Regression and Why Morghoul is Dying on the Inside.

IRL Tony

This is a high-level article on the model point costing and linear regression analysis.  I’m going to walk you through how regression analysis works (and trust me, it’s REALLY not that complicated) and then how it applies to the costing of models in Warmachine and Hordes.  Additionally, I’m going to cast light on to a potential root-cause for a common phenomena in the game that’s often answered by:  RTFC (read the frakking card) or “It’s you, not the list”.

Let’s take a trip down memory lane.

High-school math.  Think about your formula for a slope;

Y = m*X+b

This is a one-dimensional relationship.  Y depends on the single dimension: X.  M is the slope of that relationship and b is the y-intercept (where X = 0).

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Relationships can hold more than one dimension and dependant variables like Y and can be built by any number of independent X’s.

I like food (specifically pie) so let’s use a metaphor.  Let Y equal how badly I want pie.  What else affects how badly I want pie?  How long has it been since I’ve eaten?  Have I been drinking? How delicious is the promised pie?  Have I been working out?  All of these are valid factors that impact my desire for pie.  So let’s see that written as a formula;

Y = a1X1 + a2X2 + a­3X3 +a4X4+ b
Y = How badly I want pie
X1 = How long it’s been since I’ve eaten
X2 = Deliciousness of promised pie
X3 = Have I worked out recently?
X4 = Have I been drinking?

Ok.  So I see now that each of those elements has been worked into the formula.  Let’s define those other elements.

Each for the lower case a’s is a coefficient to the corresponding variable.  Those coefficients are going to control the direction (positive or negative) and magnitude of the underlying independent variable on the dependent variable.  That’s boring math talk to say it’s weighting the affect appropriately.

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Keeping with our example here, a4 is going to be gigantic.  If I’ve been drinking, I’m going to annihilate baked goods.  Conversely you could argue that a2 is probably pretty low.  I sound like a pretty indiscriminate pie-eater.  As a result, this variable would have a really small impact on my overall desire.  Pecan, Strawberry Rhubarb, Bayou Goo, Apple… who cares?  I want pie.  If I’m ABSOLUTELY indifferent to deliciousness a2 would equal zero.

Lastly, what does b mean?  b is the level of my desire for pie if all of the X values were zero.  If I’ve just eaten pie, if the promised pie is NOT delicious, if I haven’t worked out and if I’m NOT drunk, b represents how badly I’d still want pie. (probably still a little bit)  🙂

So.  That’s the math we’re going to talk about.  Linear regression is an incredibly useful tool.  We used it above to understand the effect of different factors by deconstructing an independent variable into the elements that impact it.  That’s I’ve done here in the pie example.   It has two additional applications that are commonly used in the business sector; bench marking and predictive modeling.

Under the bench marking example you build an equation and then program in all the X’s for a single point in that data and then compare the output Y from the equation and the actual Y that occurred.  This is all about comparing dissimilar assets in a fair light by boiling each of them down to their basest elements and comparing the elements rather than the whole.

Predictive modeling is similar as well.  We’re hanging out at a convention.  I went for a run with Chilly and JVM.  I haven’t eaten all day because I’ve been gaming.  I’m fully-torqued.  You could use the above equation to predict how badly I want pie!  (It’s A LOT)

I love pie.  I also love Pi.  I don’t love Pi as much as pie.

Ok.  No more pie talk.

Models in the game of Warmachine and Hordes are balanced using point cost.  Using regression analysis, that point cost could be deconstructed into descriptive elements and each descriptive element could be quantified.  Here is a short list of elements;

  1. MAT/RAT, POW, ARM
  2. HP
  3. # of Initials
  4. MAT/RAT, POW, ARM Buff
  5. MAT/RAT, POW, ARM Debuff
  6. Range Weapon
  7. Threat extension
  8. Out of Activation Movement
  9. Tough
  10. Faction

With enough data you could pretty easily calculate the point cost of each of these factors and know why models are valued the way they are.

I’d been happy to run the analysis if anyone wants to crank through a spreadsheet for me and define the 500+ variables that exist.  It’s been a dream project for a while, but I’ve always baulked at creating the data set.

Step-one was linear regression.  Step-two was how point cost could be deconstructed using linear regression.  Now I want to take you on to step-three;  How linear regression can be used to explain both the RTFC and “it’s you not the list” phenomena.

Both of these little gripes apply to players that stagnate and blame external factors.  Cognitive dissonance aside, there is a very good reason that these players are struggling.

If every element of a model has a point value, each element of a model that you forget to utilize does as well.  If you’re constantly forgetting that Ol’ Rowdy has Tremor and Counter Charge, you’re effectively only getting 8 points of work out of a jack that you purchased for 9 points.

Each element you forget costs is like playing down a point (or fraction of a point) and while it doesn’t seem a lot at first glance, they add up.  What are the three auras for the Kriel Stone?  Did you forget Duelist?  What about Side-step?  You know that model had Sprint right?  Did you remember that Shifting Stones can heal?  Do you know ALL of the details on the back of Morghoul’s card?Regression Morghoul 2

Every element that you neglect is a handicap.  It’s as if a fraction of that model is already dead.  If you start a game down 10% of your points due to forgetfulness, it’s like taking a premature alpha-strike for no good reason.

Why does the drum up difficulty?

Many new players bounce around factions, net-deck or have difficulty winning and seasoned veterans respond with “play what you know best”.

Another way to say that is “make sure you’re getting your full 50 points”.  If you know your army and you’re using every advantage the cards are giving you, then you’ll optimize chances of success.  Now you can see how Faction ADD, forgetfulness and general rule apathy have a large quantifiable effect on your results in a tournament setting.

One more example:  Let’s say I’m a Cygnar player.  I’m solid with Seige and Stryker2.  I have had moderate success, but I see Keith just killing it with Haley and Caine2 so I swap.  Would that lead to instant success?  Absolutely not.

The power of Keith’s lists would only help me if I knew how to use all of the pieces that comprised them.  It’s actually even a little more complicated than that because there are intense model inter-dependencies that I’d have to be familiar with.  Until I reach that level of knowledge through practice, I’d be playing down a large percentage of points and losing while I go through the learning process.

Start with your full 50.

It’s a simple but impactful statement.  Start with your full 50.  Don’t kill any part of your own force prior to the first dice roll.  Because knowing is half the battle… (hum the little diddy in your head when you read this last part)Regression Morghoul 3

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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