Wednesday, 25 November 2015

Mathhammer: The Hidden Obvious in Ballistic Skill

Take a look at the stat line for any model in Warhammer 40k, and you'll see that they will have a load of numbers. These numbers will show you just how good a model is at doing something, and as a rule of thumb, higher numbers means increasing competence.

We'll be looking at one number today, because it's a nice little entry to how the game mechanics, and thus the mechanics of the universe of 40k, are more accessible than you might think.


We'll be looking at how good a model is at shooting. Otherwise known as its Ballistic Skill, or BS.


Some of you are snickering, now. Stop that.


The BS (stop it...) shows how accurate a model is with a ballistic weapon, or a gun, and follows the rule of thumb above that larger numbers are better. It's used during the To Hit roll of the shooting phase, and is generally done per model.


The To Hit roll for each ballistic skill is shown in the below table, with re-rolls being the second number:


Ballistic skill12345678910
To hit6+5+4+3+2+  2+6+2+5+2+4+2+3+2+2+


Which is interesting, and indicates likelihood of hitting the target rather easily, at least between BS 1 and 5.


For that we need to know what a 6+ roll actually means.


Remember, 40K is based off of a d6, or a 6-sided dice. When we have a 6+, it means we're trying to get a 6 or higher on that dice.


Higher than a 6 on a d6 is not possible.


Simple probability now: what is the possibility of getting a 6 on a 6-sided die?


1/6


For a 5+ To Hit roll, we have two options: either rolling a 5, or rolling a 6 for success. That's 2 sides out of the 6 that wins us a hit.


i.e. 2/6





I'm going to show these probabilities underneath the BS so you can see the pattern emerging.



Ballistic skill12345678910
To hit1/62/63/64/65/6 





Can you see it now? Your BS basically tells you how many shots are actually going to hit their target. If you keep your squads in multiples of 6, you can always work out easily how accurate they will be.


ie. 6 models with BS 1 fire at a target. The likelihood is that only 1 will hit.


6 Guardsmen at BS3 fire at a target. 3 will hit.


6 Dire Avengers in formation at BS5. All but one are going to hit (meaning 10 hits with their nasty catapults!)


This pattern falls down a bit for BS 6-10, so we're look at those values next time (although I strongly suspect a similar pattern will emerge). But it's just nice to see the glaringly obvious in the assigned numbers to these models.


I'll also be looking at Twin-linking, and effective BS. Because Space Marine bikers are not BS4 with their bolt guns.


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