Purgatus- Mathlete of the Week and Happy Belated Valentine’s Day

Well, I guess there are two completely unrelated topics in my post title……or are there?   Purgatus, will you be my Valentine?  You know what a man who knows his maths does to me. (more…)

Return of the Math!

It has been a while, but I think it’s high time to resurrect the Dick Move Mathlete of the Week Program.  I just stumbled across Zheilt’s blog Custodes and was pretty well blown away by what I found there.  It’s a damn shame, but it looks like he’s been at it for a little over a month now and doesn’t have much of a following yet, in spite of some pretty good content- whore yourself out more.  Join the HoP, we’ll get you some readers

Whoring of the blog network aside, Zheilt appears to have a pretty good grasp on stats and excel and has made some pretty easily readable charts, such as this one showing why melta lances are not really going to be the end of gaming as we know it.  He does similar things for several other topics, so take some time, poke around his site and make sure to follow it if you like what you see- I know I did.  Nice work Zheilt.  I’m looking forward to seeing more of your stuff.

Mathelete of the Week: Sepharine

It’s been a while since we’ve had a mathlete of the week here on Dick Move, but the mathematics community has been very quiet in the 40 Universe lately.  All you kids must not want to talk about how awesome math is during your summer breaks or something.

Sepharine has managed to write a pretty good article about Math for 3++ without really including any math- and for that we salute him.  His post, Mathhammer In the Warhammer Community, stands as a cautionary against over-relying on mathhammer as it will let you down in time.  Keeping with my overarching theme of my love-like* relationship with mathhammer, I couldn’t agree with most of what he’s said.  Hell, he even brings up a topic that I’ve yet to see anywhere else on this subject: Diminishing Returns.  I don’t know if given the small numbers you’ll see in most Warhammer analyses this really comes into play, but it’s interesting to check out.  In practice it looks like when you’re dealing with a handful of guys shooting or saving or what have you, this will really only swing your probabilities around by a few percent, nothing too major.  Now if you’re playing a green tide, this is something you’ll need to pay attention to.

Sepharine promised to come back with some real math later.  I’m looking forward to it something fierce.  I’m waiting for the day that somebody busts out linear regressions to prove something- will you be the first?

P.S. In an unprecedented move I will be back this afternoon for a rant.  Something has gotten me incredibly worked up and I feel I have to say something.  Hint:  it’s BoLS.

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*Kind of like a love-hate relationship, but more just that I really like math but am afraid to commit.

Business 101 or the Whiteness of the Whale

In my recent quasi-Internet fight post “Warfare on the High Accountanseas,” which dealt with the the incoming price increase from GW I may have taken some things for granted in my readership.
This is not meant to be an insult to anybody, but if you’ve never studied economics, accounting, or marketing before, some of what I said may have been slightly confusing. Well a lot of what I said might have been confusing. Understanding business financials is something of a white whale even for those who do it for a living. I will now attempt to give you all a crash course in basic business acumen to help you understand what the hell I was talking about and help you get ahead in life. The more I form my own twisted views of life, the harder it is for me to separate the disciplines of accounting, economics, and marketing from each other. They cross so much of the same territory that it’s barely reasonable to view them as completely separate disciplines. So you’re going to get a taste of all of those. There is one assumption that I can’t avoid, and that is that you have at least a basic understanding of algebra and Cartesian graphing.

Now to get the disclaimer out of the way. Ignoring the class I had yesterday, I haven’t had an economics course in about 11 years. I have tried to research things to fill holes in my own knowledge base were applicable, but take all of this with grain of salt. This will no doubt be a gross oversimplification of the financial strength of GW, but there’s no way I’m digging into this too deeply. This is just a blog after all. I will also be making a few assumptions/outright guesses here and there where no data are available to me or where I am simply trying to demonstrate a point. I’ll do my best to point out that my data are made up when this is case.

Since lots of math may be involved in this (I am this week’s mathelete), it is vitally important to the mission that you be listening to math rock while reading the rest of this.

Ishamael wrote the following in the Accountanseas article, prompting me to undertake this insanity:

I don’t know jack about the proper running of a business, so I found your commentary quite interesting. I know you just got done with finals, but could you give a comprehensive analysis of this price increase? I’ve bitched about it with other people, but we’re a bunch of broke ass college students who don’t know better than to enjoy little plastic men.


It’s like watching a pro teach little kids about their abc’s.

I don’t know that I’d call myself a pro on this subject, but thanks just the same. I’ll allow it. I don’t know if this will be as comprehensive as I can possibly make it, but I’ll at least try to show you why GW can do almost whatever the fuck they what with their pricing without affecting demand for their products or their profits in any significantly detrimental way. I’ll also demonstrate that the price ass raping they’re giving us could be far far worse, so no more crying “unethical” or any bullshit like that from now on.

