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Archive for April, 2009

Mentioning money in blog title: lots of clicks

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Tobold posts today about money making in games.  I’d like to focus on a particular set of statements:

…challenged me to try to earn 100 million ISK without firing a shot, and I refused that challenge as being pointless, due to the option of legally buying 300 million ISK in exchange for a PLEX game card….if I found a way to avoid PvP, and to play a trader instead of a miner, the fact that I could legally buy 500 to 600 million ISK for $34.95 would pretty much kill my motivation.

What interests me here is the lack of motivation to accumulate ISK because of its availability via RMT.  Why would the relative ease of availability of ISK de-motivate acquiring it, particularly in the face of Tobold’s later statement that “the fun is in *getting* somewhere, not in reaching some destination.”?  This seems roughly akin to saying that the ready option of painting the faces of a Rubik’s Cube devalues solving it in the conventional manner.

Isn’t it ultimately the case that ALL games are pointless endeavors?  Aren’t achievements pointless?  At the end of the day, what material change have you made in acquiring high-level gear on your WoW toon?  What tangible value have you derived from being in a server-first guild upon achieving that sought-after goal?  In that case, isn’t it equally fulfilling to merely enter cheat codes and beat games instantly?  I suspect Tobold would answer in the negative.  I am left to think that he merely feels no interest in playing a trader.  That is fine, but then…what is the point of making money anyway?  That seems to be the crux here: what is the point of accrual of wealth in Eve, or the accrual of high-end gear in WoW?  Why does it matter if someone buys it?  Is it simply that they bypassed the achievement?  Is that all we care about?  Or is something intangible gained in having the experience, something which may not necessarily be quantifiable but nevertheless is of value?

Let’s consider ISK in Eve.  It is the case that one can purchase ISK via RMT.  This is done by purchasing a PLEX card and then placing it on the market inside the game.  Players will exchange in-game money for the game time.  You come out with ISK and they come out with additional subscription time paid for with their time, rather than their money.  Whether that’s a valuable investment is wholly dependent on the player.  But what is the point of having ISK, anyway?  Obviously, as with any currency, it lies in its exchange value: the value of the goods it can be exchanged for.  ISK, or money period, is not of worth intrinsically.  Instead, its worth lies in the opportunity it presents.

So what opportunity is afforded you by purchasing ISK?  It’s not simply a score, it’s a means of power in Eve.  What power have you gained?  Well, that wholly depends upon you.  The value of ISK, it’s leverage, derives from the fulcrum on which it is placed.  What matter if you purchase ISK if you have no idea how to leverage it, or if it’s not intended to be levered at all?

The accrual of money has nothing to do with the money itself, which is a secondary artifact of the development of one’s opportunities.  Money happens to be opportunity enhancing, so it is pursued.  If money is pursued as an end, it is materially worthless.  If there is no ultimate exchange end point for the money, if it is being acquired for an opportunity which can never arise, then it is worthless.  The only way to be able to use money, to find worth in it, is to see the opportunities of its use: to understand the working of the system in which it arises.  Money is a signal, a measure of information.  It is an indirect indication of power.  Following its movement, you can discern patterns wherein opportunity lies.  Without that understanding, without grasping the system of money, your ability to lever that money is rather limited.

The point of acquiring money lies entirely in the skill gained at its use.  As it is so often said, it takes money to make money.  Capital investments are leverage, and to shift anything, leverage is required.  But the only way you can put that money to good use is to know how to use money, and you only gain that knowledge by examining and understanding the system of money and wealth transfer.  What better way to gain that knowledge…than to participate?

Ultimately, this is a question of goals.  Talk of money usually speaks of two goals: the accrual of wealth wherein wealth is a score, and an end in itself, and the accrual of power.  I will go ahead and trivially contradict myself here: acquiring money for itself, as a means of score, can be a valid end.  In that case, it’s a means of quantifying one’s skill at the game of acquiring money.  A game consists of a set of constraints.  The challenge issued to Tobold, to acquire 100 million ISK without firing a shot, was implicitly constrained by the additional rule of doing it in the game.  Tobold correctly feels that buying it via RMT would be a form of cheating, but then concludes that because it is explicitly allowed by the rules of the whole game of Eve, it’s allowed by the rules of any sub-game.  That’s not a fair leap.  He was being challenged to do so without RMT.  That’s another game, a game within a game, and one that can have its own pleasure.

