As Phil Cape outlined in a recent TCG article, one of the most important costs of running any particular card in a deck is the card that gets taken out for it. Maximization these hidden costs is often what distinguishes the top performer when comparing two similar decks that only differ on “tech”. While nearly all players know of the concept, most of us do not spend more time thinking on it than using soft comparisons or intuition. The purpose of this first Tick by Tick article is to summarize this concept of opportunity cost and demonstrate that it not only permeates every facet of the WoW Minis game, but that understanding it is vital to being a successful team builder and player.

Opportunity cost is defined as an expression of the relationship between scarcity and choice. The most explicitly overt application of opportunity cost lies in building a team. When you choose to play a faction, model, or ABC, you are clearly giving up the ability to play something else. However, building a strong team in WoW Minis is subtle in its complexity. Unlike many miniature games where you try to min/max your team within a points and/or force organization, WoW Minis allows you free reign on the points of your models, restricting you only by the model count itself. Combine this take on team construction with the fact that all models (save legendaries) are worth the same VPs when killed and you have a game where opportunity cost is explicitly measurable.

“Why is Celenias Firemane a bad figure?”

This question was posed on the forums not too long ago in a “Swift-esque” post about the banning of Celenias because of how bad she is. What became clear by pages 4+ of the discussion was that players clearly understood Celenias from a mechanical standpoint, as they were all able to support their ideas on ways to make her better or why she seems balanced, pound for pound. The broader issue with our apparently unlovable blood elf is what you give up to run her rather than any particular weakness on her part.

Looking at a model that is widely considered one of, if not the best currently out: Haruka Skycaller, you can see that there is an implied expectation with Haruka that she will be able to score at least 8 VPs in a game. Her above average dice to tick ratio and critical effect reasonably put her at 16-24 attack dice rolled in the first 10 tick cycle. Assuming 2/2 armor/resist models, you’re looking at getting approximately 10 to 14 damage through over that same 10 tick cycle. For ease of calculation, let’s say a typical game lasts 20 ticks. 20+ damage is enough to kill two or more models over the course of a game. Finally, Haruka’s unusually high defensive abilities allow her to get at least two of the possible four VPs from positioning on a single objective map and assuming your nameless enemy has the same offensive punch as Haruka (16-24) dice, you’re looking at approximately 8-11 damage getting through giving up only one kill.

Thus, after all is said and done, Haruka’s expected VP gain is 6+ (10+ earned minus 4 given up) while her expected VP value is 2+ (10+ earned minus her honor cost of 8 although she’ll probably get 3 kills making 6 likely as well) assuming 2/2 defense enemy models with Haruka level offense in a 20 tick game. Using the same assumptions on a Celenias reveals that she will get through 10-11 damage for one kill while she will be taking 22+ damage over a 20 tick game. Celenias’ “kiting factor” could half that damage and she would still be killed twice in a game. This puts her expected VP gain at -4 (-12 without kiting) while her expected VP value is 0 (1 kill at 4 honor). So while you could say that Celenias will typically break even or make up for her sub par value with synergies, you are actually giving up 10+ expected VPs to save 4 honor when you play her instead of Haruka. Thus, your opportunity cost of running Celenias is 6+ VP. Put it another way, your team that runs Celenias might as well be playing with 6 extra honor for no benefit.

All of those calculations are generally too in depth for something that is as conceptually obvious as Celenias Firemane. However, it is still an excellent example to refer to when comparing models that are either functionally similar or when determining whether one model’s offense is worth another model’s defense. If I were to do this analysis for a large swath of models, I would definitely adjust the assumptions to fit an expected Meta. Obviously the calculation doesn’t cover even most of the facets of the game, but it does give you a good baseline with which to compare models. Ultimately, it is the decisions during the play of the game that will determine the outcome, but through some very methodical analysis we can objectively measure the quality of a model in a given Meta.

In Part II of this discussion I will go over opportunity costs that are present during game play. Thank you very much for reading!

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My top 8 appearances are limited to bringing good players water and crabs.

WoW! This was a really amazing piece of writing here, congrats. I agree in your calculations of oppurtunity cost for each figure. Oddly enough I am taking microeconomics in college right now so the oppurtunity cost is something I have been studying a lot lately lol. Anyway cant wait for part 2.

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The difference between a democracy and a dictatorship is that in a democracy you vote first and take orders later; in a dictatorship you don't have to waste your time voting.
- Charles Bukowski

I had to give you the benefit of the doubt here. It took me about 4 seperate readings to figure out what on earth you were getting at, because the calculations and additions in your article are far from intuitive to me. to me. others may love the hell out of it.

It's poor to give your examples for opportunity cost between a melee figure with magic attacks and high defense to a low offense ranged attacker. I think you'd have a stronger argument measuring Celeneas to Azarak and Ona.  I like her over Azarak but prefer Ona over both. giving them all the same ABCs of Hunters Mark and Arcane Shot, in a generic game, Ona attacks for 6 dice with a reroll against a target for 3 ticks, and she can make that attack magical once per round, if not moreso from crits.  She has more dice per attack and has a better chance of getting the crit than either of the other two hunters a Horde player can choose from.  For double the honor cost of Celeneas, Ona packs double the wallop and is even better at kiting if she crits.  Hands down, she's worth the cost several times over compared to the other hunters if your team needs a hunter. I'll leave the specific breakdown to analytical minds like yours and just go with my gut, my intuition, and my raw understanding of the game over 20 ticks, without the number crunching or breaking out any caluclations.

