the players total attack power.

This allows for an easier calculator formula.

The titan steel destroyer at 186.6 dps, and 3000 AP was 5612.4 Total AP
1% crit was equal to 56 ap
56.12 AP / 5612.4 = .009999 so 1%

1% of your total attack power is how much 1% crit or haste is equal to

Looking back at my previous post, I didnt even think to divide the attack power instead of the dps, which is perfectly alright since both integers hold the same value. That was real dumb of me. All the numbers were even the same, just the decimal was moved, that was real dumb of me for not being able to link the reverences together.

I've been trying to think of ways to relate haste and crit to a characters total attack power when itemizing, naturally with someone would say just get as much attack power as possible, but with the gear available in the game, its easy to assume that one set of items will out perform another.

The problem is calculating hit rating into the formula, if an item loses 1.5% worth of hit rating when equipping a new item, then the whole formula still has to be multiplied by by the players chance to hit.

The only way I can think of to compare items is to take the attack power it gives * haste * crit * chance to hit once the item is equiped to calculate the items effective dps

Then you have items such as trinkets that will only have one stat such as the dark moon card with 90 strength

With an item with only 1 bonus, it has to be compared to the stats on the character sheet juxtapose with the stats of the other item.

dark moon card vs 90 crit rating trinket, in this case ill just round up to 2% crit. The math is is simple, it means you need at least 9000 'total attack power' for the critical trinket to even hold a candle light to the nobles trinket.

Remember
Total attack power is the dps of your weapon converted into raw attack power + the attack power on your character sheet.
1% crit is equal to 1 % of your total attack power.

Why not use the dps listed in the character sheet you ask?? Because that dps is caclulated after talents and I wasnt 100% sure if it would effect the numbers, or how it would effect the numbers to give false values. So this way I know nothing weird will take place before talents. And haste effect that dps directly.

Dbf · 04/06/09, 4:45 PM

I've searched through a bunch of posts but can't seem to find a definitive answer about haste stacking.

If my base haste rating is 558 (17.02% increase), my spell casting time is reduced using the formula: casttime = spellcasttime / (1 + haste rating/3279). So a FB (normally a 3 second cast) will cast in 2.564 seconds.

When a haste buff like heroism is applied (30% haste for 40 seconds) the haste is not added but multipled. 17.02% * 30% => 52.13% for a haste rating of 1709. Now a FB would cast in 1.972 seconds.

My question, if another haste buff is applied, for example: Speed pot (+500 haste for 15s), or Embrace of the spider procs (+505 haste for 10s) is this also multiplied?

Which is correct? 17.02% * 30% * 15.25% (+500 haste) => 75.53% or 17.02% * 30% + 15.25% => 67.38%

And if all four haste buffs were present, is the correct haste increase? 17.02% (base) * 30% (heroism) * 15.25% (speed pot) * 15.25% (Embrace of the spider) => 137%

Rallik · 04/06/09, 11:43 PM

Originally Posted by Dbf

I've searched through a bunch of posts but can't seem to find a definitive answer about haste stacking.

If my base haste rating is 558 (17.02% increase), my spell casting time is reduced using the formula: casttime = spellcasttime / (1 + haste rating/3279). So a FB (normally a 3 second cast) will cast in 2.564 seconds.

When a haste buff like heroism is applied (30% haste for 40 seconds) the haste is not added but multipled. 17.02% * 30% => 52.13% for a haste rating of 1709. Now a FB would cast in 1.972 seconds.

My question, if another haste buff is applied, for example: Speed pot (+500 haste for 15s), or Embrace of the spider procs (+505 haste for 10s) is this also multiplied?

Which is correct? 17.02% * 30% * 15.25% (+500 haste) => 75.53% or 17.02% * 30% + 15.25% => 67.38%

And if all four haste buffs were present, is the correct haste increase? 17.02% (base) * 30% (heroism) * 15.25% (speed pot) * 15.25% (Embrace of the spider) => 137%

Effects that increase your haste rating stack additively with your gear rating. So, if all four were present, you'd have (1+.1702+.1525+.1525)*1.3 = 1.91776, giving you a cast time of ~1.564 seconds.