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Monday, August 16, 2010

Guest Article: Mathammer in the Warhammer community

Here is an article by Sepharine on Mathammer which was e-mailed to me. Some very good points are made so enjoy reading!

Hey Kirbs!

I promised you an article a while back after you posted my comment about Vanguard Vets on your blog. Since then I realized the article I was going to write requires a bit more easing into. I have a very clear view of what message I want to get across I just have my doubts about who wants to hear it and how. As you’ve probably guessed by my previous article, I can be considered something of a math-oriented player. With me catching a cold and being kept awake by my own sniveling I figured now would be a good time to put my thoughts into words.

Unlike other games like World of Warcraft, Magic the Gathering or Poker, Warhammer has very few communities dedicated to ‘mathammer’. Whilst there are definitely some people putting in an effort, the style of my previous article is a good example of the average depth such analysis reach (that is: not very deep!).

While I’m not here to convert anyone, I do find it odd that the Warhammer community seems to ignore mathhammer or even actively shun it. More pressingly, I notice that the lack of a hard-edge math community for this game has its results on the information being put out there. In fact, I notice allot of the posts circulating forums such as Warseer are leaving out explanations at best or are plain wrong at worst. Though I doubt anyone reading this blog is hoping for some elitist jerk to teach them math, I do think people should learn how to interpret mathammer.

First off: Math is a language. Anything you can analyze with math you can also learn by playing the game. In the end Math and experience will tell you the same truths. This means that using mathammer is optional. So why bother using it at all (especially if you hate math!)? Mathammer has three advantages: Precision in explanations, experience without playing games and objective reviews.

The foremost is that explaining Warhammer through math is easier than through plain English. Explaining the difference between Banshees and Scorpions becomes more tangible with numbers. Instead of being merely ‘better or worse’ one can read the minute differences.

The second is ease. Not everyone can play more than two games a week and because of that don’t gain experience quite so fast. Mathammer can be done without an opponent to play and without buying questionable models.

Finally, mathammer is easier to spot faults in. You might luck out with las cannons 50 games in a row and think they’re amazing at killing Land Raiders whilst you were just lucky. Or you may read my articles and notice mistakes when you run the numbers again, spotting mistakes in my analysis.

That said, mathammer is like wishing for something with a genie. Math takes your question literally and instead of getting a spurt of growth in your genitals you’re suddenly hanging like dead horses do after the slaughter. Practically: If you calculate the difference between melta-guns within 6” and las cannons effect on tanks you will learn just that. You will not learn how to get your melta within 6” of a Land Raider or how suppression fire brings advantages. And that’s not even mentioning the chance someone is plain bad at math.

Props to anyone still reading by this point. I realize this is getting dangerously close to being uninteresting. Depending on the responses to this article I might take this anywhere people find interesting. In the mean time however I’ll limit myself to a quick guide to reading mathammer. The internet is an uncensored place and seeing the difference between proper advice and plain nonsense is all up to the reader. A list of common mistakes if you will.

Diminishing returns:
The first and foremost mistake I see is that if one meltagun has a 33% chance to kill a tank then it takes three meltaguns to kill said tank. In fact, three said meltaguns will only have slightly over 70% chance to kill said tank. Implying anything else is ignoring the fact that even if you roll 200 dice you can still roll 200 1s. Mathammer won’t ever tell you how many guns you need to take out a threat. It will help you decide how to spread your resources (meltaguns) amongst the threats (enemy tanks) to stop the highest amounts of those threats. It will help you decide how much of your forces to spend to stop that rock and how many to retain to stop the rest of your opponents army.

This means that whilst saying that 10 bolter shots kill 4.4 guardsmen might be useful, it isn’t accurate.

Question everything:
Secondly, don’t trust anything you see which you can’t understand. Math is a science and because of that relies heavily on everyone second guessing whatever someone writes down. If you played allot and think the direct opposite of what some math article is suggesting, you should trust yourself. Math is precise and might not take things into account you value or it might be miscalculated. Hell, it could even answer questions which aren’t interesting in the first place!

Problem > Solution, not the other way around!
On the subject of which questions to answer: Ideally you have a question and you use math to answer it. 10 bolter shots averagely kill 4.4 guardsmen but if you must absolutely kill 4 guardsmen this round of shooting then you don’t want to know that. You want to know what the chance is that you will kill 4 guardsmen with those 10 bolter shots instead. This actually helps you decide whether or not to pile on another 10 shots or to use those elsewhere. Be specific in your questions and realise what it is you're asking.