Price Elasticity of Demand

This is the first concept that we need to discuss here, as it will by itself pretty much prove my point without having to try too hard.

The first thing you need to understand is that graphing supply and demand can be represented in an oversimplified way by the standard equation for a straight line: y= mx + b. I think there is a slightly different version of this equation for business, but it’s the same thing with different variables. Using this, you should be able to relate to better anyway. m is the slope (percentage change of x relative to y) of the line and is very important in economics. Real supply and demand graphs usually don’t follow a linear or curvilinear pattern very well, but we are looking at this from a very basic level today.

The slope of a graph of supply is positive where the Y axis is Price and the X axis is Quantity. This means that if you increase your price, the quantity also increases. As the price goes up, a company wants to produce more.

The slope for the demand of a product will be negative. Increases price decreases the quantity of product demanded. Generally speaking the higher the price, the less consumers will want to buy.

The intersection of the lines “supply” and “demand” (S and D on a graph) represents the most efficient quantity and price for a product. This is where profit is highest. Finding the area under this intersection will also give you the total revenue (this is money earned without paying any expenses, so not your profit) at this point. Rarely does a company ever hit this point exactly, as in real life there is pretty much no way to gauge exactly where this intersetion is. Most companies are either producing too much or too little product, putting them at the right or left of the efficient point, respectively.

A basic graph looks like this-

Now back to the line slope. The slope of your line represents something called elasticity. From this point on I don’t give a shit about supply, so we’ll only be talking about demand. For demand, elasticity shows us how much quantity of product demanded changes in response to a change in price.

This is the formula for finding the price elasticity of demand-

A price is considered Elastic when E is < -1 A price is considered Inelastic when -1< E < 0 So elastic prices suffer great swings in demand when price changes and inelastic products demand changes less relative to a change in price. A perfectly inelastic item has a E or slope of 0. This means that the quantity demanded will always be the same regardless of price. The graph looks like this-

The closest real world example to a perfectly inelastic good I can think of is insulin. People will still demand insulin almost regardless of price. According to Wikipedia the elasticity of demand for insulin in the US is -.01. If the price of insulin were increased 100%, the demand for insulin would only drop by 1%. This makes sense, as users of insulin pretty much need it to live or at least live comfortably. Conversely with an elasticity of -4.4, Mountain Dew is very sensitive to changes in price. Rednecks and gamers would respond to a 100% price increase with a 440% drop in demand.

You’ll see why shortly, but we will only be concerned with inelastic demand from here on out. This is what a generic inelastic demand graph looks like. You may need to refer to this later-

As you can see, the line is very steeply sloped, indicating that the price demand relationship is very minor.

Demand for GW Products

Here is where I will make my first assumption. Luxury goods (cars, helicopters, leisure items like hobbies, airfare, jewelry, high class call girls, etc) normally follow an inelastic demand pattern. That means, as shown above, changes in price do not greatly affect quantities demanded. Treating it as a luxury good, we will have to assume that GW products have an inelastic demand. From here on out we’ll assume that the Elasticity of a Landraider (which will be used as an example) is -.5. I feel that is a very conservative estimate as theater tickets for teenagers have a elasticity of -.2, beer -.3, and cigarettes -.3 in the US. This shows us a trend for leisure and (slightly) addictive products to be pretty damn inelastic. This just means that my conservative estimate will overstate the change in demand relative to price, meaning GW demand is less sensitive to price change than my assumptions would lead you to believe.

A Landraider currently costs $57.75. As mentioned in a previous post, it is believed that the profit margin on this is 72% (if sold through direct channels, I’m not going to figure out retail channel markup, but it’s probably 20 and 40 something % ). From that we can assume that the cost of producing a Landraider model is $57.75 x (1-.72) = $16.17. This number will be important later.

Let’s pretend that there is a current demand for 10,000 Landraiders. With the assumed elasticity of -.5, what will our revenue and profit be at the new proposed price of $62? What was it at the old price of $57.75?

Pencils down, here’s the solution: +edited.  I screwed up the % change and therefore units at new price fixed now+

Old revenue at 10,000 units. 10,000 units x $57.75/unit= $577,500
Gross margin $ is $577,500 x (.72) = $415,800

Price is changing by ($62-$57.75)/$62 * 100% = 6.85%

Therefore our demand will change by -.5 * 6.85% = -3.43%

Our new quantity demanded will then be 10,000 units * (1-.0343) =  9,657 units

New revenue is 9,657 units * $62/unit= $598,734
Gross margin % is now ($62- $16.17)/$62 * 100% = 74% (this assumes that the cost is the same as last year)

Gross margin $ is now $598,734 * (.74)= $443,063

So in spite of selling 343 less units, we wind up making an additional $27,263 in gross margin (profit before taxes and other miscellaneous charges).

