Undercosted 4th Mass Argument: Supply and Demand Analogy

[mccombju]

There is some discussion going on in the Book of the 4th Mass Line as to whether this squad is undercosted.

Rather than spam the book with what will be a lengthy post, I have created a new thread.

I know the topic of undercosted units has been discussed before, but I am going to briefly provide a justification for how you might establish that a unit is undercosted, using the concept of economic supply and demand.

This train of thought was inspired by the following comment:

Originally Posted by Dredd Stev

The fact that some (for the sake of argument lets say half) would be willing to pay more doesn't really mean that they are undercosted.

When people are willing to pay more, in economic theory, then the good or service in question is undercosted (other stipulations must be met before a good or service is actually undercosted - see below). If you assume that people would be willing to pay more points for the 4th Mass Line, then this is a basis to argue that they are undercosted.

In economic theory, something is undercosted when demand exceeds supply, for a given price. More people are willing to pay for an item than there is sufficient supply to accomodate. In the marketplace, this is characterized by shortages, and this scenario is referred to as Excess Demand.

Demand > Supply

Conversely, Equilibrium occurs when only the number of people who are actually willing to pay are able to purchase the item in question, because there is sufficient (not insufficient or excess) supply. That is, when demand equals supply.

Demand = Supply

The following figure illustrates these concepts.



Situations of excess demand are created artificially by the advent of (import) quotas and price ceilings on products. When these artificial instruments are removed, the quantity supplied increases, as does the price charged. The increase in price and quantity supplied occurs until the equilibrium point is reached.

Obviously, the prinicples of supply and demand don't apply literally to Heroscape. However, the concept of A+ units underscores the idea that you get more bang for your buck (points-wise) from certain units, in a tournament kill-em-all 24 hex starting zone setting on standard BoV maps.

Allow me to postulate the following:

In an entirely theoretical and ideal Heroscape world, Equilibrium would occur when any given unit could operate in an army where that army would be just as likely as any other army to win a tournament (on standard kill-em-all 24 hex starting zone BoV maps).

That is not to say that all units would be equal, just that all armies would have an equal chance of winning. The tournament metagame would represent a paper-rock-scissors environment where certain armies would be favoured in certain matchups, but no army, on the whole, would have any advantage over the others.

e.g.

Army Type 1 - 20% tournament win rate
Army Type 2 - 20% tournament win rate
Army Type 3 - 20% tournament win rate
Army Type 4 - 20% tournament win rate
Army Type 5 - 20% tournament win rate

True game balance is not impossible, but it is extremely difficult to achieve. Fans of Starcraft claim that Starcraft Broodwar is a ~perfectly balanced game and one where skill decides matchups (thanks to the balancing efforts of beta testing, countless iterations, constant patches, etc. by Blizzard). Thus, for the sake of argument, you could say that the three races in Starcraft are in equilibrium.

Heroscape is a great game, but the dominance of certain units and armies (e.g. A+ units) suggests that it is not at an equilibrium balance point.

Therefore, I will use the example of the 4th Mass Line to suggest how artificial and theoretical point adjustments could be used to drive the metagame towards equilibrium.

The argument that I present is:

If you can construct an army that *would* still be able to win a highly competitive tournament, despite an increase in the point cost of its units (and provided that other unit substitutions are made), then you might have the basis for arguing that a unit is under-costed.

I don't think this claim is too outlandish (or original for that matter).

Consider the following army:

Charos - 210
4th Mass Line x4 - 280
------------------------
490 Points, 18 Hexes

I don't think it is too far fetched to suggest that this army could win a 500 point tournament (on standard kill-em-all 24 hex starting zone BoV maps). In fact, Spider_Poison went 5-0 at Tree Town Open II. Sixteen valiant (3D) 4th Mass wielding four attacks of 2A, 3A, or 4A per OM at Range 6 is powerful. Charos provides the durability and attack power to penetrate the defenses of the heroes that threaten the 4th Mass (i.e. Q9). Thus, this army has very few bad matchups and has an answer for practically any army it faces.

Now, consider the following army, where the 4th Mass Line's point total has been adjusted from 70 points/squad to the hypothetical 80 points/squad.

Sgt. Drake (SotM) - 170
4th Mass Line x4 - 320
------------------------
490 Points, 17 Hexes

Could this army still win a tournament? The 4th Mass still retain their sixteen figures with valiant defense (3D) and four attacks of 2A, 3A, or 4A per OM at Range 6. This time around the can opener has changed. Is Sgt. Drake (SotM) up to the task of penetrating the defenses of the heroes that threaten the 4th Mass (i.e. Q9)? I would argue that yes Sgt. Drake (SotM) is, indeed, up to the task.

MattserTruckRally finished in the top 16 at GenCon in 2008 with

Sgt. Drake (SotM) - 170
4th Mass x5 - 350
---------------------------
520 Points, 21 Hexes

However, what we can see from the above army composition, is that with each incremental 10 point increase in the point cost of the 4th Mass Line, their tournament viability decreases relative to their substitutes (e.g. Stingers, 10th Reg.).

The last army I will suggest consists of 4th Mass Line whose point totals have been adjusted from 70 points/squad to a hypothetical 90 points/squad.