Beyond that, even within the broader game of Eve, being able to acquire wealth without the use of RMT provides a certain substantive edge over others.  Presumably the ability to do so implies a knowledge of the internal economic system, a knowledge which helps amplify one’s existing capital base.  That knowledge allows one to detect opportunities, and to rearrange the board to your advantage.  Simply purchasing ISK does not confer THAT advantage, one gained through the effort of analysis of the underlying system.

As it happens, I have earned 100 million isk without firing a shot.  After finishing the tutorial sequences, I gave up entirely on both mission running and mining, focusing my mind entirely on trade opportunities.  One learns fascinating things by looking at the economics of Eve.  The game encourages specialization, not merely through the skill system, but also because of the time investment any activity requires.  Successful mining, for instance, requires specialized equipment, proper understanding of the various places to mine, the skills to use the equipment, and time.  Let’s say I have found a very profitable field, chock full of asteroids and pleasantly free of pirates or competitors.  This situation is time sensitive.  I need to spend time harvesting the materials and transporting them to the nearest station.

Let’s say I manage that, refining the ore into a treasure trove of minerals.  I am not an industrialist, so I want to sell my minerals.  I have a few options.  I can attempt to haul them out of this station elsewhere and then come back to mine more.  In general, the highest bids for minerals can’t be found local to good mine fields.  Industrialists congregate in high population areas, and haulers like to use trade hubs to move goods.  High quality minerals can only be mined, sadly, in the lowest security sections of the galaxy, which are naturally not trade hubs.  Here is where specialization comes into play: I have a comparative advantage in mining.  I can effectively mine at a very rapid rate.  By keeping my mining operation mobile and adaptable, I can avoid pirates and maintain a steady churn of new minerals at fields spread all over the galaxy.  However, that severaly limits my ability to haul my own minerals.  I can’t guarantee I’ll have minerals in the right locations to have nearby haulers.  Instead, I’ll have to give up mining time in order to do hauling myself.  The local station likely has bidders for my minerals, though they are likely priced well below the price I could get taking them to, say, Jita.  Which is worth more to me: attempting to put together my own hauler and hauling operation to safely gather my minerals and haul them to Jita to sell, or sell them locally, using the saved time to mine more minerals?

The answer to this involves examining tangible and intangible costs and benefits.  Tangibly, we can look at the cost of maintaining a hauler plus fitting, of training the associated skills, of the time spent hauling, and of the risk of loss (from, say, a pirate attack).  That all needs to be subtracted from the benefit of the price premium gained selling at a trading hub.  Intangibly, the cost is giving up mining in favor of hauling.  Which do you prefer doing more?  Obviously, which you prefer more adds an unquantifiable factor to this analysis, so I will leave it out of the numbers.  Nevertheless, it is very important that it be considered, as it bears on how well you invest, how well you do your job, and how much fun you’re having playing what is ultimately a game.

As for the tangibles, the cost of hauler maintenance is likely some portion of the cost maintaining your mining vessel.  Depending on your skill layout, you may literally be unable to fly a decent hauler, but even if you can, you may not be able to fit one for maximum efficiency.  Because the amount of time needed to haul is function of your hauling efficiency and the amount being hauled, it will relate directly to how much time you spend mining between hauls (as that determines the amount of minerals you need to move).  That means that time spent hauling can be considered a ratio of mining time.  So let’s look at some equations: Let R be the ratio of hauling time to mining time, r be the premium gained from selling at a trading hub, M be the value of mining and selling locally per time, and C be some constant representing the cost of the risk of losing your hauler + mineral load.  The benefit to hauling, then, is r * M.  The cost is the time lost no mining, R * M minus the risk factor of hauling, C.  The final equation is:

r * M – (R * M + C) = M * (r – R) – C

So the obvious points of concern here are C, which is always positive and non-zero, and the relative size of R and r.  We assume that r is greater than 1, since the price you’ll get where you’re hauling the minerals is higher than the local price.  It’s important to note that the value of C is also likely related to M, since the larger M, the larger C (the larger M, the more time hauling.  The more time hauling, the larger the risk cost).

