## Guest Post: Yuki Learns You Stat Weighting (p1)

June 23, 2009*As stated last week, here’s the post outlining how to determine weights to plug into lootrank to figure out your best in slot. It’s a general list written by (alas) a DPS-type, so it’s not aimed at healers specifically, but I hope you all can still find it useful. Yuki’s been my guildie, my buddy, and enabler of my anime addiction for several years now. He’s also the first person who told me that such a thing as mathcraft exists. Be warned, there’s numbers ahead.*

## Step 1: Choosing A Baseline

In order to compare various stats that scale in wildly different ways, the easiest solution is to **create a baseline** to compare. Traditionally, this is either Attack Power (Effective Attack Power or EAP) for physical classes or Spellpower (Effective Spellpower or ESP) for casters.

Why are they chosen? Because their effects on damage are very easy to measure. You could potentially model in terms of direct effect (that is, you could chose the baseline of “1 Effective H/DPS”), but that would make some of the calculations a bit messier and would make the resulting values a bit harder to read, as well as making the model even more sensitive to changes in other stats, so it’s generally better to stick with the simpler version.

You also need to decide at this point whether you’re going to model things that simply provide a **percentage increase to your baseline** (for instance, the 10% AP buff). You can in theory leave them out because they can be “canceled out” in that they provide the same benefit to all stats once you’ve converted them to the baseline, but this may not work entirely in practice, which is why you sometimes see stat weights with have things like “1 AP = 1.1 AP” or the like. I prefer to leave them in even if they’re notationally confusing, simply because it makes the model more robust.

## Step 2: Doing the Easy Math

This is the easy part: **calculating the stat weights for things that simply convert directly into your baseline.** For instance, a paladin gets 2 AP from a point of Strength, so before considering other matters, Str would have a value of 2 EAP.

Next, **include other scaling factors like talents or percentage-based buffs.** Because most paladin builds that care about strength have a talent that increases your total strength by 15%, a point of Strength from gear actually gives you 1.15 strength; furthermore, you should have Blessing of Kings for another 10% (and these are multiplicitive), so the final weight is 1 Str = 2.53 EAP (actually it’s not because I haven’t included Sheath of Light, but I’m simplifying for pedagogical purposes)

You should also take this opportunity to **convert stats into their “effective values” of other stats.** For example, 166.6… Int = 1% spell crit = 45.91 Critical Strike Rating, so 1 Int is approximately equal to 0.2754 Critical Strike Rating (this math is, of course, for the base value of Int; once you include any talents that increase Int by a percentage and Blessing of Kings, you will of course have a higher amount of effective critical strike per point of Int).

Mana regen is a bit of a special case since it scales with other stats, so we’ll leave it to the side for now.

## Step 3: Setting the Baseline Stats

Because some stats scale as a percentage of your totals (Crit, Hit, Haste, ArP, etc), and other stats scale with each other (Int & Spi => Mp5), in order to compare them, you need a baseline set of stats. **This step is why stat weights will always vary as your gear varies**: where the baseline is set has a fairly direct effect on the values of the various stats, so as you move the stats of the baseline around (by changing the gear, which adds and subtracts stats from your baseline values), your values for each stat will change. This step is also why people calculating these things rarely agree on the exact value of any given stat.

Most stat weights are done with either a sort of “average” stat mix for a given tier of content (that is, “we expect that most people doing this content will have X spellpower, Y% crit, and Z% haste on their gear when they start”), or by taking the best or average gear from the tier below and using that as the base. This produces numbers which are not terribly accurate to anyone in particular’s circumstances, but it can be useful to spot trends in gear scaling at your content level; it’s also the only option you have if you’re looking to provide weights for a class/spec rather than for yourself.

**If you’re doing this for yourself, the ideal choice is your actual current stats!** That way, your final results will tell you what effects adding or subtracting stats will actually have on you. This is a very good approach for checking out a single piece of gear, but it’ll still be problematic if you’re just trying to figure out what the best overall pieces of gear are for you, since it’s somewhat piecemeal.

At this point, you should also be able to calculate your “effective mp5” per int or spirit, since you can plug the base values into the regen formula (which I don’t have handy since I don’t ever use it), and then figure out how much MP5 a point in either one would be worth.

Continued in: Yuki Learns You Stat Weighting (p2)

*Thanks for reading part 1 (of 3) of this week’s Overwhelming Numbers series. God I love guest posters!*

Nice overview Yuki.

by BobTurkey June 23, 2009 at 5:41 pm> t’s a general list written by (alas) a DPS-type

To be fair, when I wrote it I was asked “explain stat weighting” rather than “explain stat weighting for healers”, so I wrote it in as general a manner as possible 😀

And I did used to be a healer, back in the grim olden days of 1.0 ^_~

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by The Daily Quest: Tuesdays are no fun without maintenance | Top WarCraft Blog June 23, 2009 at 8:39 pm[…] Guest Post: Yuki Learns You Stat Weighting (p1) As stated last week, here’s the post outlining how to determine weights to plug into lootrank to figure out your […] […]

by Top Posts « WordPress.com June 24, 2009 at 7:56 pmVery interesting. I also like how you keep a clear mind about the limitations of stat weights.

For example, I would like to elaborate on one of your final paragraphs:

“your final results will tell you what effects adding or subtracting stats will actually have on you. This is a very good approach for checking out a single piece of gear, but it’ll still be problematic if you’re just trying to figure out what the best overall pieces of gear are for you,”

This is an extremely important point. If a starting raider in half epic gear and blues would do this for intellect and spirit he will soon find MP5 as one of his supreme regen stats. If he gears for MP5, he’ll keep obtaining results where MP5 is the best regen stat. Yet… if he would have collected spirit and intellect he would have outscaled the mp5 regen by the time he farmed naxx. In this case, the stat weights failed to give him a view on the future value of stats. If he would have chosen stat weights based on high level gear, he would have gone straight for int and spirit instead. While awesome at the end of the show… it will give him a harder progression path as spirit and int are inferior first.

The reason for this scaling to be so complex is because of 1 incredible piece in our regen formula:

regen = blablabla “spirit” * “square root of int”.

This product gives an incredibly complex behavior:

– it scales better than anything else

– it implies an optimal balance

Now let’s look at an HPS (or dps) formula:

HPS = (Baseheal + coeff*SP) * (1+Bonus) * (1+Haste%) * (1+Crit% * crit-effect) / Base_cast_time

Bonus tends to be talent based, and typically fixed. “Crit-effect” is how much you get from a crit heal/dmg. This could just be 1/2 for healers and casters or 1 for melee but it can be upped by talents and tends to be fixed.

When we fill in the talents etc, what we get is another product between haste, crit and spellpower. This means they work in conjunction and they have an optimal balance. It also means they scale in a non linear way and their stat weights suffer from the same problem as our regen model.

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