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Thursday, March 3, 2011

Fallacy in 40k Part 1: Mathhammer

Lately I felt the need to contribute to the 40k community a little more besides chatting around in 'the box' and replying now and then to mind baffling comments on Warseer. Then the issue arises: What can I contribute? I decided I can do some sort of series about common mistakes/misunderstanding/false assumptions or, as I like to call them, 'fallacies' regarding 40k and/or it's (online) community. I don't know exactly how many posts I can do on this, but looking around there is enough input for quite a few. This time I'm going to cover some major mistakes people make when they apply mathhamer, or alternatively, probability in 40k! So, here we go. In my opinion one can recognise four different groups of people 1) People who don't understand anything of it. 2) People who understand bits of it, but don't acknowledge that it is a useful tool. 3) People who understand bits of it and apply it a lot, often in wrong ways. 4) People who understand it pretty well and so know how and when to apply it. The first group is (getting) satisfied already by some basic mathhammer articles, the second group doesn't realise they belong in the first group and the fourth group don't need to be told more things about it. That leaves the third group for today. Almost every mistake comes forth from one thing: People only work with averages when they try to calculate things in 40k. Not comparing these averages with other averages (in the case of weapons for example) is another one. I'll look at the most glaring issues with actual examples now.

During games.
Oh my god, you are so lucky! That Terminator should have been dead!
This line should sound pretty familiar to almost anyone, although probably with some other kind of unit. What happens a lot: People figure that failing a 2+ armour save is a 1/6 chance. The average amount of wounds needing to be caused to kill a Terminator would be 6 then, no problems here. But that does not mean that it "should be dead" if somebody rolls for it! Why? Because you need to know what the chance is that somebody passes all 6 saves. It's not too difficult in this case, 5/6^6 x 100% = 33,5% (!)

Look at that number, that's a pretty high chance isn't it? It's roughly the same as failing a single 3+ armour save... Yet a lot of people don't realise things like these and might find themselves complaining a lot during games about dice rolls. One could take a more complicated example, the chance to fail 4 out of 5 armour saves with a marine squad (3+ save), what's the chance of this happening? It's 1/3^4 x 2/3 x 5nCr4 x 100% = 4%. Now this number isn't nearly as high, but can you call it bad luck? Not really; it's still a significant, at least when you realise that failing all 5 or 3 of them are also below average... and even more when realise you roll for these kind of situations a lot during games. They happen and it's completely logical, shocking isn't it?

Above all people should realise one thing: In most situations the chance of not rolling the average result is way higher than rolling it.

Example: Passing exactly 6 out of 9 Marine armour saves is a lower chance than getting a different result. (27,3% chance that you roll the average in this case)

Overall: Think before you whine, is it justified or are you being unreasonable maybe? When you blame the dice for your loss you not only take away a bit from your opponent his achievement, but you're also lying to yourselves ultimately. (if you blamed the dice unrighteously at least)

During theoryhammer.
Person A: A Storm Raven just isn't that hard to kill with its Av12
Person B: Bullshit, a missile launcher only has a 7,4% to destroy a flat-out Raven!
Person A might not have a clue about mathhammer, but at least he's not drawing conclusions on a number which is meaningless in a vacuum, which person B is guilty off.

The problem is here: What does that 7,4% chance mean? Is it high or is it low? Person B uses it in such a way that it looks really low...righteously so? There is no clear answer to this and that is okay, I'm only here to point out what goes wrong here.

The problem is that the number 7,4% is useless without reference. Now, the guy could have compared that number with other examples himself but I doubt it... My internal alarm went of right away, I 'know' that 7,4% in this case are relatively high odds. How do I prove this? Let's look at some other numbers. I'll list the chances of a single Missile Launcher destroying other vehicles in cover against their front armour (double the chances if you want the odds of getting immobilised being included, same for getting results without cover):
  • Rhino – 5,55%
  • Chimera – 3,7%
  • Ork Truck – 12,0%
Now the worst part, what do these numbers mean? Does this mean the Raven is relatively easy to kill? I mean Rhinos get killed by Missile Launchers too! And there arrives another problem with mathhammer: it's just mathhammer in the end. It's hard to argue how well one could stay out of range of such weaponry with the Raven for example.

Another example:
Howling Banshees are excellent Marine killers, they kill 10,1 on the charge with Doom support!
How hard is it to get such a charge of with them? How easy is it to get Doom support? Point investment? This line is false by the way, they aren't excellent at anything.

In the end my point is: Please think before you decide to try and back up your opinion with numbers. Be honest and make sure they are relevant, you help nobody when you deceive people with useless statistics. To the people on the receiving end: Don't be afraid to question the usefulness of numbers when someone uses them.

Now it may seem that I think mathhammer is pretty much useless, which isn't true. Far from that actually, but I'll cover that in a future article.


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