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This was originally a couple of posts that I wrote in a tryanid-armament thread that sort of siderailed. I found it full of interesting math and helpful theories, so I figured I'd try to make it into a dakka-article. First I want it properly proofred, both for grammar, spelling and most importantly for the facts and the numbers. So if you want to lend a hand, please read this and give me some constructive critique.

The effectiveness on blast templates depends on how your targets are spread out. This is a tutorial on how blast markers works in practice. If you really want to understand this, and get a feeling for how it works, go grab a handful of 25mm-based miniatures and the small and large blastmarker and set up according to the descriptions I do below. Then place the blast marker and roll the scatter, to see what happens. Repeat about 20-50 times for each setup. Maybe even write down your statistics. If you want to, you can repeat this excercise with different sizes of bases. Just to see how much difference a 25mm or a 40mm base does. In this math all scatters that I talk about are the ones you get AFTER reduction for BS. Later in the article I will do some calculations on how much difference BS makes. (hint: not that much)

For reference: the small blastmarker is 3" across = 1,5" from center to edge. So if you place it centered over a 25mm base, it will extend 1" outside of its base. The large one is 5" across =2,5" from center to edge, so if you place it centered over a 25mm base it will extend 2" outside of it's base. All models I'm referencing to are assumed to be 25mm. A HIT using caps lock references to a result on the scatter die. A hit with small letters references to a model covered by the blast template.

Lets try a couple of possible setups for squads.

First setup, maximum spread, singe line: Set up a squad in a single straight line with exactly 2" coherency. If you have expensive models in small units (warriors etc) this is the way to set them up to minimize casualties from blast weapons.
Attacking with a small blast: On a HIT you will hit exactly one model. If you have a lucky scatter along the line you might hit two models, but most scatters larger than 1" will just make you miss entirely.
With the large blast you will hit eactly three models on a HIT. Most scatters will reduce this numbers. Scatters along the line and/or 2" or less will still grant you at least one hit.

Second setup, base to base, single line: Set up a squad in a single straight line, with base to base contact. If your models have a lot of parts sticking out outside the base, it can be tricky to put them this close.
Attacking with a small blast: On a HIT you will hit three models. If you claim to be able to hit more, you are cheating. Most scattters will seriously reduce the number of hits. There is however one lucky scatter where you deviate at a slight angle to the line and just a few inches, that might let you cover 4 models. But that chance is mostly academical.
Attacking with a large blast. On a HIT you will hit five models. Most scatters will seriously reduce the number of hits. Same as above, there is a "golden scatter" that is very unlikely to happen that might let you hit six models.

Third setup, maximum spread, hexagon grid: Set up a large squad, preferrably 20+ models, in a hexagon grid. Start with placing one model in the middle, then place 6 other models in a circle around this center one. All coherency should be exactly 2" from base edge to the nearest base edge. Then place more models around, so that all distances are kept at 2" and you get as dense a cluster as possible. This will be a hexagon grid (if I managed to explain the setup properly, it looks a bit like the honey-comb of a bee-hive...). Theoretically speaking, if you want to minimize your losses from blast and template weapons this is the way you want to deploy your gaunts and similar models that comes in large units. In practice they become very unvieldy when placed this way, so most games see them in a tighter formation. Anyhow, I find it useful to have a small piece of card that is exactly 2" along one edge, and use it to space up my units when I have a lot of room and time to move them about.
Attacking with a small blast: On a HIT, you will hit exactly one model. Most short scatters actually have a good chance of increasing this to 2 hits. Short scatters are any scatters that lets the blast marker stay within the "borders" of the unit.
Attacking with a large blast: Now this is a tricky one, both on a math perspecitve and a rules perspective. The coherency distance is stated in the rules as not allowed to be "over 2" (p12), and the large blast extends exactly 2" outside of the target base. In practice however, the coherency is placed with human error margin, and thus must err on the short side, so the large blast will touch every model that is within coherency of the original target. So on a HIT you will hit 7 models (the one under the template and the 6 in the hexagon around) Any short scatters will reduce this a little.

