[Maths] Balance arena sets: MP/5 vs Crit

#0 - July 24, 2007, 8:07 p.m.

Introduction
This post is fairly long, there is a TLDR version at the bottom.

After reading a lot about people requesting the MP5 on the arena sets be converted to spell crit rating, I wanted to look into how that change might affect a balance Druid's damage output and staying power. This is the fruits of my labour and I hope it proves useful to someone somewhere.

As background for me: I am a "new" balance Druid having specced into it a few weeks ago. My gear and arena ratings are poor and I am not going to attempt to imply I have the experience or skill to truly analyse balance arena play at the high levels; but I am a mathematician and I do the numbers for those more experienced than me to read and understand.

What do we have at the moment, what could we have?
I have based my numbers on the season 2 arena and BG PvP gear, that is the Merciless Gladiator's Wyrmhide arena set and the Veteran's Wyrmhide Boots, Bracers and Belt. These are the items in question being designed specifically for balance Druids.

My conversions are done using the information found on WoWWiki.com (http://www.wowwiki.com/Formulas:Item_Values).

How does that MP/5 benefit us in arena fights?

So in a 5 minute fight, that 58 MP/5 will have generated 3480 mana for you; or 10 Starfires.

What is the effect of arena water?

So if you can drink for 15 seconds, you will regenerate about the same amount of mana as that MP/5 would generate over a 5 minute fight.

The conversion is 1 second of drinking water is equivalent to 21 seconds of in-fight time with 58 MP/5.

Case studies
For the following comparisons I have used two armory profiles as reference, that of two druids:

http://armory.wow-europe.com/character-sheet.xml?r=Nathrezim&n=Tradix

http://armory.wow-europe.com/character-sheet.xml?r=Al%27Akir&n=Lithanial

I believe these Druids are well geared and show expected stats you would find on a well-geared balance Druid. I am only interested in spell crit.

What do we get from increased crit rating?
145 spell crit rating gives 6.6% spell crit, this is not reduced by resilience; 145 spell crit rating will always give 6.6% spell crit.

To look at the above case studies, they have the following spell crit chance before talents or Moonkin form:

Since Lithanial uses Void Spheres in his sockets unlike most, the crit chance is lower. On average I would say a balance Druid will have roughly 11.5% crit if well geared.

After talents and Moonkin form, the numbers are a bit higher:

If the MP/5 was replaced with spell crit rating, the crit chance's would look like this:

Enter "Resilience"
Resilience reduces crit chance and crit damage by the following amounts:

By comparing current gear and "new" gear (if the MP/5 was converted to crit rating), we can see the increase in crit chance:

What this means is that against a target with 400 resilience you would crit 64% more often with "new" gear compared to the current gear - but, this is not to say you would gain 64% crit chance!

How does this affect damage output?
Taking Wrath as an example (but it doesn't really matter): if Wrath hits for 1000 non-crit, it'll crit for 2000 (assuming a balance build). This will be reduced by resilience:

Let's see how that translates into a "DPS" scenario. See what the average hit is. This is calculated by: average hit = [chance to not-crit * non-crit dmg] + [chance to crit * crit dmg]

So what damage increase is this on average:

Nature's Grace
"All spell criticals grace you with a blessing of nature, reducing the cast time of your next spell by 0.5s"

This talent does not affect Wrath; it does not reduce the GCD and so Wrath gains no benefit from it if other than making it cast a little quicker thus reducing the chance of an interrupt. It is my believe that this is wrong and a bug, but I'll say no more on the subject.

So how does this affect Starfire? Lets assume a crit rate of 20%, by chain casting Starfire a typical cycle will look like this:

This means that a cycle that would normally take 15s actually took 14.5s; that means there has been an increase in DPS of 3.45% (15/14.5) from Nature's Grace alone (ignoring bonus damage from crits). If calculations are performed for a 40% crit chance, the DPS increase from Nature's Grace increases to 7.14%. Some of you may have noticed, but this is not a linear relationship; as crit increases the DPS increase from NG scales slightly better than linearly although it's hardly noticeable.

If we take our above examples against a 400 resilience target, spamming Starfire against that target would yield DPS increases:

This is just from Nature's Grasp alone, it doesn't take into account the increased damage from the fact that the spell crit and thus dealt more damage.

What if Wrath's GCD was affected by Nature's Grace
Wrath could be affected much more by Nature's Grace than Starfire if NG reduced the GCD as well as the cast time. Using the above examples again, against a 400 resilience target with new :

Once again this is just from Nature's Grasp alone.

Final DPS upgrade values for "New" gear

was

Conclusions
Against a target with 400 resilience, taking the spell crit instead of the MP/5 would result in an increase of 4.65% DPS if spamming Starfire. If spamming Wrath there will only be an increase of 3.5% since Wrath does not benefit from Nature's Grasp; however, if Wrath did benefit from Nature's Grace it would increase by 5.87%.

As resilience increases, that extra bit of crit rating for gear becomes more and more noticeable since the base crit chance is being reduces so much. We've seen that by changing the MP/5 to crit rating you would see 64% more crits in comparison to the gear with MP/5; that's a big jump: akin to saying where you would have crit three times in a given time period, with the new gear you'll actually crit five times.

What I would suggest to all balance Druids out there is to look at your mana pools after a typical arena match and decide if you have too much mana left over. If you do, maybe we should petition for changing the MP/5 to spell crit as a community, but until we reach a consensus I doubt Blizzard will do anything.

Another thing to think about is whether we prefer the mana regen or the increased DPS (and utility if chained for quick Cyclone/Roots) of Nature's Grace. As resilience increases, that extra bit of crit becomes more and more noticeable (64% increase vs current gear remember) and crits can make the difference between a kill or not; but only experience will tell how much it all matters and that is what I lack.

Thank you for reading, constructive posts are always very welcome.

TLDR version
Choose between 58 MP/5 and 6.6% crit.

If the MP/5 was converted to crit rating, you would crit 64% more often versus 400 resilience targets: from 10.3% crit chance to 16.9% crit chance. The 6.6% crit translates into a 3.5% DPS increase versus a 400 resilience target if using Wrath and 4.65% if using Starfire.

The mana gained from 58 MP/5 over a 5 minute fight is the same as drinking arena water for ~15 seconds.