Math by Request: Screamers vs Landraider

I had a request from reader Jon Glas for the probability related to screamers attacking a landraider.  Landraiders can be tough to kill, especially for daemons.


We are going to look at two cases here: attacking normally, and attacking with prescience.

Attacking Normally:

With 9 screamers there is an overall 20.28% chance of destroying a landraider in one round of combat.  Within that chance there is a 15.48% chance of exploding it, and a 4.8% chance or glancing it out.

Initially this doesn't look good. A one in five chance is not all that great.

**Warning: here is my work**

I started by calculating the chances of an 'explodes' result.
2/3 * 1/6 * 1/6 = 1/54  

Using this we find that there is an 84.52% chance of not getting an 'explodes' result which means there is a 15.48% chance of getting at least one 'explodes' result.

and the chances to cause a hull point without causing causing it to explode.
2/3 * (1/9 + 1/6 * 5/6)= 1/6

Rather than finding the chances of getting 4-9 hull points I instead found the chances of 0-3

0: (5/6)^9 = 0.1938

1: 9(1/6)(5/6)^8 = 0.3489

2: 36(1/6)^2 * (5/6)^7 = 0.2791

3: 84(1/6)^3 * (5/6)^6 = 0.1302

This gives a 95.2% chance of doing 0-3 hull points which means there is a 4.8% chance of doing 4+ hull points.  If we combine this with the 15.48% chance to explode this gives an overall chance of 20.28%

**End of math**

Attacking With Prescience:

Now if we look at what happens when the unit has prescience the results are fairly dramatic.  All of a sudden we have a 40% chance of destroying the landraider.  The chance to explode increases to 20.15% and the chance to glance out the vehicle increases to 19.85%


**More math!**

Chance to explode:
8/9 * 1/6 *1/6 = 2/81 = 0.2015

Chance to glance:
8/9 * (1/9 + 1/6 * 5/6) = 2/9

Same style as last time:

0: (7/9)^9 = 0.1042

1: 9(2/9)(7/9)^8 =  0.2678

2: 36(2/9)^2 * (7/9)^6 = 0.3061

3: 84(2/9)^3 * (7/9)^8 = 0.1234

This adds up to an 80.15% chance of 0-3 hull points and a 19.85% to do 4+ hull points.  Combining this with the chance to explode this leads to a 40% overall chance.

**End math**

Wow!  I was completely shocked by this result.  The increase to the chance to explode was about what I expected, but the chance to cause 4+ glances increased by a dramatic amount!  Having a 40% chance to destroy a landraider in one turn doesn't seem incredible, but consider four melta guns in melta range only have a 44.14% chance of destroying that same landraider.  All of a sudden our attacks look much better.

If we manage to knock a single hull point off of the landraider (with all that daemon shooting) our chances of destroying it with the screamers jumps up to 52.34%.

Now if you opponent is letting a squad of 9 screamers run around they are doing things wrong.  What happens if you get knocked down to only 5 screamers?

Without prescience 5 screamers have a 9.25% of wrecking a landraider with 8.92% of that chance being an explodes result.  With prescience our chances increase to 12.24% overall with 9.4% for exploding.

What we see is that when the unit gets smaller prescience becomes less helpful. With a full unit prescience increases our unit's damage to 197% of our normal damage, but when we are at half strength we only do 132% of the normal damage.

So, if you want to wreck a landraider fast make sure your screamers get there in one piece, or be prepared to dedicate more than one squad to the job.  This falls in line from most of what I had learned while playing daemons.  Half strength squads are not going to get the job done, and it is generally better to make sure you kill your target the first time.