Don't put all eggs into this basket:
Finally, math is no substitute. Math will answer questions you’ll be hard-pressed to answer without, but knowing which questions to ask in the first place comes from playing the game. When it comes down to it, mathammer is merely a single avenue in meta gaming.

I hope you’ve enjoyed reading so far. I had a hard time gauging the level of interest and knowledge for an article like this so I would love some feedback. If you want me to address a specific example or if I should assume you folk know more than just basic math I’ll be happy to hear it. If people are interested then I’ll make an effort to write a more applied article with some practical knowledge.

Leave feedback for Sepharine people!

10 pinkments:

fester said...

Well... my brain doesnt hurt yet.

Bring the numbers!
More knowledge is always better then less, especially given the number of retards on the net.

Saying that, It wouldnt be the first time I had 3 PK hits on a stationery Railhead (S8 v A10) not blow it up over 3 rounds of combat... Regardless of the maths!

AbusePuppy said...

Well said.

I think an explanation of expected returns and what that means would help out a lot, I think. Also some links to lay articles on some of the relevant equations could help out. And actually...
A good tool for doing quick calculations of shooting and assault results. Also gives you (non-cumulative) chances of various results, i.e. killing one dude, killing two dudes, killing three dudes, etc.
A more generic program for doing calculations of dice probabilities. Doesn't have the same detail, but very useful for figuring your chances of moving at least 4" through difficult terrain and such. Also good for those who play RPGs.

Von said...

The first and foremost mistake I see is that if one meltagun has a 33% chance to kill a tank then it takes three meltaguns to kill said tank.

I see variations on this one all the time and now I have an answer of sorts to it, so I'm happy so far.

Something I'd like to see is an address of the myths about probability. I imagine that's what AbusePuppy is talking about when he mentions expected returns, and what silly people are talking about when they mention "average rolls" on a single die. I've never been able to understand how that's supposed to work, if indeed it does.

MasterSlowPoke said...

Good to see some real math discussion that's not Kirby trying to say that 2/3*1/2 is greater than 1/2*2/3.

I usually look at the probability of not getting the result I want. I think that's a little more useful in a planning sense.

I usually use a binomial distribution to calculate most probabilities.

Von, the average result on a D6 is 3.5, but I don't think I understand your question.

Jt3n said...

Awesome intro! Can't wait for more! I attempt "mathammer" often but just plain suck at working out statistics for some reason. I can figure most in my head but I try to put it on paper to work out more difficult problems and get very, very odd (and wrong) results. ^.^

For those of us reading while building an army or otherwise not playing I can speak for many when I say we want things like this... and battle reports!


Messanger of Death said...

Always good to see someone explaining why Mathhammer has its merits.


Max said...

Yay math! The best (and worst) part about it is that you can work out probabilities whenever you have spare time, like driving to work or whatevs. I will admit that on a few hunting excursions I have turned to Mathhammer to break the boredom of sitting in a treestand for 3 hours.

And yes, I am a dork. :)

lyracian said...

I love Mathhammer (which being a Maths teacher is probably good). There just seems so few other people around that also calculate what performance to expect from their units...

Zheilt said...

I love mathhammer and utilize it constantly. I have spreadsheets all over the place with all sorts of statistical analyses for the effectiveness of X vs Y and etc. Many choices (tactically, and list building both) I make based on math. It gets a lot of bad press on the internet, but as long as you understand it and its shortcomings then, all other things being equal, a player who uses math will beat a player who doesn't every time.

Also, anyone who likes math should check out the very brief mention of it on Brent's blog:

This post contains a picture of Brent's WGC man-servant Herr Fernseher's notebook which he mentions has some mathhammer in it about deep striking. It's all fun and games until you look at the picture and realize that it actually is a notebook full of the insane scrawlings of someone trying to statistically analyze deep striking. And then I had to change my pants.

Marshal Wilhelm said...

What do you mean 'killing 4.4 Guard is not accurate'?
You are slightly more likely to kill 4 than you are 5.

I don't follow what you are trying to say....

What myths on probability?

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