http://en.wikipedia.org/wiki/Special...orycraft&go=Go

How to begin?

Actually, now that I think about it, the topic I had in mind had kind of drifted away from WoW, really having more to do with StarCraft than anything.

I was thinking about the topic of abstractly predicting the outcome of combat based on the aggregate statistics of the participants. Maybe it could be applied to imaginary large-scale WoW PvP, which would be kind of neat.

I can't start on my next project so I'm attempting to write a DPS calc in C# for warriors. :|

Hey, I'm still technically an intern.

The fun part, is that, in essence, this is work. It's just that I'm a theorist at heart, so when I'm assigned to try to balance the stats of some units, the quadratic formula soon gets involved.

The problem is that WoW doesn't have anything that really lends itself to abstract modeling. Fights aren't won by strategy; they're won by puzzle-solving.

The only possible exception is raid-wide healing strategy. It might be kind of fun to model a few different incoming DPS patterns, and see how they interact with a variety of different healing schemes. For example, find the lower bounds for overheal%, and things like that.

Maybe I'm just on a crazy theorycraft kick after reading that ludicrous Four Horsemen thread.

I hate my job, so I made a gigantic gear comparison/healing calculator for priests :x

where at? In R&D?

Yeah. It was kind of fun, although my guess is that it's not seriously useful for people trying the fight.

http://forums.worldofwarcraft.com/th...p=1#post639595

(Is public discussion about the Horsemen kosher yet? Are they in pre-fix C'Thun territory?)

If you create that article the many overzealous Wikipedia admins will probably nuke it right away for:

- not being encyclopedic
- not being notable
- veering too much into "fancruft"
- insert admin's pet peeve here

Yeah, more likely I'm going to start just pursuing some uselessly esoteric theory topic on this thread. Anything I'm doing would be too technical for Wikipedia. It would be fine for WoWwiki, but WoWwiki generally annoys me.

Actually, let's talk about Mages for a bit. I'd like to refine the workings of my spreadsheet and otherwise think about this. (Aside: this analysis all applies well to Hunters).

Basically, as a Mage, you're always in some casting cycle, defined by
1) What you do on Clearcasts
2) What you do otherwise.
[3) What you do on NW procs]

For example, my most commonly used casted cycle is [NCC: Frostbolt 11; CC: Frostbolt 11], but when I'm trying to regen, I might use [NCC: Frostbolt 4; CC: Arcane Missiles 8]. For any cycle, it's not very hard to compute the average DPS and MPS; my chart already has the machinery for this.

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The next step for real Mage optimization is how to correctly use different cycles to do the highest possible damage in time T with mana M. For now, we will assume that all mana gain abilities (pots, gems, and Evocation) are simply added to your starting mana to determine the target net mana consumption (i.e. we won't worry about the intricacies of using them in the right order, and assume it works out ideally).

So we a have a variety of cycles i. For each one, the DPS d_i and MPS m_i are known. Within a fight, each of the cycles is used for time t_i (note that order does not matter). Our goal is to maximize d_i*t_i (summation implied) while m_i*t_i = M and \sum(t_i) = T. At first glance, the problem seems well-defined.

Mathematical interlude, because applying topology to WoW is a rare opportunity to put my degree to use :ph34r: :
In fact, the second constraint gives a hypersphere in the n-space of possible choices, and the first constraint gives a surface which intersects it in a compact subspace. As we all know, continuous maps on compact spaces have extrema. Hence, there exists a best strategy. (if the two surfaces don't intersect, it means that using all your mana in the fight is impossible, in which case the optimum strategy is clear).

Conjecture: there will be no more than two nonzero t_i. This is based on intuition for the moment, but I want to write it down so I can revisit it later.

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Assume for the moment that there are only two cycles worth considering (as is the case for many Frost mages, much of the time). The behavior in the fight is already fixed by a system of two simultaneous linear equations:
t_1*m_1 + t_2*m_2 = M (note to self: don't make a sign error if you put this in the spreadsheet.)
t_1 + t_2 = T
. . .
simple algebra
. . .
t_1 = (M - T*m_2)/(m_1 - m_2)

D = (M*(d_1 - d_2) + T*(m_1*d_2 - m_2*d_1))/(m_1 - m_2)

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Not a bad conclusion in itself, but it raises the question: assuming the conjecture is true, how do I pick the right two cycles based on my setup, on M, and on T?

To be continued.

Actually, I'm still interested in this question (I took the Mage theory to a new thread).