Elitist Jerks A Tale of Two Ratings

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# A Tale of Two Ratings

Posted 03/03/09 at 3:38 PM by Adoriele
Updated 03/04/09 at 9:16 AM by Adoriele
Another week, another case. Dropped in my inbox yesterday, this one's not looking for help so much as asking a question:

Quote:
Originally Posted by Fillos
hello,
well I've been reading the moonkin topics since i started to "pewpew" in LK and I can follow the logic of the common opinion about gear and rotations and stuff. I stick to it, because it makes sense.

However I am kind of curious if you ever thought about leaning more torwards crit? Tell me if it's total nonsense but even despite the fact that crit-rating is more expensive than haste, I somehow cant help the feeling that it might be worth trying.
With wrath wasting an awfull lot of castingtime because of the GCD after a crit, if you have loads of haste.

Feel free to proof me wrong and/or mock me for missing some obvious fact.

This is a semi-obvious question if you're not familiar with the math; we have Spellpower, which has obvious effects, hit which everyone knows about, and then haste/crit, which are less obvious. Why, then, do we stack haste, and not crit?

Pros for Crit: Double damage (more than double if you have a Chaotic Meta), Moonkin Form Regen (though this doesn't directly affect DPS, so I'll ignore it), Nature's Grace and Eclipse both proc on crits.

Pros for Haste: Makes your spells cast faster.

Crit seems to have a lot more going for it. Here's the case against Crit:

1.) "Diminishing returns"
While neither crit nor haste have diminishing returns, they are affected by something similar. Adding a single rating of either will always produce the same amount of DPS. They will, however, increase the benefit of stacking other stats.

For instance, take a Moonkin with 0% crit (yes, this is impossible). If we were to add 1% crit to this Moonkin, his DPS would go up by 1% (ignoring, for the moment, a Chaotic Meta). If he were doing 2500 DPS, he would now be doing 2525 DPS, an addition of 25 DPS. Now let's put him at 40% crit, which is easily attainable right now. He's doing 3500 DPS. Add 1%, like before, and he does 3525 DPS. Again, a 25 DPS increase. But the % increase over what he was doing before is .71%, not the 1% he got when he had no crit at all.

Haste works the same way. When you have 0 haste, adding 1% will make you do 1% more DPS. When you're at 40% haste, adding 1% will give you another .71% DPS. This not-quite-diminishing returns is what encourages us to nominally diversify our stats. As one stat is increased, the others get better. So far, no difference between Haste and Crit.

The difference between the two comes from the following; Crit is always additive from all sources. If I have 20% crit, and a mage puts up Imp Scorch, I'm now at 30% crit. Pop into Moonkin Form, and I'm now at 35% crit. Add 1 crit rating, and I'm at 35.000202% crit. Haste, on the other hand, is multiplicative from all sources. If I have zero haste, and a shaman drops WoA, I now have 5% haste as expected. If I then spec into Celestial Focus, my haste is now (1.05)*(1.03)= 1.0815, not the 1.08 like crit would be.

Take the previous example. Let's say I have 20% crit and 20% haste from rating only. I would be doing 2500*1.2*1.2=3600 DPS. If I add 1% crit, I now do 2500*1.21*1.2 = 3630 DPS, a 30 DPS increase (note how adding 20% haste increased the value of additional crit. The same 1% is now worth 30 DPS instead of 25). How about I add 1% Haste from rating: The same result, 2500*1.2*1.21=3630 DPS.

If we add Wrath of Air to the equation, he does 2500*1.2*1.2*1.05=3780 DPS base. Adding 1% crit gives 2500*1.21*1.2*1.05=3811.5 DPS. Adding 1% haste from rating gives the same. They're still equal.

Now let's add Moonkin Form instead of WoA. Same 5% buff, but to a different stat: The same moonkin now does 2500*1.25*1.2 = 3750 DPS. Because Crit is additive, we already see a loss. We're not getting as much benefit from the 5% crit as we were from the 5% haste. But there's more. Let's add 1% crit to this moonkin through gear: 2500*1.26*1.2 = 3780 DPS. We had to add 6% total crit to get the same amount of increase as adding 5% haste!

This is just the effect of being additive, though. Adding that 1% crit gave 30 DPS, as expected. Let's add 1% Haste instead, through gear: 2500*1.25*1.21 = 3781.25 DPS. A larger increase as well! This is because we're increasing from 1.2 to 1.21, instead of 1.25 to 1.26. If we'd had 20% crit and 25% haste from rating, Crit would have given us the larger benefit.