Sgt. Drake (RotV) - 110
Eldgrim - 30
4th Mass Line x4 - 360
------------------------
500 Points, 18 Hexes

Again, the 4th retain their sixteen figures with valiant defense (3D) and four attacks of 2A, 3A, or 4A per OM at Range 6. However, the can opener of Sgt. Drake (RotV) is considerably weaker than Sgt. Drake (SotM) or Charos. Obviously, the viability of the 4th Mass Line army is decreasing, since fewer viable valiant cleanup heroes are available to the 4th Mass as their point cost increases.

Through this example, I have illustrated how marginally increasing a unit's point cost can decrease its tournament viability, based on the availability of superior (or comparable) substitutes.

Thus, I have been providing a basis for suggesting that increases in the cost of the 4th Mass would drive Heroscape towards a metagame equilibrium, under the standard kill-em-all 24 hex starting zone BoV map enviornment.

Excess Demand, in the context of Heroscape army creation, is when a unit is more viable in a standard tournament setting based on its abilities relative to its undercosted point requirement and lack of comparably competitive substitutes.

Demand, in the context of Heroscape army creation, is a function of that unit's ability to contribute successfully to a tournament winning army as a main component of that army.

Supply, in the context of Heroscape army creation, is a product of what you can "buy" to fill out an army and complement it with supporting figures, synergies, etc.

Increases in the cost of the squads in question coincide with unfavourable shifts in the supply curve, as shown in the figure below.



In the above figure, the red excess demand line represents a potential supply curve shift for the 4th Mass Line. In reality, since figure availability is not the limiting factor in army construction (as might be the case in a collectible game), there is no shortage or excess demand for the 4th Mass in potential armies. Instead, the 4th Mass flourish as undercosted units (hence the A+ ranking).

[Onacara]

I didnt read it all but the use of graphs is always a thumbsup in my book.

[Devil's Advocate]

Great post, I totally agree. I think at even 90 points they would at worst be a B+, probably closer to an A- or so

[GreenLanturn]

I'm lost as to where your supply curve comes from. Is it the supply in my box of figures or is it the supply that all the factories could produce? Or am I missing something more important?

Your progression of armies was very well done, and I think it makes a point.

[padlock]

Interesting post. One house rule I was thinking of trying out with my friends was to vary unit costs based on popularity. My plan was to keep a detailed log of which units get used during our gaming sessions, and then, maybe once a month or so, adjust the price of the units using a simple formula. ie:

- Any units not choosen at all during the month would have their cost decreased by 5 points

- Top X units choosen in the month would have their cost increased by 5 points

- All others stay the same

The adjustments would be cumulative month after month.

My thinking is that, eventually, after several months, we'd reach a state of equilibrium where the units reach their "correct" cost, at least as it pertains to how my group perceives them. I think it would be interesting to see how those costs differs from the official values.

[Killometer]

So to boil your post down to it essence, mccombju, are you suggesting that tourney organizers look at popularity and success of units and add a premium to certain units point cost and, inversely, deduct from the point costs of others?

Obviously Hasbro/WotC would be reluctant, to say the least, about officially recosting all the figures, as they are not going to replace everyones army cards for them (although based off DnD's extensive errata they have no qualms about completely restructuring things after they have been released).

[Devil's Advocate]

Padlock there isn an easy way to do that which would be fun to use in Tournaments.

-If a Unit is selected then then next time it costs +10 more. If I select Rats 1 game then the next they are 50, if they get picked the enxt game then they are 60, etc

-If a Unit is not selected then its cost -5 less. If nobody selects Sudema then the next game she is 135, etc

[Dredd Stev]

in a tournament kill-em-all 24 hex starting zone setting on standard BoV maps.

With this basic assumption in mind I have to say that I totally agree with your analysis. Well thought out, well pout together post man(woman?). I am very impressed with the economic analogy and the use of graphics (I'm a visual learner!).

Dreddrep on the way!

[Clarissimus]

I'd love to join a tournament that did that . . . or for that matter a tourney that had some kind of drafting involved. It would be tricky to work out the logistics but I think it's certainly doable.

[Devil's Advocate]

The other fascinating way for a Tournament would be to have everyone prior to the Tournament PM their armies to the organizer and assess penaties or reward bonuses based on popularity.

For example for every person over 3 that selects a unit its cost goes up 10. If 6 people choose Deathreavers then suddenly all those people's rats cost 70 points per squad

Similarly if only 1 person selects a unit they get an additional 10 or 20 points they can use to add to their army

[GreenLanturn]

Originally Posted by Devil's Advocate

The other fascinating way for a Tournament would be to have everyone prior to the Tournament PM their armies to the organizer and assess penaties or reward bonuses based on popularity.

For example for every person over 3 that selects a unit its cost goes up 10. If 6 people choose Deathreavers then suddenly all those people's rats cost 70 points per squad

Similarly if only 1 person selects a unit they get an additional 10 or 20 points they can use to add to their army

That is definitely an interesting twist to a tournament, but how many rounds of army drafting would you do? Because after everyone send their armies in at least one person will be over points allowed, then after round 2 people may change armies completely reshifting someone else over the cap... etc... etc

The only real way to do this sort of thing would be as Padlock suggests.

[Dredd Stev]

There are several idea similar to this kicking around the forums. Its a very interesting idea, but very hard to properly organize and realize. It would require an amazing amount of time and co-ordination by the tourney host.