In the previous post we looked at the probabilities when deep striking against a wall of troops. What we saw was pretty straightforward; the farther you are from your target the less likely you are to mishap. This time around we are deep striking by a large round base such as a daemon prince or dreadnought, and the results show something interesting.
Once again all of my calculations are done in a vacuum. The only thing I am concerned about is avoiding one large round base. In an actual game it is going to be rare that there is a single model of this size far away from everything else.
Last time I also talked about how units of up two five models aren't any less accurate than a unit of one. We are going to follow the same information here. I used the law of cosines to find the angles where I would hit a large base when starting a certain distance. As with last time the red circle is the starting location (in this diagram exactly one inch from the large base), the dotted line represents the one inch radius around the large base, and the other 4 circles represent the angles where I can land for 2, 3, 4, and 5 inches (moving right to left). If the red circle scatters 6 or more inches then it cannot mishap.
With these angles I combined the chances of rolling that amount with the chances of not rolling a hit. All of this together gives us this table which represents the chances of being safe when being placed by a large round base.
Distance

1”

2”

3”

4”

5”

6”

7”

8”

9”

10”

11”

12”

Chance

96%

95%

94.8%

94.8%

95.2%

95.9%

96.8%

97.8%

98.6%

99.3%

99.7%

99.9%

The first thing we notice is that all of these numbers are very safe (especially compared to the numbers from the last post), but more interesting is the fact that the most dangerous distance is not actually the closest. Since the chances of scattering each distance are not uniformly distributed (rolling a 2 does not have the same chance of rolling a 7) it is actually more dangerous to try and land 3"4" away from a large base than anywhere else.
If we think about this it all makes sense. Putting your model right next to your target means you MUST roll a 25 AND scatter within the appropriate angle. For a bit of perspective a rerollable 2+ save has a 97.2% chance of success.
When our squad gets above 5 models we must start adding models on to the front. This isn't quite as simple as when we were facing 'the wall' and I had to run my numbers through excel again in this situation. Here is what I came up with.
If we think about this it all makes sense. Putting your model right next to your target means you MUST roll a 25 AND scatter within the appropriate angle. For a bit of perspective a rerollable 2+ save has a 97.2% chance of success.
When our squad gets above 5 models we must start adding models on to the front. This isn't quite as simple as when we were facing 'the wall' and I had to run my numbers through excel again in this situation. Here is what I came up with.
Distance

1”

2”

3”

4”

5”

6”

7”

8”

9”

10”

11”

12”

Chance

92.8%

91.5%

91.5%

92.1%

93.1%

94.4%

95.8%

97.2%

98.4%

99.1%

99.6%

99.9%

IMPORTANT NOTE: This chart uses the initial distance of the front model not the first model placed. To incorporate this in your game you would place your first model back about an inch. If you don't take this into account you will mishap on a hit at 1" away
What we see is that as our squad gets larger it does get more dangerous, but only by a slight amount. All of our chances are still above 90%
Finally let's take a look at deep striking a large round base by another large round base.
Distance

1”

2”

3”

4”

5”

6”

7”

8”

9”

10”

11”

12”

Chance

93.2%

92.3%

92.2%

92.6%

93.5%

94.6%

96.0%

97.3%

98.4%

99.1%

99.6%

99.9%

This is a bit safer than the previous squad, but once again everything is pretty safe overall.
If you are going after something on a large round base feel free to deep strike anywhere by them. Even being right at 1" away your chances of causing a mishap are relatively small. Most of the time I am deep striking units they are generally suicide squads, but what this shows is that they don't necessarily need to be guaranteed death. Since our chances of having a mishap are low you could buff up the unit without too much worry.
This is some lovely work! The increase in safety at 2" has a pleasing 40K aesthetic to it...you're better off going in hot than lingering in tepid regions! Do you want to live forever?! I guess/intuit/arsepull that dropping in on a Knight Titan base has a different range of 'safer' distances but a similar effect if you are approaching it from a 'wide' facing. It would be interesting see the relative safety between approaching the narrow end and the wide end.
ReplyDeleteI am also willing to bet an "Attack on Knight Titan" post would be very popular among the Obliteratorloving hordes of Chaos!
Don't worry. I am planning on running the numbers for large oval bases and comparing different starting points with regards to the probability.
DeleteThis post took about 2 days of planning before I came up with what I needed to put into excel. Ovals are more complicated than circles, and I will have to do a bit more brainstorming on how I can do the calculations.
I am also planning on having a post about deep striking against a squad. since squads can be bunched up or spread out I am going to do a few different formations and show how those affect the potential danger.
WOW... It seems I can begin to deepstrike my venoms almost without worry...
ReplyDeleteWOW... It seems I can begin to deepstrike my venoms almost without worry...
ReplyDeleteReally informative as usual, my BA melta squads will be pressing right next to their target from now on, right in pistol range :)
ReplyDeleteHi Andrew, I must admit I'm a complete maths dunce. I was always far more comfortable with languages etc when attending school, but in a short layman's version can you explain why rolling 2 is not the same as rolling a 7 ( or any equivalent I guess)
ReplyDeleteVery informative and interesting regardless though :)
Let's say you have two dice one green and one red. If you want to roll a combined total of 2 there is only one possible way (double ones). As we move to other numbers we find that there are more possible ways. There are two ways to roll a combined total of 3 (1 on the green with a 2 on the red and a 2 on the green with a 1 on the red). Once you get to 7 you find that there are 6 possible ways to roll a combined total of 7 on two dice.
DeleteOh... of course, When I made that post I was literally only thinking that you could only get a roll of 7 one way (4 and 3)... It didn't even cross my mind that there were other ways.
DeleteOh... of course, When I made that post I was literally only thinking that you could only get a roll of 7 one way (4 and 3)... It didn't even cross my mind that there were other ways.
DeleteHi there. A friend of mine once worked out a deep strike probability matrix that showed the same results. It is very interesting. At my gaming club I regularly say this but it seems so counter intuitive that nobody believes me. If you extend your ideas then the angles become important. If you deep strike close to something, a fun line and other large bases thus combining both posts, you see straight away that danger only lies in one direction. Even if this takes up ninety degrees straight away the out of four of all deep strike results are safe. You may miss out on melta range but will most of the time be safe. Strike away.
ReplyDeleteJust as an update for everyone, I am still working on the probabilities for squads. Things are fairly difficult since they can be in different formations, but I am hoping to get my calculations finished relatively soon.
ReplyDelete