Now if you were to keep going at higher and higher prices, you’ll notice that your gross margin % and $ keep rising. My theory is that GW is on the left side of the intersection of Supply and Demand. This means that until you hit the “efficient” price, GW can continue to raise their prices without negatively impacting revenue. In short, they could raise prices even more and not have to give a flying fuck about loss of revenue and margin and they aren’t increasing their prices as much as they could.

Where does all the money go?

If GW is making 72% profits currently on their products and may be increasing that to 76% or better how is it that they only retained 10% of their operating income in 2009? Well there are a lot of reasons. The 72% margin above is something called product gross margin. It only represents the costs needed to produce the item. Subtract out all of your other expenses and you get something called net income from operations. Subtract out your insurance expenses and you get net operating income. Take out taxes and you’ve got net operating profit after taxes (NOPAT). This is the important number. It represents how much profit you have left after all the bills are paid. GW, being a manufacturer, wholesaler, and retailer has a fuck load of expenses to pay for to stay open. Could they cut their costs to keep prices down? Possibly, but they are already addressing that according to the annual report, as I mentioned in my previous post. Also cutting costs usually means cutting jobs. Do you really want somebody to lose their job so you don’t have to pay $4.25 more for a plastic tank? There is only so much fat that they can trim, and a lot of their long-term cost cutting measures, such as switching over more and more to plastic models, cost a lot in the short-term.

What happens to the 10% profit that GW realizes? Well that is something called retained earnings or earnings kept by the company. This can be used to reduce debts, make investments, pay dividends to shareholders, make equipment improvements, or sit there for emergencies. A company doesn’t want to have too much money laying around not doing anything, bu having some free capital to pay for shit is necessary.

How does GW’s 10% NOPAT stack up to other companies? Procter and Gamble netted about 13% in the first quarter of 2010, down from a 4th quarter 2009 high of nearly 25%. Kraft foods international posted about a 7.5% NOPAT in 2009. As you can see GW is right in there. They may have obscene product margins, but running a business is quite expensive. It is important for investor’s in the company to increase the NOPAT as much as possible. If the company is not performing up to shareholders’ expectations they can do anything up to and including taking legal action against the company in question. For GW to continue to operate they must continue to try and increase their profits as much as able.

And what of this recession?

Seriously, fuck off. According to the Federal Reserve Economic Database (FRED), the US recession ended a while ago. Though it was the worst drop since te early 80s, the US Gross Domestic Product (GDP, amount of goods and services produced in a country in total and a strong indicator of a country’s financial health) only dipped about 2.5% anyway. Unemployment peaked at about 10% and is on the decline. That sucks, but things have been a lot worse- I’m looking at you early Reagan administration. The so called “recession” is not an excuse for you to become cheap all of the sudden, since there’s a good chance that you have been in no way directly affected by the market (unless you are trying to buy a home or get financing). I am sorry if, like me, you have been directly affected by this, but things will look up. For the overwhelmingly vast majority of people, taken as a whole, the economy didn’t tank like many would have you believe and has left them in about the same position as they were in in 2007. The sky isn’t falling. Need I also mention that we’re talking about a luxury/leisure item here. It’s a non-essential good that is bought primarily by a demographic who has had little to no change in disposable income. So the economic downturn or whatever you want to call it shouldn’t affect GW sales dramatically, unless it has increased their manufacturing or selling and administrative costs in some way.

Conclusion

If nothing else, hopefully you know can see why GW can raise their prices without worrying much about their profit. You should also see that things could be much worse and be happy that GW appears to be balancing your desires with their own needs pretty well, meaning you will keep buying their shit and they will continue to be a business (this is called the going concern assumption- we assume that GW will continue to operate in the future). I haven’t really touched on why they need to increase their prices as much as why they can do it, but suffice to say that their costs are going up and they have a lot of past good equipment and licensing investments that still need paying off. They also need to step up their marketing efforts to continue to grow their customer base, as they have admitted that their acquisition of new customers is stalling out a bit. That will cost money, but ensure that we still have a hobby in 10+ years.

Warhammervierziegtausendnovelle: jetzt noch mehr Mathe!

Every now and then I come across something that completely blows my tiny little mind. I don’t mean this in a positive way either; what fun would that be?

Early last week, while I was deep into finals and having my dog’s leg x-rayed, Maxx* sent me a link to one of the most entertaining Internet fights I’ve seen in a long while. It has it all: Multiple personality disorder, belligerence, and statistics. I really really wanted to use this for the Friday Night Fight last week, but couldn’t figure out a way to get the Reader’s Digest version of the offending poster’s epic wall of text rants to be anything approaching coherent. You’ll see why. So sadly, this became my first of two failed attempts to write FNIF last week that will be materializing throughout this week in various forms.