So, other than all that, great article.

Cheers!

-teh Sig

 

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Christopher "Siggie teh Sig" Nugent
Find me on facebook with liiamealone @ yahoo dot com
email me at teh_Sig @yahoo dot com

not to derail the thread here, but I take Az over Ona everytime.  I have never really used either of there secondary abilites (well once I killed a totem with raptor strike) so I call that a wash.  For armor I'll take 3-1-7 over 2-1-8, its a close call, but I like 3 armor.  Then their attacks are the same except for Ona throws 1 more die.  So you are getting 1 more die at the cost of 3 honor.  I like Az.

To the OP (I have forgoten your name right now, my bad), I would be interested in your oppurtunity cost analysis of these 2 characters, if you ever get to it.

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Master Tactician and Rexxar...

Actually, the point is that it doesn't matter what the figure is thematically, which is to say, ranged vs melee or magic vs physical, opportunity cost is merely a measure of trade in terms of overall utility. It isn't more specific than that. That's where your gut, intuition, and raw understanding of the game will make the distinctions and the combinations. This math is just there for the evaluation of two models.

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My top 8 appearances are limited to bringing good players water and crabs.

1913468:

This math is just there for the evaluation of two models.

Ah. then I think the math is counting apples to oranges, but the wal-mar shopper wanted bananas.

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Christopher "Siggie teh Sig" Nugent
Find me on facebook with liiamealone @ yahoo dot com
email me at teh_Sig @yahoo dot com

I like what is being addressed here in this thread. The problem is, to truly analyze figures in the manner the OP is suggesting requires a MUCH more complicated approach because while in one category a figure may be much stronger than another, it depends on what purpose a fig plays in a team.

I think what is being broken down is generally what most of us summarize in our heads. When done correctly, what he is showing is a systematic approach of what we jump to conclusions about. When we do it wrong, it hints at where we went wrong.

I think that in most games, you can certainly scientifically justify including or not including cards/figures. I think with WoW minis that theres so many aspects of the game, and with the lack of a real dead set resource count besides " you get 3 figs " that it becomes extremely complicated. To fully flush out the theory behind all of this would be a very indepth series of articles.

For reference, of the three horde hunters, I like Az the most, so far. I do like Ona's passive ability though, you just need to find the right figures to use with her. It lets melee figures close the game, but all of the powerful figures who could benefit from it are very high honor and do little to compensate for her inflated honor cost. I think she is a bit weak in 3 person games, but if you build 4-5-6+ fig games, I think her utility skyrockets. She is likely costed fairly...any less, or too much stronger and she gets too strong in bigger games, but how she is now, shes a bit too timid for an 8 honor fig in 3 man games.

2465615:

I think what is being broken down is generally what most of us summarize in our heads. When done correctly, what he is showing is a systematic approach of what we jump to conclusions about. When we do it wrong, it hints at where we went wrong.

This is exactly the point. For the most part we can make these calculations in our heads intuitively. All I'm showing is a quick and dirty way of doing it quantitatively.

As for the point about too many aspects of the game, having the biggest restriction be on model count actually makes the math easier as far as opportunity cost goes.

For the hunters, using that same set of assumptions in my article, you can see that Ona pushes through ~14-20 damage in a 20 tick game leaving her at 2- kills. Since she likely won't be getting any objective points and she's likely to take 22+ damage totaling 3 deaths. If we halve her damage taken due to a "kiting factor", she sits at 8- earned vs 4+ given up. This puts Ona's expected VP gain at 4- and her expected value at 0-.

Going through the same calcs with Azarak has him pushing through 12-16 damage while taking 20+. Thus he also sits at a worse 4- VP gain with an worse expected value of 0-.

All this said and done means that when you run Azarak instead of Ona, you are gaining only her aspect of the pack for 3 honor. The bigger concern is that his 6 fewer rolled dice over the course of the game puts him at real risk of not getting 2 kills and lowering him to 0+/-1+.

This means that when you run Ona instead of Azarak, You've given up 3 VPs for aspect of the pack and the removal of a significant risk of losing 1 kill. If you value the risk at 2 VPs, then you have to decide if aspect of the pack is worth paying 1 honor for.

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My top 8 appearances are limited to bringing good players water and crabs.

1913468:

2465615:

I think what is being broken down is generally what most of us summarize in our heads. When done correctly, what he is showing is a systematic approach of what we jump to conclusions about. When we do it wrong, it hints at where we went wrong.