Fourth setup, minimum spread, hexagon grid: This is how models will stand when they have arrived into play by use of the Deep Strike rules (see page 95). Make a large squad again. One model in the middle, then make a full circle around it, as close as possible. If your models have very few parts that stick out outside of their bases, you will get 6 models in this circle. If you have a lot of things in the way, you can get seven (or maybe even more) models in this circle. Then keep stacking models as close as possible. This is the best possible target for blast markers (and templates...)
Attacking with a small blast: On a HIT, you will hit the model in the middle, and everyone in the inner circle. Usually this means 7 or 8 models. How bad a deviation is depends entirely on how big the unit is. A short deviation will give you just as many hits, but most of the time a short scatter is only 1", since the unit is so compact.
Atacking with a large blast: On a HIT you will hit the model in the middle, everyone in the first circle and everyone in the second circle. This can be a lot of models, depending on how tight you placed them. Around 15 hits is not a problem. Unless the unit is huge (30+), almost any scatter over 1" will reduce the number of hits.

Fifth setup, more than 1" spread, random grid: Place a big unit just about as you would place it during a battle. A sort of unshapely blob with about 1.5" between models is what I usually expect. It makes a huge difference for the small blast marker if the distance between models is less than 1" or more than 1". So always try to place your models more than 1" apart.
Attacks with a small blast: On a HIT you will hit exactly one model. On a short scatter this can increase to two models. This setup makes frag missiles just as effective as a bolter shot against your infantry.
Attacks with a large blast: On a HIT you will hit roughly 6 to 8 models.

Sixth setup, less than 1" spread, random grid: Place as in fifth, but make sure the distance between models is roughtly 0.75". This we do to see the different effect that small blastmarkers will have.
Attack this with a small blast: If you move the marker around a bit, you will probably find one or more target model that lets you hit a total of three or four models on a HIT. Short scatters will probably reduce this number of hits by one, or not at all.
Attacks with a large blast: Move the marker around a bit, you will probably find one or more targets models that lets you hit up to eight models on a HIT. Short scatters will probably reduce this by one, or not at all. Please note for the large blast the difference between less than 1" spread and more than 1" spread is not that big, but for the small blast it is huge. Keep that in mind when shooting blasts and when deploying to minimize casualties.



Second part of this article is about scatter and chances of scatter distances.

First of all, you do always have a 1/3 chance to roll a HIT on your scatter die. This works as an equalizer between units with high and low BS.

As for distance rolled. Here is a list of the different possible results of rolling 2D6, and the chance of them happening, given both as chance on 36 and as a shortened possibility. All percentages are approximations.

Chance of rolling each result on 2D6
2 - 1/36 - 1/36 - 2.8%
3 - 2/36 - 1/18 - 5.6%
4 - 3/36 - 1/12 - 8.3%
5 - 4/36 - 1/9 - 11.2%
6 - 5/36 - ~1/7 - 13.9%
7 - 6/36 - 1/6 - 16.7%
8 - 5/36 - ~1/7 - 13.9%
9 - 4/36 - 1/9 - 11.2%
10 - 3/36 - 1/12 - 8.3%
11 - 2/36 - 1/18 - 5.6%
12 - 1/36 - 1/36 - 2.8%

When rollig for scatter distance you want to roll as low as possible. What we are interested in here is the chance of rolling equal to or less than a target number. This target number is usually the firing models BS. Many times it is quite allright to get 1" or 2" of deviation without loosing a significant number of hits, in that case the target number is BS+1 or BS+2. Check the distance in inches that the blast can scatter without having some part of it outside the target unit. If the unit is not circular or you are not aiming for a model in the middle, just take the shortest distance and round up. To find the chance of rolling equal to or less than your target number, all you have to do is add upp the probabilities up to and including that number. I'll make a table here. Once again. All percentages are approximations, I've done most of them in my head so don't trust all the small digits. As a bonus: This list can be used to see the likelihood of passing a Ld test.

