Hi there, my brethren-in-arms!
I spontaneously visited the Imperial Guard forum last night and came across a thread about drop troops. Since I myself am hardly ever concerned of the issue of scattering (drop pods are pretty safe to land close to the enemy, my terminators usually come in in the vincinity of veterans with teleport homers) I have never before cared much to translate the risks into seizable numbers.
Last night, though, I juggled some probabilities and did some calculations. And since today I was confronted with the problem of estimating the risk of scattering fatally upon deep-striking to a specfic position here I thought it would not hurt to share my results.
Scattering has two components: distance and direction. For our purposes we will measure range in inches (who could have guessed) and direction in degrees. While the latter is indicated completely by the scatter die the first is determined by both the distance dice and the scatter die (which can turn up with a "hit"). Do not be bothered with that too much yet, though.
Distance
Our scatter distance is 0" and 2-12" in increments of 1" each. Note that it is impossible to scatter 1". The following list provides percent chances of scattering the given number of inches or less.
0" (or less): 33.3%
2" (or less): 35.2%
3" (or less): 38.9%
4" (or less): 44.4%
5" (or less): 51.9%
6" (or less): 61.1%
7" (or less): 72.2%
8" (or less): 81.5%
9" (or less): 88.9%
10" (or less): 94.5%
11" (or less): 98.2%
12" (or less): 100.0%
This is pretty much it.
Direction
Now we need to work in the direction. Following the assumption that it is equally probable to scatter in any one direction we can calculate the risk of scattering into certain unopportune locations (enemy units, friendly units, impassable terrain) by dividing all possible directions (360°) by the arcs that pose a threat.
Example
This may sound complicated and can indeed be in some situations. Let me elaborate these theoretical considerations in an easy example as to show how the given ideas are supposed to be used.
A unit of terminators is to deep-strike near a squad of Necron warriors. As the terminators will want to be sure to be able to assault the enemy in the turn following its arrival it is supposed to land within 6" of its target, that then could not foot-slog out of the 12" effective assault range of the terminators. But more important than deep-striking this close is the safety of the terminators who should hit secure ground (and not be destroyed due to bad scatter) with a probability of about 80%. The terrain is free of other units or impassable terrain.
When the terminators are placed in front of the squad of Necron warriors the latter will probably occupy an approximate 120° arc of the terminators' surroundings. Since 120° is a third of 360° the danger of scattering into the Necrons at any given distance can be divided by three. If you are willing to run a risk of 20% (100% - 80% safety) of your terminators scattering into the Necron warriors you can thus take a 60% (3 x 20%) of scattering too far because only a third of all directions are positively dangerous. Thus you would deep-strike your terminators 4" from the Necron warriors, the probability of scattering a maximum of 3" being 38.9%, the risk of scattering further (and eventually coming within 1" of enemy models thus being destroyed) therefore being 61.1% (100% - 38.9%), in the direction of the warriors only about 20% (a third of it). [Of course this is a little approximated since if you don't scatter directly towards the warriors but a little diagonally to them you could probably even scatter 4" without being harmed.]
Trying to deep-strike 4" in front of the enemy then still leaves you with an approximate 40%+ chance of effectively landing within 6" of the enemy squad (2" or less scatter away from the enemy squad with a probability of 35%/3 being negligible, 3" or less scatter towards the enemy squad with a probability of 39%/3 not being a problem either, and a scatter of 4" or less parallel to the enemy squad with a probability of 45%/3 being tolerable too, for a total of tightly calculated 40%).
Of course those calculations remain rules of thumb due to the arcs in our calculations remaining rather large increments instead of infinitely small ones like in an integral. Still these numbers and considerations are perhaps inspiration or orientation guide enough to prove useful to some player intending to deep-strike his troops with a rather carefully calculated (in comparison to purely intuitive estimation) amount of risk.
But regardless of this hopefully useful breakdown it is of course completely up to you to decide where you draw the line! Your style of play determines just how much risk you are willing to take in order to gain certain advantegous positions...
Enjoy the game and good luck with your scatter dice!
Regards,
Archer
P.S.: sorry if things are difficult to understand. I am still having problems expressing myself on complex matters in this language.
