**WARNING MATHHAMMER AHEAD**-- If you find that probability and statistics cause you to experience headaches, nausea or ED, you may wish to skip this post.

First, we need to calculate the Probability of Hitting (Phit)the target, this varies based on the size of the target as well as the ballistic skill of the shooter. The probability of rolling a direct hit is 1/3. Now when we roll a deviation the we roll 2D6 and (in most cases) subtract the ballistic skill. So here are the probabilities of rolling various deviations for each ballistic skill:

Given this info, we now need to know what the maximum deviation that we can roll that will still yield a hit, to figure that out, the target size matters, I'm ignoring sponsons because come into play over a small range of angles. Here's the picture for hitting a Land Raider:

Let's look at 5th Ed first; to score a meaningful hit in 5th, the center hole needs to touch the hull, so for all angles we need a deviation of 2 inches or less, due to the shape of the LR, we can pick up an extra range ring over an arc of 90 degrees to the front and rear. So the Phit for the land raider is

Phit = Prob Direct Hit + Prob Deviation * (Prob Dev <= 2 + (90 + 90)/360 * Prob Dev = 3)

For BS3 this is

Phit = 0.333 + 0.667 * ((0.03 + 0.06 + 0.08 + 0.11) + 0.5 * 0.14) = 0.56

For BS 4 this is

Phit = 0.333 + 0.667 * ((0.03 + 0.06 + 0.08 + 0.11+ 0.14) + 0.5 * 0.17) = 0.67

Let's not forget Indirect Fire or Barrage where we just use straight dice (BS 0)

Phit = 0.333 + 0.667 * ((0.03) + 0.5 * 0.06) = 0.37

Phit = Prob Direct Hit + Prob Deviation * (Prob Dev <= 5)

For BS3 this is

Phit = 0.333 + 0.667 * (0.03 + 0.06 + 0.08 + 0.11 + 0.14 + 0.17 + 0.14) = 0.81

For BS 4 this is

Phit = 0.333 + 0.667 * ((0.03 + 0.06 + 0.08 + 0.11+ 0.14 + 0.17 + 0.14 + 0.11) = 0.89

Indirect Fire

Phit = 0.333 + 0.667 * (0.03 + 0.06 + 0.08 + 0.11) = 0.51

Now we're hitting at all angles with a deviation which is 4" or less. For BS 3 this works out to

Phit = 0.333 + 0.667 * (0.03 + 0.06 + 0.08 + 0.11 + 0.14 + 0.17) = 0.72

For BS 4

Phit = 0.333 + 0.667 * (0.03 + 0.06 + 0.08 + 0.11 + 0.14 + 0.17 + 0.14) = 0.81

Indirect Fire

Phit = 0.333 + 0.667 * (0.03 + 0.06 + 0.08) = 0.44

Next time we'll look at the 3" Blast to see how the Devil Dog's Melta Cannon and the Plasma Cannon have improved.

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