## Tuesday, November 13, 2012

### MathHammer part 3. Deep Strike

Today I will show you this calculation that shows you the chances of scattering into an obstacle when deepstriking. I was actually surprised how safe deepstriking is. This, combined with the newer mishap table means that deepstriking isn't all that bad. And at the end of the article I show you my new method of deep striking into dense terrain based off these calculations. More below...
First thing's first. Here is the link to download my Mathhammer Calculator which allows you to calculate the chances of getting a mishap when deep striking near any sized obstacle.

So let's assume you are deep striking your unit of terminators in to the battle. You want to assault the enemy as soon as possible so you want to get as close as possible with  an acceptable amount of risk. So let's say the enemy unit is a five man devastator squad in a loose formation as shown in the diagram below. The first thing we want to know is how wide the obstacle (enemy unit) is. So we see it is about five inches wide with an additional inch on each side that we aren't allowed to enter, so the total size of the obstacle is about 7 inches.
So we put 7 into the calculator and look at the chance of a mishap vs. distance to the obstacle. (Remember that you aren't allowed to move within 1 inch of an enemy, so 5 inches from the obstacle is actually 6 inches from the unit.) So if we place our deep strikers 1 inch away from the unit which is as close as we can get, there is only a 33% chance that you will scatter into that unit (2/3 chance to roll a scatter, and half of the time you roll a scatter it will be in the direction of the enemy). As you move further away, there is less of a chance that you will scatter into the obstacle.
This picture shows how I used a little bit of trigonometry to figure out the arc that the enemy unit occupies. One thing to keep in mind is that this model doesn't take into account the possibility of scattering past the obstacle. So remember that if you place your deep strikers right next to the unit and it is about 5 inches deep than there's only about a 24% chance of a mishap (33% rolling a scatter in the direction of the unit and 72% getting a 6 or higher). overall, by looking at the table you can say "I want to get as close as I can while still having a 90% chance of not scattering into the unit. So I look at the "chance of mishap" column and see that if I place my unit 5 inches away, there is only a 9.4% chance of getting a mishap. And from 3 inches away there is a 16.8% chance of a mishap. Pretty good odds if you ask me.

If you are a Blood Angels player, than you have it even better. Your drop pods and land raiders will still have to use the normal table, but anyone with a jump pack can deep strike with only 1 D6 on the scatter. This means you can have your 90% certainty within 3 inches! That is pretty awesome.
Finally, I have something to keep in mind when you are placing your deep strikers. Consider the diagram above. When I would place my deep strikers before I would try to make the safest drop by placing my squad as far away from everything as possible. In this example, my unit is 6 inches away from the enemy unit I am trying to assault, and 6 inches away from each of the obstacles around it. I figured that I'm as far away as possible from everything, so I am as safe as possible. But what I am finding out is that isn't quite true.
So to simplify this a bit lets look at the average distance to the obstacles if we place our deep striker directly in the center. Since it's 6 inches from each obstacle we know the average is 6 inches. So if we assume each obstacle (including the enemy unit) is 7 inches wide and sum up the chances of a mishap that we are given in the first table we get a total chance of a mishap of 4*6.5%=26%. Now lets look at an alternative placement.
So now lets move our deepstriker over 3 inches to the right. So now we are much closer to the enemy than I would have thought was safe before. But when we look at it, we are 3" from the enemy, 9" from the obstacle to the right, and 6.71" from the top and bottom walls (using the Pythagorean theorem). The average distance now is 6.35 inches. So now there's a small increase in the average amount of space around our unit.
Now lets estimate our risk of getting a mishap for this model by summing up the chances of mishaps from each obstacle at 3, 9, 6.7, and 6.7 inches. 15.3%+1.1%+2.1%+2.1%=20.6% total chance of a mishap. So let's look back at the first placement. When we were 6 inches away there was a 26% chance of a mishap, but now that we're 3 inches away we only have a 20.6% chance of a mishap! It's not a whole lot safer, but knowing that I can be closer to my target and have less of a chance of a mishap is win win!
So to conclude, deep striking is much safer in 6th edition due to the new mishap table. in addition, we can see that you don't have to place your deep strikers 12 inches away from everything to have a relatively safe drop. You can drop your units in just 4" from the enemy and still have only a 12.7% chance of a mishap. I would say that this risk is definitely worth being closer to the enemy. More weapons are in range and it is much more likely that you will be able to assault the next turn to keep the enemy from being able to shoot you.

I hope this was helpful to some of you. Let me know if you have any other strategies for deep striking. thanks for reading!

1. Great analysis! Its good to see I'm not the only one who does this stuff.
Another option for getting these kind of probabilities (or introducing yourself to programming) is to write quick simulation program to scatter a bunch of times to find the probability experimentally rather than analytically.

1. It would be fun to try that out. Unfortunately I know nothing about programming. Maybe I'll ask my brother to make a program like that. that would also be useful to let me figure out the confidence intervals and things like that.

2. Hi,

my question isn't about your Deep Strike analyis, but about your formula to describe the chance to hit with blast weapons. Can you explaim me your thoughts about that?

Greets

1. Just to let you know, I'm not ignoring you. I'm studying for a midterm tomorrow (Coincidentaly it's my biostatistics class). I'll give you the rundown when I get home tomorrow. It really isn't as crazy as the excel formula makes it look.

2. No hurry, take your time. So good luck then!

3. Okay, so your question has been answered in the latest post. Sorry it's a little long. http://40kangelsofdeath.blogspot.com/2012/11/mathhammer-part-4-rolling-to-hit.html

3. Of course if you are using a Mycetic Spore which means you can move it to within 1" of impassable terrain [units] if it lands on them it makes it even more fun. I managed to hit directly between two parked Chimeras once, then moved it backwards behind them so I could get 6 hits on their rear armour [that's not even including the Doom of Malantai when he gets out] ;) The only worry is if it deviates off the table.

1. I thought it just reduced it's distance if needed like a drop pod. Do the spores have something like the Mawloc?