Just how accurate are blast weapons? The maths revealed

Its been a fair while between posts, I don't update as often as I used to do.  I have however been thinking about just how accurate a blast weapon is, opposed to a regular shot from a unit.  Consider some basic units;

Ork: BS2
Guardsman/fire warrior/termagant: BS3
Space Marine: BS4

These are some of the common basic unit types in the game.  They cover the three most common ballistic skill levels.  An ork has 1/3 chance of a hit, a guardsman a 1/2 chance of a hit and a marine a fairly high 2/3 chance of a hit.

So how does this compare to blast weapons?  Lets consider the two basic sizes, small blast at 3 inches and the larger one at 5 inches.

All blast weapons have a 1/3 chance of a hit, from the off.  This matches what Orks already get, but is worse than the other races standard BS.  So straight away, you might be thinking, why would you use such an innacurate weapon?

Well the good folks at GW allow you to take your BS into account when seeing if you hit.  As you know, you have a mighty 3/36 or 1/12 chance of rolling a double one, or a one and a two.  This is a bonus chance of hitting, should your shot scatter.

So you will find an Ork has roughly a 0.36 chance of a hit with a blast weapon.  Except that in reality he doesn't.  Because, as you know the template is bigger than 1 inch wide, so if it scatters only 1 inch, you will still hit at least the target model.  With the larger blast, you will still hit them if it scatters 2 inches.  So what does that do to the maths?  Well it improves the chance of the ork hitting to a mighty 0.39 for the smaller blast and a fairly impressive 0.50 with the larger blast.  You also have a chance of hitting other models in the squad!

So for orks, its an entirely positive experience using blast weapons.  Unfortunately, if you have more than BS2, they get less of a boost and with bs4 small blasts are less accurate than firing a normal gun.

Chance of hitting the exact model with bs 3 is 0.42 and with scattering the small blast hits 0.50 and the larger one 0.61.
Chance of hitting the exact model with bs4 is 0.50 and with scattering the small blast hits 0.61 and the larger one 0.75.