The issue stems from the fact that, since Crit is additive, you're much more likely to have a higher Crit than you will Haste just from gear. Fully talented in a raid, you'll have 21% crit from buffs alone, and generally at least 5% each from int and rating. You'll have maybe 15% haste from gear if you're gearing specifically for it. Because of this, 1% of haste will almost always be worth more than 1% crit:

2500*1.31*1.15 = 3766.25 DPS.
2500*1.32*1.15 = 3795 DPS.
2500*1.31*1.16 = 3799 DPS.

2.) DoTs
Haste affects DoTs, even if it's only by a small amount; haste lowers the GCD incurred by casting instants. Crit, on the other hand, has no effect on DoTs whatsoever. If Blizzard decides to give us a talent to make DoTs crit, this might change, but that's currently not the case.

3.) Rating Coefficients
This takes less time to explain than the previous. Quite simply, it takes about 1.5 times as much crit rating for 1% crit than it takes haste rating for 1% haste.

How about what Crit has going for it?

1.) Nature's Grace
Crits proc Nature's Grace. Let's look at Starfire for this, since we get the best benefit there. Nature's Grace reduces Starfire's cast time by .5s, and is applied before all haste effects. We can treat this as a type of haste effect in itself. Specifically, since we reduce from 3s to 2.5, it's a 20% haste effect. So, if we have 100% crit, we could constantly apply a 20% haste effect to Starfire. How about if we had a normal amount of Crit? If we were to add 1% Crit, Nature's would effectively cause us to be adding .2% Haste as well. This isn't quite exact; This haste effect is not the same source as haste rating, so we would be adding a little bit more than .2% worth of haste rating.

2.) Time to proc Eclipse
Both Haste and Crit decrease the expected amount of time it takes to proc Eclipse. The math works out such that the ratio of added benefit from 1%Haste to benefit of 1% Crit is:

$\frac{\Delta E_t(1\% Haste)}{\Delta E_t(1\% Crit)}=\frac{Crit+1\%}{1+Haste+1\%}$.

The numerator can never be greater than 1, so 1% Crit will always reduce the time to proc Eclipse more than 1% Haste will. By how much depends on your current values, but crit will always be better.

With all this math floating around, and a lot of effects being ignored (Wrath's interaction with lag, CSD, etc.), why are people so confident that Haste is better than Crit? Because there have been multiple separate models developed to account for these issues intrinsically, and all of them have reports on the various ratings of stats. And all of them have pointed to Haste's benefit outweighing that of Crit on a point-for-point basis. It's not a gigantic lead. Haste is, using data from a recent set of gear I use, only about 40% better than Crit when comparing using WrathCalcs, nothing like Hit (which is ~145% better than crit) . But it's better nonetheless, so when given the choice between Crit and Haste, you should pick Haste every time.
Posted in Moonkin

 That was quite a read, I can feel my brain expanding... Posted 03/03/09 at 8:45 PM by Krixooks
 I had read the 'haste > crit' statement several times and had only a vague understanding of its justification. This summary is a great clarification of why this is the case. Great read. Posted 03/11/09 at 10:06 PM by Passthesugar
 Thank you for these (and all your posts in the various moonkin threads)! Posted 03/13/09 at 10:22 AM by princeinexile
 one small question: Is it worth taking the Celestial Focus Talent? i mean, does the 3% haste from it actually translate to 99 haste rating on your gear? Posted 03/18/09 at 10:48 AM by rightclick
 Yes it's worth it. No, not for the reason you mentioned. It's actually better than 99 haste rating because, as I stated above, Haste from different sources stacks multiplicatively. Posted 03/18/09 at 3:58 PM by Adoriele
 Thanks a lot for this really detailed explination, I've been afraid you might dismiss such a redundant question on this old topic The question now is how the changes to Nature's Grace in 3.1 might affekt all that. Posted 03/18/09 at 4:22 PM by Fillos
 Nice post. I'd suggest adding somewhere something to the effect of: "When it is all said and done, DO THE MATH! If you are lazy like me and most of us, download WrathCalcs or Rawr or Simcraft etc. Plug in you stats and\or your exact gear\enchants\buffs etc and then compare with Item A vs Item B. Please note the difference of say a potent gem vs a reckless gem will be small but like anything else, repeat that 10-20 times and the difference adds up fast, otherwise we all be in hero's gear with green quality gems" Posted 04/06/09 at 11:17 AM by Kaug Updated 04/06/09 at 11:23 AM by Kaug

### Oceanic Lag?

How does haste stack up with oceanic level lag?