I spontaneously visited the Imperial Guard forum last night and came across a thread about drop troops. Since I myself am hardly ever concerned of the issue of scattering (drop pods are pretty safe to land close to the enemy, my terminators usually come in in the vincinity of veterans with teleport homers) I have never before cared much to translate the risks into seizable numbers.
Last night, though, I juggled some probabilities and did some calculations. And since today I was confronted with the problem of estimating the risk of scattering fatally upon deep-striking to a specfic position here I thought it would not hurt to share my results.
Scattering has two components: distance and direction. For our purposes we will measure range in inches (who could have guessed) and direction in degrees. While the latter is indicated completely by the scatter die the first is determined by both the distance dice and the scatter die (which can turn up with a "hit"). Do not be bothered with that too much yet, though.
Distance
Our scatter distance is 0" and 2-12" in increments of 1" each. Note that it is impossible to scatter 1". The following list provides percent chances of scattering the given number of inches or less.
0" (or less): 33.3%
2" (or less): 35.2%
3" (or less): 38.9%
4" (or less): 44.4%
5" (or less): 51.9%
6" (or less): 61.1%
7" (or less): 72.2%
8" (or less): 81.5%
9" (or less): 88.9%
10" (or less): 94.5%
11" (or less): 98.2%
12" (or less): 100.0%
This is pretty much it.
Direction
Now we need to work in the direction. Following the assumption that it is equally probable to scatter in any one direction we can calculate the risk of scattering into certain unopportune locations (enemy units, friendly units, impassable terrain) by dividing all possible directions (360°) by the arcs that pose a threat.
Example
This may sound complicated and can indeed be in some situations. Let me elaborate these theoretical considerations in an easy example as to show how the given ideas are supposed to be used.
A unit of terminators is to deep-strike near a squad of Necron warriors. As the terminators will want to be sure to be able to assault the enemy in the turn following its arrival it is supposed to land within 6" of its target, that then could not foot-slog out of the 12" effective assault range of the terminators. But more important than deep-striking this close is the safety of the terminators who should hit secure ground (and not be destroyed due to bad scatter) with a probability of about 80%. The terrain is free of other units or impassable terrain.
When the terminators are placed in front of the squad of Necron warriors the latter will probably occupy an approximate 120° arc of the terminators' surroundings. Since 120° is a third of 360° the danger of scattering into the Necrons at any given distance can be divided by three. If you are willing to run a risk of 20% (100% - 80% safety) of your terminators scattering into the Necron warriors you can thus take a 60% (3 x 20%) of scattering too far because only a third of all directions are positively dangerous. Thus you would deep-strike your terminators 4" from the Necron warriors, the probability of scattering a maximum of 3" being 38.9%, the risk of scattering further (and eventually coming within 1" of enemy models thus being destroyed) therefore being 61.1% (100% - 38.9%), in the direction of the warriors only about 20% (a third of it). [Of course this is a little approximated since if you don't scatter directly towards the warriors but a little diagonally to them you could probably even scatter 4" without being harmed.]
Trying to deep-strike 4" in front of the enemy then still leaves you with an approximate 40%+ chance of effectively landing within 6" of the enemy squad (2" or less scatter away from the enemy squad with a probability of 35%/3 being negligible, 3" or less scatter towards the enemy squad with a probability of 39%/3 not being a problem either, and a scatter of 4" or less parallel to the enemy squad with a probability of 45%/3 being tolerable too, for a total of tightly calculated 40%).
Of course those calculations remain rules of thumb due to the arcs in our calculations remaining rather large increments instead of infinitely small ones like in an integral. Still these numbers and considerations are perhaps inspiration or orientation guide enough to prove useful to some player intending to deep-strike his troops with a rather carefully calculated (in comparison to purely intuitive estimation) amount of risk.
But regardless of this hopefully useful breakdown it is of course completely up to you to decide where you draw the line! Your style of play determines just how much risk you are willing to take in order to gain certain advantegous positions...
Enjoy the game and good luck with your scatter dice!
Regards,
Archer
P.S.: sorry if things are difficult to understand. I am still having problems expressing myself on complex matters in this language.
but intead of complaining i will congratulate you on your calculations 