Without throwing in values, we can see this at least produces cases where the miner is better off selling locally at a lower price and spending what would be hauling time mining.  This becomes more the case as the time spent hauling is longer than the time mining…in fact, unless the haul time is very short, it’s almost definitely in your interest to mine and sell low.  That, essentially, is the principle of comparative local advantage.  You don’t have to have a natural advantage in mining for it to be advantageous for you to invest there, especially when you already have momentum in that area.

Because of that, there exists arbitrage opportunities.  A merchant takes advantage of people exercising comparative davantages, such as the mining example.  If demand is higher at trading hubs, a merchandise mover can specialize in moving, selling, and purchasing merchandise in order to facilitate comparative advantage of producers.  In this case, the trading hubs exhibit high demand because they are proximate to the consumers of distant goods.  If the majority of goods producers need to take time from production to move the goods, prices must rise to justify that.  We can also see this will happen due to the reduction in supply.  Time spent hauling is time not spent mining.  If the miners haul, that reduces supply compared to demand, tending towards a higher price.

Obviously the reverse is also true: if consumers of goods have to spend more time acquiring goods, for instance by hauling goods to where they can be consumed, then that lowers demand, decreasing the price.  Either case lowers the final benefit of consumption along the chain, reducing total revenue.  A merchant hauler, by developing a comparative advantage in hauling, purchasing, and selling, can facilitate producers and consumers maximization, because that ultimately benefits their margins.  Consider: if the cost in time of purchasing a good for consumption is reduced; that is, if the rate of consumption is increased, that increases aggregate demand.  That in turn boosts the price.  Because the merchant facilitates increased supply due to more rapid hauling and allowing miners to continue mining, there is a downward pressure on prices.  In this situation we see that, rather than reducing their margins due to oversupply, merchants can maintain them due to indirectly boosting demand.  I won’t say these effects precisely offset one another, but it is obvious such a counter-balancing effect is in play.  In this situation, margins become controlled by the ability of dedicated haulers to move goods and the number of such haulers compared to producers and consumers.

Learning all this by doing that sort of hauling was precisely what I enjoyed playing a trader in Eve.  This is different from market specualtion; I was not beholden to the market rising or falling, merely to the margin between the lowest and highest buyers of a given good.  Given the size of the Eve market, I was able to dabble in a number of good markets, all of which had different feels.  While the mineral market was my bread and butter, ship resales also returned some solid value.  In general, though, I found that goods which moved in high volumes were the easiest to trade, and that meant minerals.

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A note on blog stats

Entering a controversial discussion: more clicks.
Having controversial discussion trackback here: more clicks.
Being linked: tons more clicks.
Theorycraft: a few more clicks.
Lengthy discussion of abstract points of game design: no clicks.

This should probably impart a lesson…

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Game Design

I am linked off Lum’s Blog under “Game Design”.  That is interesting to me.  I actually asked him about it, and he said he figured I’d talk about Game Design at some point and that was as good a place as any to link me.  Professionally I’ve bounced around game development enough that I have been asked many times whether I’m a designer or programmer.  Usually it’s at an interview, wherein I am applying to be a designer and asked if I’d rather be a programmer, because my resume has so much programming experience in it, or it’s the reverse (applying for programmer, but I look like a designer).

If you look through my categories, you’ll see game design really isn’t terribly frequent.  In fact, some might argue with me regarding my choice of categorizing certain posts as “Game Design” when they are more clearly things like “Theorycrafting“.  You may also note that I have entries on Economics, philosophy, and (arguably) community interaction (i.e. Ghostcrawler Watch).  So in all fairness, how can I be a game design blog, even peripherally?

Well, I’m not really about game design primarily.  I am about thoughts.  That said, the best game design you’ll find among my current content comes from my GC watch posts; there I use GC as a convenient foil for anecdotally demonstrating game design principles I tend to give credence to.