I find that I lose so much of my theoretical DPS with wrath lag with 200ms latency + network jitter. So I prefer to stack a little more crit (working towards 25% base crit) to ensure I get more wraths crits to proc eclipse faster.

ie. my time spent wrathing to proc eclipse is my lowest DPS time due to network latency.

Once eclipse has procced I can use network queueing to ensure back to back casts.
Posted 04/12/09 at 7:12 PM by bubblecannon
 Now everytime I see a post from Adoriele I feel like House is staring at my brain to see if its soaking in the info. I just wanted to say that I appreciate all the work you put into making this an effective forum and the addon you made works great. Thanks. Posted 05/19/09 at 7:20 PM by Magneson
 I finally understood it. Thank you so much! P.s. like your avatar very much Posted 06/26/09 at 5:22 PM by aleatorvb
 40%? Using your wrathcalcs 1.3.1 spreadsheet with my gear+talents (all the main dps talent except imp MF) i show next point of crit at .79 and haste at .89, which is is 12% difference give or take. You also skipped the soft haste cap (likely the cause for the narrowing noted by the spreadsheet). Where total haste + NG puts Wrath under 1.0s resulting in dps loss since you can't queue wraths anymore. Which you can sometimes avoid now but won't be able to avoid with 3.2 Code: Spellpower: 2305 1.32 DPS Spell Crit: 431 0.79 DPS 0.24 MP5 Spell Hit: 278 0.00 DPS 0.00 MP5 Spell Haste: 429 0.89 DPS -0.06 MP5 Spirit: 546 0.22 DPS 0.00 MP5 Int: 1008 0.47 DPS 0.83 MP5 MP5: 25 Reaction Time: 0.1 Latency: 0.2 -11.87 DPS 1.07 MP5 PS The copied cells from excel looks better marked as code then as a table, anyway looks readable. If i move the reaction time back to the default of .2 the numbers narrow even further to .75-.78. But .2 seems like a long time when one can spell queue Edit I set the reaction time to 0 and played a bit with the latency and i was able to make crit nearly= to haste at .4 and to have haste at 35% better with 0 latency. In short as latency goes up the value of haste went down. Crit seemed mostly unaffected by latency. Interesting Posted 07/22/09 at 11:16 AM by Kaug Updated 07/22/09 at 4:05 PM by Kaug
 Thanks for being a complete moron. This post was written two days before the 3.1 change to NG, which drastically reduced the benefit of Haste and introduced the soft cap, was even released in patch notes, let alone Live. The version of WC active at that time was 1.2, not 1.3.1, and you'll note that, per what I said before, it doesn't include the changes to NG. And yes, before that change, Haste was in fact a giant leap over Crit in value, very closely approaching the value of Spellpower. No, this is not true now, the two are much closer together, largely because of those two changes. The entire fucking point of the post was not to give hard data, but to tell people the complex dynamics behind the two ratings, how they are in fact being taken into account in multiple models, and that people are coming to the same conclusions. Yes, those conclusions change as changes are made to the way Moonkin function. Yes, Rawr (and Hamlet's extensions to WC) continue to take those changes into account. There is a REASON that the guidelines are what they are, they're not just plucked from thin air or the result of someone's "feelings", which some Moonkin feel the need to rely on. Also, no shit lower latency increases the value of Haste, and has no (direct) effect on Crit. Haste can't change your latency, so as your cast time gets lower your latency, the part you can't change with gear, becomes more of a factor. Imagine you have 1 minute ping. Who the fuck cares how much haste you have, you're still only casting one spell per minute. Posted 07/23/09 at 6:29 PM by Adoriele Updated 07/23/09 at 6:35 PM by Adoriele
 Wow, who pissed in your coffee? Oh that was me for not somehow "knowing' the exact date of of 3.1 info release vs your 'latest' blog post. Only a complete ASSCLOWN would make a technical post, have several portions invalidated by patch notes 2 days later and never update or add a disclaimer to the post. A post you've replied to several times since 3.1 hit. Then call others morons for your oversights. Posted 07/27/09 at 10:36 AM by Kaug