Setting Phasers to Maximum and the CAPM

IRL Tony

This is a high-level article on the Capital Asset Pricing Model (CAPM) and Market Portfolio from Financial Analysis and how they come into play with the upcoming Warmachine World Team Championship.

I recently made my way down to Houston.  A very close friend moved from Chicago to the Lone Star State.  The trip was as much of a vacation as it was a means of offering him congratulations.  When I scheduled the trip, I promptly informed him that he’ll have access to one of the Country’s best Warmachine and Hordes metas on a routine basis.  Needless to say, the first stop after I arrived was Asgard Games. 

The Road to War guys (and then some) were a blast.  Nik, Chilly, Billy and Will are tremendously welcoming gamers and their community shows for it.

We came.  We saw.  We rolled dice.  We had our asses handed to us.  All in all it was a great time. Although, across the evening I let slip a long standing grudge that I have had with the RtW podcast.  You see, some grievances can lie dormant and fester.  The hatred building inside of me was hitting a breaking point and I really needed to make sure it was dealt with in an appropriate manner.

The end of every RtW podcast seems to end with pie; delicious, delicious pie.  Now, if I were gaming with them or worked in a bakery this wouldn’t be so bad.  Unfortunately, I’m a lame grown-up that listens to this podcast on a thoroughly pie-less commute.  Each reference to pie grates me like salt rubbed into wounds on my soul.  To bury the hatchet on my ever-mounting contempt, I insisted on a post-gaming pie (and then margarita, because why not?).Setting Phasers1

Trust me… I’m going somewhere with this…

Houston’s crème de la crème of pie joints, The House of Pies is just down the road from AsgardFifty-four different pies to subdue my aching pie-thirst, I was in heaven.  Texans go big with everything and this was no exception.  I watched my buddy (Karl) eat a Monte Cristo (deep-fried sandwich) with jam, a slice of blue-berry pie, ice cream and fries.  I on the other hand was a purest.  Pie only.  Coconut-cream and Strawberry Rhubarb.  It was a celebration of everything American.  We take things to the limit.  We go to the edge.  We test boundaries, maybe foolishly so, but damn it we do it!  Maybe all that food wasn’t the best idea.  Maybe Karl looked like he was crying half-way through the meal, who cares?  You only live once.

In the wake of our pie coma, conversations about the upcoming World Team Championship (WTC) began to bubble.  It was at this point that Manny Menchaca professed to the group “America takes skew-lists.  I’m telling you.  That’s going to be an advantage in the WTC” and after thinking through the implications, I’ve got to tell you.  He’s absolutely right.

The skew list feels American at its essence.  It’s all about taking something to the limit, sometimes irrationally so.  Americans love that.  We set phasers to maximum.  We super-size our meals.  Of course we want as many Doomreavers as we can fit on the table.  Who cares?  Let’s roll some dice!  It makes total sense that Americans skew.

The interaction of list pairing at the WTC has a few consequences to it.  One of which is the root of why I think Manny is such a brilliant man.  To show you my reasoning, I need to introduce you to a little Finance, the Capital Asset Pricing Model and the market portfolio.

I’m going to assume you’re familiar with stocks.  You’re an adult and you have Google if you’re not.  Most stocks are priced on the concept of risk versus reward.  If the underlying company or asset is going to make money, FOR SURE, then there is very little risk.  As a result, the expected return on their stock doesn’t need to be as high.  The stock doesn’t need to reward you for holding risk because it’s a ‘sure thing’.  On the flip side, if a stock or asset is seriously unlikely to payout, then they have to pay you more.  The expected return needs to be higher to compensate you for bearing that risk.  You are being paid more IF it does pay out as a reward to compensate you for tolerating the likihood of it not paying out.

One formula that quantifies this relationship is the Capital Asset Pricing Model (CAPM). 