That said, I would like to talk about Game Design abstractly. When I talk about game design here, I’m going to focus on top-level design.  The stuff lead designers for a game do.  This is about the design of the entire game, from world to systems to the general manner of level flow to character package and so on.  The rubric of game design in the industry includes a whole range of people who do other sorts of design, including story detailing, level design, monster design, system design, etc.  I’m going to focus on game design at the top level, and state that the manner of thought given to good top level game design is consistent with the manner of thought which tends to good design in games, period.

First, I’d argue that game design is an art.  As such, there exist two questions about game design: “How does one design a game?” and “How does one design a good game?”.  The second question is presumably a superset of the first.

The answer to the first question involves a sort of practical toolset: answers may include “write a design doc” or “build levels in a level editor” or “insist on production enhancing tools” or “learn lua” or whatever.  Probably the single best answer is the first I gave; writing a design document amounts to coherently developing a description of the game model such that it may be implemented.  Ultimately, that’s what game design is directed to: developing a model.

I have a game design friend who always attempted to sort out people with game ideas from people with game designs.  It wasn’t really something he could explain.  When you asked him what made a game idea different from a game design, he had a tough time coherently elucidating the differences; he just knew it when he saw it.  Being something more of a philosopher, I have spent a lot of time trying to conceptualize the difference in a descriptive manner.  The difference seems to lie in how one thinks about a game: externally versus internally.  A game idea is concerned with the appearance of the game, the experience had while playing.  In contrast, a game design is concerned with the model which moves from input to output: a description of the game which produces the experience had while playing.

Here’s an example: let’s say you’re describing a level that needs to be designed.  Someone with a level idea describes the sort of experience they expect the player to have.  In general, that is a sort of walkthrough of the normal play experience, like “The player enters the level and is greeted by a jungle vista.  As they move between the trees, towards an ancient ruined structure, they come across vast stone pillars that have been long-since overgrown by vines and creepers.  Suddenly, two enemies burst from behind pillars carrying guns.  Once the player has dispatched his opponents, he proceeds, entering the sturcture through a massive doorway.  Through a long hallway, dimly lit by the sun shining through cracks in the ceiling far overhead, he eventually comes upon a central chamber.  There, in the center, is a small stone pedestal upon which rests the object of their search: a golden statue.  As they move towards it to take it up, though, a vast robotic behemoth shatters the rock ceiling, pointing blazing guns at the player.  A mighty battle ensues…” and so on.  That describes the experience of the level.

A level design for the same level, however, would read differently.  It might proceed thus: “The level is arranged as a large rectangle.  The first half is essentially flat, populated relatively densely with trees from our jugnle palette.  Their placement should break up the player’s view, but allow them a view of the second half of the level, a large building, 3 stories high.  The jungle surrounding the building is enclosed by impassable, dense foliage (yes, standard gaming trope, but effective in communication).  Fallen trees and rocks are also spread amongst the trees to provide cover for the player in any firefights.

Several enemy types should be placed around the structure.  This includes two at the main entrance, hidden from view by pillars who will come out to engage the player when the player enters a certain radius of the doorway.  Additionally, on each side of the structure are 2 additional enemies, also hiding.  They will engage, again, when the player enters a certain radius of them.  Along the base of the structure runs a ledge, which can be reached by jumping.  Along with rocks and fallen trees, this provides a way for the player to acheive height.  Also, at the very back of the structure, there is a nook in the building which can be reached by jumping to the ledge and simply walking back.  Out of sight from groundlevel, but perfectly visible from the ledge, at the back of the nook, lies an ammo cache.

The interior of the structure consists of a single long hallway which ends at a large, circular chamber.  The chamber is approximately 20 feet tall and 40 feet in diameter, with a domed ceiling.  The walls are flat and decorated with murals.  About 10 feet from the wall to the center of the chamber are a ring of pillars reaching to the ceiling.  In the very center of the room is a chest high pedestal, on which is placed a golden statue.  The room is otherwise barren.