This is exactly the point. For the most part we can make these calculations in our heads intuitively. All I'm showing is a quick and dirty way of doing it quantitatively. As for the point about too many aspects of the game, having the biggest restriction be on model count actually makes the math easier as far as opportunity cost goes. For the hunters, using that same set of assumptions in my article, you can see that Ona pushes through ~14-20 damage in a 20 tick game leaving her at 2- kills. Since she likely won't be getting any objective points and she's likely to take 22+ damage totaling 3 deaths. If we halve her damage taken due to a "kiting factor", she sits at 8- earned vs 4+ given up. This puts Ona's expected VP gain at 4- and her expected value at 0-. Going through the same calcs with Azarak has him pushing through 12-16 damage while taking 20+. Thus he also sits at a worse 4- VP gain with an worse expected value of 0-. All this said and done means that when you run Azarak instead of Ona, you are gaining only her aspect of the pack for 3 honor. The bigger concern is that his 6 fewer rolled dice over the course of the game puts him at real risk of not getting 2 kills and lowering him to 0+/-1+. This means that when you run Ona instead of Azarak, You've given up 3 VPs for aspect of the pack and the removal of a significant risk of losing 1 kill. If you value the risk at 2 VPs, then you have to decide if aspect of the pack is worth paying 1 honor for.

You entirely and woefully misunderstand how to calculate hunters. I think I'll skip your future articles.  you seem to have a grasp for the math, but you lake the skill to apply it effectively.

if this was for the contest, good luck. you'll need it, friend.

Cheers!

-teh Sig

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Christopher "Siggie teh Sig" Nugent
Find me on facebook with liiamealone @ yahoo dot com
email me at teh_Sig @yahoo dot com

2465615:

You entirely and woefully misunderstand how to calculate hunters. I think I'll skip your future articles. you seem to have a grasp for the math, but you lake the skill to apply it effectively.

Hey, I appreciate what you're getting at but as I said and will say again, there are a ton of factors that I am deliberately excluding from the calculation that will CLEARLY make up more of their worth than is immediately apparent using the calculation. This is JUST a quantitative means to do a quick and dirty calculation on the cost of using one model over another.

That said, just because you've missed a point reflects more on your own deficiencies than mine. Disagreeing is fine, but what I'm trying to say is that my method does miss the softer side of the game, such as positioning and luck.

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My top 8 appearances are limited to bringing good players water and crabs.

I didnt miss the point roark; I entirely disagreed with it.

Your quick and dirty is neither quick nor accurate.

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Christopher "Siggie teh Sig" Nugent
Find me on facebook with liiamealone @ yahoo dot com
email me at teh_Sig @yahoo dot com

Comparing two figs in the same class, I think your analytical breakdown might be on the right track. The thing is, it's hard to really know what role a mini should have from a single standpoint because you have no idea what your enemy is bringing to the table. Halving a mini's damage taken due to a "kiting factor" is essentially useless if you end up playing a kiting team because she's still likely to take that damage that you factored out. Now what happens if you end up against a team that absorbs damage well or a team that can lock down minis at will. You may end up using your kiter as a baiter and then that throws your calculations all out of whack.

But again, using your analysis strictly from a single view, with minis that all have access to the same ABCs, then you can rack and stack your options accordingly. But until you incorporate the benefits of the ABCs into EVERY calculation related to a mini you can't really compare Haruka to Celenias in this way because Haruka has access to shaman cards and Celenias' has hunter cards. I think this is where raw math really fails and intuition has to take over. Like Siggie said, you're comparing Apples to Oranges.

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What few people fail to understand until the very end is that First Blood is not nearly as important as Last Blood.

Sig, are you sure your vehement assertion that he is wrong is not simply that his method said that Az was a better selection than Ona, and you clearly prefer Ona?

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Master Tactician and Rexxar...

2144941:

Sig, are you sure your vehement assertion that he is wrong is not simply that his method said that Az was a better selection than Ona, and you clearly prefer Ona?

has everything to do with his misapplication of the math he so quickly and filthily applies.

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Christopher "Siggie teh Sig" Nugent
Find me on facebook with liiamealone @ yahoo dot com
email me at teh_Sig @yahoo dot com

I liked the discussion, you have some good points.  The biggest flaw I see in your current analysis method (and you obviously see that it's flawed, I'm just saying this one is more fixable with educated guesses) is that it's against a generic 2/2 armor/resist field, as compared to a metagame analysis of match-ups, i.e. if you're expecting 50% Haruka, 20% Ogres, 10% Warlocks, 10% Murlocks, 10% Miscellaneous, you'd analyze with your method against some 3/3 8 health reroll match-ups with whichever of a 6 for 3 phys or 4 for 2 magic is worse for you (asuming rrs the whole way), then multiply that cost by 50%, repeat with the rest of the expected metagame (with the Misc category being filled w/ your assumed 2/2, or possibly your worst match-up), and reanalyze with regards to your match-ups.  This probably works best when considering the third character to use in two otherwise identical builds, but if you're analyzing entire parties with your method it's hectic no matter what.  Overall, it's a very interesting and useful tool for mathematically analyzing parties against an assumed meta, although, like you said, the fact that it can't incorporate skill or luck will work against it; then again, that's not a party-designer's job, that's a player's job.

Also, I agree with Teh 100% on the Hunter issue.  Az is the best Horde hunter by far, and what I mean when I say "by far" is "by 3 honor".

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"And I thought my jokes were bad!"
Proof of my insanity: here and here.