Setting Phasers2

Now, most assets have risk and risk can be defined in two ways; systemic and idiosyncratic.  Systemic risk applies to everyone.  You can’t get rid of it by diversifying.  It’s just there.  Think of Haley2 or Denny2.  It just sucks to face them.  Everyone hates it.  Some hate it more than others, but still it’s bad for everybody.  That’s kind of like systemic risk.  Idiosyncratic risk applies only to the stock or asset uniquely.  By holding another asset that’s different you can mitigate (or diversify) this risk away.  This is like protecting your primary list with a smart secondary pairing.  My Caine2 list is for cracking armor and it’s not too strong on scenario.  My second list is going to be Haley2 to make up for that.  That pairing reduces my overall “risk”.  It’s diversified by selecting assets (lists) that are different and make up for one another’s weaknesses (risks).

Now we need some pictures.  So you take all of the stocks in the world and throw then on to a graph (and even throw in partial blends and mixes called portfolios) you’ll get something like this.

Setting Phasers3

Everything on the upper most portion of the grid is worth investing in because at that particular risk-level, it’s the maximum pay-out you’ll ever get.  Bottom portions of the curve are useless.  At that level of risk there is clearly something with better return right above it.  The upper edge of this shape is called the Efficient Frontier.  Once again, the Efficient Frontier marks the maximum expected return you can get for any designated level of risk.

Now, let’s take it a step further.  You don’t just want the maximum payout at a given risk level.  You want the maximum payout PER unit of risk.  A little calculus will find this best ratio line called the Market Portfolio.  The line extends from the return of a risk-free asset (commonly 30-90 day US Treasury Bills) and intersects the Efficient Frontier at just one point.  Any portfolio (grouping of assets) along this line has the maximum payout per unit of risk.  The Market Portfolio is a combination of the most efficient expected return per unit of risk and the risk-asset.  Movements along this line are still equivalent in payout/risk ratio, they’re just all about risk-preference.  As you move toward the risk-free asset you’re less risky and vice versa.

Setting Phasers4

An example of risk-preference is the following.  Do you want $0.50 or would you like to flip a coin for a chance at a dollar?  They’re equivalent in expected payout.  One has a 100% chance (sure thing) of getting $0.50 so the expected payout is… you guessed it, $0.50.  The other has a 50% chance of getting $1.00, so the expected payout is $0.50.  One has more variance (risk) but otherwise the expected payouts are identical.  Risk-preference comes down to your personal preference and tolerance for variability.

As I promised, the long awaited chat about how in the hell this applies to gaming.  Each team is bringing five players with different lists.  This is a portfolio.  As I alluded to prior, if we’re using this financial metaphor we want to generate a portfolio that’s well diversified such that it only faces systemic risk (the usual bad match-up’s), with the maximum expected return (likelihood to win) per unit of risk.

To create this portfolio, you don’t do it with a bunch of medium expected return stocks with low idiosyncratic risk (balanced lists).  You do it with stocks that have INTENSELY high expected returns (skew lists) with idiosyncratic risk (list weaknesses) that can be diversified away through sound portfolio diversification (list match-up and team construction).

Manny was absolutely right.  Skew lists are an advantage in this format if they’re intelligently executed.  Your team is playing a portfolio.  More so than in Steamroller.  More so than in Masters.  This format in particular will cast this simple fact to light.

Good luck to all of the gamers headed to the WTC.  We all wait with baited breath to net-deck the hell out of your lists and become figurative giants in our local metas.

The more you know… (hum the little diddy in your head when you read this last part)

Author: Tmage

I'm a gaming and math enthusiast. I find games that balance strategic interaction with economic principles (delayed option, resource control, etc.) are some of the most rewarding for me as a player. I concentrated in Finance, Analytic Consulting, Decision Sciences and Management Strategy while getting my MBA at Kellogg (Northwestern University) and majored in Chemical Engineering during my undergrad at University of Illinois. I view gaming through this lens and share my perspective via periodic articles. Thanks for reading!

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