If the player enters the ring of pillars, they will trigger a scripted sequence of a robot breaking through the ceiling.  Upon the sequence’s completion, the room will be changed.  The pillars will have been crumbled, and the ground will be littered with stone slabs of various heights.  Particularly, the doorway through which the player entered will be entirely covered and impassable…”

And so on.

The difference I’m aiming for here is that the first, the description of the experience, does not actually describe the design of the layout.  It gives little indication of what sort of interaction the player might have with the environment or what goes on beyond the narrative.  It instead captures the expected feelings of play.  However, a game is not simply a narrative.  It is instead an environment which is manipulatable.  It is a venue for stories to be made.  A game design is a description of the venue and the props, but can have no reference to the actors beyond describing the sort of acts they can viably perform.  It is up to the player to tell the story.

That, then, is my answer to “how does one design a game?”  By knowing the difference between having a game idea and a game design, and by having the latter.  In crafting a description of a venue in which stories may be told, rather than attempting to craft a story, you design a game.  A design doc is a description of this venue, it’s rules and props, the sorts of actors who might populate it, etc.  Therefore, writing a design doc, or having the ability to, even if no such document is written, is the core of designing a game.

Perhaps the more important question is “How does one design a good game?”

That is tougher.  To be honest, I’m not sure I can tell you, any more than an author can tell you how to write a good story or a painter can tell you how to paint a good picture.  I can perhaps introduce you to a toolset which might be applied to the production of a quality piece, but simply using the tools is insufficient.

The most important thing to keep at the forefront of your mind is that you are aiming to make a good game.  Everything is secondary to that.  Obeying good design principles, using successful design tools, even the above design doc formulation, all of that is a distant second to the production of a good game.  If solid flow is conducive to your good game, then follow that rule.  But understand that all art is about the art primarily.  Rules are convenient constructs which help settle the subject, not laws constraining the object.

How will you know it’s good?  You’ll know it when you see it.  This is one of the reasons prototyping is so damned important to building a good game: unless you have a  trained imagination, one in which the currents of cause flow into experience precisely as they would in a finished product, you will have a hard time guaging the quality of your game design until it’s been put into place.

Even if you are prototyping, train your imagination: every system being put into place should be a question mark, and its answer a consequence of interest.  Something as small as adding to the jump distance parameters on your character in a platformer can alter the terrain of your levels dramatically: know this!  Exercise your imagination in the context of your world.

Questions, it seems to me, are more important than answers.  A game is a what if; if the world of game is a stage, then the question is what types of plays might be performed upon it?  And that, I think leads into the final assessment of a good game: a good game makes good stories.  It’s important, I think, to maintain the difference between the story told by the game, the narrative of the world and the story the player creates advancing the narrative.  These are very different.  We, as gamers, don’t tell our stories about cutscenes or dialogue; those are environmental flourishes which help cohere the world in which OUR story is set.  Even if the narrative is ostensibly about us as players, or the actions of our avatar, that is a period after our story (perhaps an exclamation point if it’s a Square Enix title).

Does playing your game make for good stories?

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http://www.popcap.com/promos/wow/

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Nourish v Regrowth

With the changes in 3.1, it’s interesting to examine the case of Nourish v. Regrowth.  I didn’t get into it with my last post on resto, because I got a bit too deep into lifebloom numbers.  I’d like to look at these two spells now.

Of utmost importance to me here is the direct heal portion.  Specifically, I think Blizzard has positioned these two spells in competing niches within the druid healing repertoire.  I’d like to examine the numbers and see if I am correct.

Nourish is the easier of the two to examine.  Let me look, first, purely at its healing output.  Nourish is a 1.5 sec. cast spell which heals for

(1 – crit) * M * (base + coeff * SP) + crit * 1.5 * 1.3 * M * (base + coeff * SP)

= (base + coeff * SP) * ((1-crit) * M + crit * 1.95 * M)

= M * (base + coeff * SP) * ((1 – crit) + crit * 1.5)

= M * (base + coeff * SP) * (1 + .95 * crit)

The crit value is based on the 1.5x multiplier critical heals receive plus the bonus from the Living Seed talent.