Now we all know how fun dicking around in the BoLS Lounge can be. Well, it’s fun if you think that sitting in a Judas Cradle sounds like a good time… But Judge is responsible for what may possibly be one of the craziest posts I have ever seen, in which he provides a battle report for a game he played against himself, in his own head! I’m aware of at least one top player out there who also employs this technique, but I’m calling bullshit on it. More on this after the aside…

As an aside, this gives me a rare opportunity to talk about one of my all time favorite books: Schachnovelle, written by Austrian author Stefan Zweig while in exile in South America during WWII. Es handelt sich von…. Entschuldigung- Sorry, got a little carried away there-anyway, Schachnovelle (or Chess Story) is about a man named Dr. B_ who is a captive in a concentration camp where he becomes the subject of experiments involving isolation. He is basically left in an empty room by himself for months or possibly years to see how much being cut off from society will damage his psyche. After finding a book about Chess strategy in his room (or smuggling it in, I can’t remember, it’s been a while since I read this), he starts to use chess as a way to keep his sanity. After studying classic games, moves, and strategies endlessly, he ultimately begins to play games against himself in his head. After doing this for some time, he eventually completely separates his brain into a white half and a black half, causing him to suffer a mental breakdown.  He is then placed in a sanatorium.

Once he comes back down again, he is cleared for release from he institution. Wanting to get away he soon finds himself on a steamer bound for the US, I believe. Unfortunately, the steamer is full of Chess enthusiasts and the reigning world champion from some eastern block country. Eventually there is a game between Dr. B_ and the champion. B_ wins easily, given his ability to play as both players and think many many moves ahead of even his skilled opponent, analyzing all of the possible moves with lightning fast mental agility. Recognizing how quickly his opponent makes his moves, the champ challenges the Dr. to a rematch, employing a new strategy. The champion begins taking as long as possible to make his moves, to throw off his opponent. This strategy ultimately works as B_, with too much time in between moves, begins to play all of the potential moves in his head over and over again until he suffers from a short nervous fit/mental breakdown. When he recovers from this he makes a bad play and loses the match, giving us our happy ending#.

So there’s a lot in that aside that applies to Warhammer, but specifically right now I’m concerned with playing with yourself (ummm, what-fucking-ever laugh all you want you plebes). I’m not saying or implying that playing a game against yourself is the result or cause of some form of insanity, even though it is funny to think that it might be in Judge’s case. What I would like to address is that this doesn’t fully represent a real game of 40k. Just like Mathhammer is only part of the equation, self-Warhammer love only approximates what a real game is like.  Mathhammer doesn’t take terrain or your foe’s behavior into account.  Playing yourself leaves out a number of important factors too, the most important being your opponent.

To use yet another example, take my own experiences with poker. I am an epically bad poker player. I’m no Kenny Rogers, for sure, since I certainly don’t know when to hold ‘em or when to fold ‘em. I’ve never really taken the time to try and figure the game out and only play once every few years. This has actually worked to my advantage on a few occasions. My play is so erratic and poorly strategized that the other players at the table can’t make any sense of my actions and get thrown off of their game. Then I take their money.

What I’m driving at above is that no matter what you think is going to happen in a game or how certainly you “know” how your opponent will behave, you’re likely to be proven wrong. Not just a little wrong, but really fucking wrong. When playing with yourself, you get the unfair advantage of complete omniscience. Knowing how your opponent will react puts a very unrealistic slant on the game. So theorize in your brain all you want, you will never be able to predict your enemy’s actions to a 100% certainty.

Self exploration of this kind can also be affected by any other number of variables from your own prejudices to your incomplete knowledge of strategy. You don’t like the white chess pieces? Black will probably win the game. You hate Space Marines? Looks like Tau are going to whoop the Blood Angels’ asses in the game in your head. …and don’t even get me started on how presumptuous brazenly declaring that you know what the best move is in every situation. If you really knew the optimal play for each piece in any game 100% of the time, you’d have a perfect record. Oh you don’t, then get the fuck out of my face with that shit and go diddle yourself away from my corner of the Internet.

I think it’s about time I stopped ranting and just gave you the goods. Judge’s post and the ensuing fight can be read here. If you can make it through all 7 pages of that shit you are a far bigger man than I. Good luck with that…

By way of coming to some type of conclusion I will simply say that there is some value in playing out mock games in your head. It is a very imperfect system, though. If you come at me saying that because you worked something out in your head X cannot possibly beat Y, then you can fuck right off. What do you guys think? How much value do you put in this type of Theoryhammer? Did I miss any easy cracks at masturbation jokes?

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*Big ups to Maxx for sending me another e-mail of some good shit even after being snowmobiled over the last one . I think I figured out his screen name** and don’t feel too bad about hurting his vagina during FNIF, I was much nicer to him than anybody else in that thread.
**I’m not stalking him or anything, I just like watching him shower ~wait, what?
#Well at least this didn’t end in the death or suicide of the main character like 75% of the other German language novels I’ve read.

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