M is similar to Lifebloom (see my last post) but without Genesis.  That puts it at (1 + (.04 + .1)) *  1.06 = 1.208.  However, if you have any of the main druid HoTs on the target, it heals for an additive .2 before the ToL aura more.  We’ll assume that is the case, ao M = 1.42.  Additionally, Nourish has a new glyph incoming which increases M by .06 for each of your HoTs on the target.  Let’s assume that lifebloom stacks only count once.  That would mean Wild Growth, Rejuvenation, Regrowth, and Lifebloom in the best case scenario.  That increase M as above, so M = 1.675

base = 2035.

coeff = .6611

So, the equation thus far is 1.675 * (2035 + .6611 * SP) * (1 + .95 * crit) = (3408.6 + 1.107 * SP) * (1 + .95 * crit)

A two variable function is not optimal, but we’ll leave it like this for the moment.  One thing to note is that Nourish will, in the best case, scale well with both spell power and crit.  Keep in mind that crits will proc Nature’s Grace, reducing the cast time of Nourish to 1 sec and further increasing it’s output.

Let’s turn to Regrowth.

Regrowth’s direct heal is based on an equation very similar to Nourish:

(1 – crit) * M * (base + coeff * SP) + crit * 1.5 * 1.3 * M * (base + coeff * SP)

= (base + coeff * SP) * ((1-crit) * M + crit * 1.95 * M)

= M * (base + coeff * SP) * ((1 – crit) + crit * 1.5)

= M * (base + coeff * SP) * (1 + .95 * crit)

Crit value functions the same as Nourish.

M is, in the worst case, the same as LB: Regrowth benefits from Genesis, MS, GoN, and ToL Aura.  That leads to M = (1 + (.05 + .04 + .1)) * 1.06 = 1.261.  However, with the glyph, regrowth heals for 20% more if the target has regrowth.  As we already assumed the best case for Nourish, let’s do so for regrowth as well, which means that M = 1.473.

base = 2364

coeff = .6468

Regrowth’s avg direct heal is 1.473 * (2364 + .6468 * SP) * (1 + .95 * crit) = (3482.2 + .952 * SP) * (1 + .95 * crit)

From the above, we see that glyphed Nourish, in the best case, will, with 0 stats, be inferior to glyphed regrowth in the best case.  However, do to higher scaling coefficients, Nourish will eventually pull ahead.  Since the critical hit component is the same for both spells, we’ll ignore that in finding the SP at which Nourish overcomes Regrowth:

3482.2 + .952 * SP = 3408.6 + 1.107 * SP

73.6 = .155 * SP

SP = 474.84

So for any resto druid, Nourish will beat out Regrowth in healing output at any reasonable gear level.  Remember, though, that this is in the absolute best case that you have all 4 major hots on the target.  Having fewer increases the SP needed for Nourish to catch up.  While the base coefficient on Nourish is slightly higher than Regrowth’s, Nourish doesn’t benefit from Genesis.  That implies that, first, that when no HoTs are on the target, Nourish’s heal will be strictly inferior to Regrowth’s.

We have so far not accounted for the Regrowth HoT.  Let’s do that now.

Let’s first look at a single tick of regrowth:

Healing per tick = M * (base + coeff * SP)

base = 111.7

coeff = .2256

M is a bit interesting.  According to wowwiki, “The Regrowth Glyph increases both the Direct Heal and the HoT by 20% if there was already a regrowth HoT on the target when casted.”  That implies that the HoT receives the  same M as the direct heal in both cases.  In the best case, then, M = 1.473, or M = 1.261 if no HoT was present.

That gives a best case per tick healing value of:

1.473 * (111.7 + .2256 * SP) = 164.53 + .3323 * SP

In order to assess how this impacts Regrowth’s overall healing, we need to examine how regrowth might be used.  The perhaps worst case scenario is casting regrowth on a target on whom it hasn’t been cast before.  That is, let’s assume a target who is newly in need of healing and completely lacks for any of your HoTs.  We know that in this case, Regrowth is strictly superior to Nourish in terms of absolute healing.  In order to provide the advantage to Nourish, we would need to first supply a HoT, such as rejuvenation.  Having that in place would tend to put Nourish ahead of Regrowth, in the case that Regrowth is not present.  We’re ignoring, however, the HoT component of Regrowth in that case, and that needs to be watched.  In a situation of heavy raid damage, that HoT component may just be worth taking the time to cast Regrowth.  Consider that, talented, that HoT lasts for a full 27 seconds.

Using the equation above, we know the regrowth HoT will heal for

1.261 * (111.7 + .2256 * SP) = 140.85 + .284 * SP per tick if regrowth is not present.  That amounts to 46.95 + .095 * SP hps.  While that doesn’t compare to nourish or regrowth spam, it is essentially free.  That is, Regrowth provides a Nourish level heal, though not quite the HPS, and applies this additional buffer.

I think examination of HPS is probably warranted at this point.  We know that the nominal value of Nourish exceeds Regrowth in the best case, and that it has a faster cast time.  That implies that, in the best case, Nourish is naively the highest HPS cast.  Additionally, it is cheaper than Regrowth (even accounting for the ToL reduction).  If you are simply spam-casting a single healing spell, once hots are refreshed, Nourish is hands down the best choice for throughput.  However, what about the case where a single tick of Regrowth is allowed to occur before it is recast?  This is the situation where the spell is used as a semi-irregular top-off heal.  For instance, you cast all your HoTs on the OT and then look elsewhere.  Every once in a while you recast HoTs, stack LB, and top off their health.  Should you use Nourish or Regrowth in this case?

First, total healing throughput is less of a concern…that is, cast time is not an issue, since this isn’t repeated casting and both casts finish in the allotted time.  Rather, this is a matter of total healing done.  To find regrowth’s avg heal, considering direct heal + 1 tick, we simply add the two together:

(3482.2 + .952 * SP) * (1 + .95 * crit) + 164.53 + .3323 * SP

We can then compare to Nourish.  Since we’re basically calling this a best case scenario, we’ll assume Nourish with all HoTs:

(3408.6 + 1.107 * SP) * (1 + .95 * crit)

What falls out of this is that critical strike chance plays the role of determining which is the better choice.  In the case where crit is 0, Regrowth is superior nominal healing: it’s scaling from SP will be strictly superior, and it will have an advantage in base amount healed.  Beyond 0% crit, the coefficient on Nourish’s SP component will need to be greater than the direct heal + tick coefficient for Regrowth at the same crit value.  To find that point, we can ignore constant values (the base healing value for each) and assume SP is 1.  That leaves us strictly with a comparison of coefficients:

.952 * (1 + .95 * crit) + .3323 = 1.107 * (1 + .95 * crit)

.952 + .9044 * crit + .3323 = 1.107 + 1.051 * crit

1.284 + .9044 * crit = 1.107 + 1.051 * crit

.177 = .1466 * crit

crit = 1.207

So, at a critical strike chance of 120%, Nourish will begin to scale faster with SP than Regrowth.  As this is an impossible number to achieve, in the event that regrowth exists on the target and you will be able to allow it to tick at least once before you would either cast regrowth or nourish, casting regrowth is always superior.  The difference should grow even greater in the case that you do not have WG on the target.

Assuming that you have both the regrowth and the nourish glyph, there exist two potential spaces where Nourish is the better cast option compared to regrowth: in the case where the Regrowth glyph does not apply, i.e. Regrowth is not on the target, Nourish potentially a better choice, particularly when the target needs additional health as rapidly as possible.  The other case is when all possible HoTs are on the target and they need maximum additional throughput from you.  In all cases between these two extremes, regrowth is the better option.

Keep in mind that this implies that if you are casting Rejuvenation on everyone, perhaps to generate the revitalize proc, Nourishing a target with Rejuvenation but no Regrowth is almost definitely better.  If the target is not taking sufficient damage to warrant anything more than rejuv and simply needs topped off, a regrowth will be slower, less efficient, and substantial overkill compared to Nourish.

Of course, if that is the case, a lifebloom may be a better alternative than Nourish, depending on the state of their health and your prediction of incoming damage.

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Can you hear the pitchforks being put away and the torches being doused?

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