Chance to roll target number or lower on 2D6
2 - 1/36 - 2.8%
3 - 3/36 - 8.4%
4 - 6/36 - 16.7%
5 - 10/36 - 27.8%
6 - 15/36 - 41.7%
7 - 21/36 - 58.3%
8 - 26/36 - 72.2%
9 - 30/36 - 83.3%
10 - 33/36 - 91.6%
11 - 35/36 - 97.2%
12 - 36/36 - 100%

Now I'll do some behind the scenes math, because it's so much faster than explaining how. I'll make a table that gives the total chance of hitting your intended spot, expressed as a list dependent on your target number. This chance will include the 33% chance to roll a hit on the scatter die.


2 - 35.2%
3 - 39.0%
4 - 44.4%
5 - 51.8%
6 - 61.2%
7 - 72,1%
8 - 81.5%
9 - 88.9%
10 - 94.3%
11 - 98,1%
12 - 100%

An example: If you are firing your spacemarine frag missile (small blast) at a 20+ unit with less than 1" coherency you will probably have a target number of 6, that is BS4 and up to 2" deviation will not reduce your number of hits. This means that you have a 61% chance to make that shot as effective as it can be. You also have a chance to clip the unit and get some hits, lets say this can happen on a scatter roll of 7 or 8. To find the chance of this happening, add up the chances of rolling 7 and rolling 8 from the firt table, and multiply that with 0.667 (wich is the chance of having to roll a scatter distance at all). This gives us (0.167+0.139)*0.667=0.20 so 20% chance to clip the unit for at least some effect.

In practice units on the table top are rarely as well structured as these mathematical models assume. But I still hope this article gave you some food for thought, illustrated some effects and inspired you to further experimenting and thinking around the use of and defence against blast weapons.

Thanks for reading
/Mellon

Very cool article idea and some interesting numbers to consider. I often play my small squads as the blob/hexagon setup but clearly with terrain taken into consideration the line has some solid potential versus blasts that I had not considered. Good to know.

Mellon wrote:
Now I'll do some behind the scenes math, because it's so much faster than explaining how. I'll make a table that gives the total chance of hitting your intended spot, expressed as a list dependent on your target number. This chance will include the 33% chance to roll a hit on the scatter die.
2 - 35.2%
3 - 39.0%
4 - 44.4%
5 - 51.8%
6 - 61.2%
7 - 72,1%
8 - 81.5%
9 - 88.9%
10 - 94.3%
11 - 98,1%
12 - 100%

Great post. Things like this are really helpful when you try to figure out just how (in)accurate blast weapons are in comparison to normal weapons.
I think you might want to make a quick/easy version that discusses the main conclusions of your post as we know that not everyone will take the time to read everything.

For accuracy, I think mentioning the chance for a target of a given BS to land a direct hit is sufficient. From my understanding it would look like this:
BS2 = 35.2%
BS3 = 39.0%
BS4 = 44.4%
BS5 = 51.8%

OR

the chance to be within 2" of your target (which is usually enough to hit the target)

BS2 = 44.4%
BS3 = 51.8%
BS4 = 61.2%
BS5 = 72,1%

This allows you to understand that a normal LRBT will have a 52% chance to land its Battlecannon within 2" of its target.


As far as squad orientation, I remember someone else doing some math on "V" formations and they worked out well for minimizing incoming fire. Might be worth looking into.

Some of these formations can be completely thrown off by placing the blast marker slightly off the center of the model. Watch out for that.

When I'm worried about blasts, I usually position my models in circular formations. This usually means that a large blast can only hit 3 models, and it mostly eliminates the problems caused by arranging in a line with 2'' gaps.

Thank you for your feedback everyone.

Minigun, you might be right that a more compact guide with only the results would be good. I don't think there is a need to have a separate list with chances of being within 2". It's much easier to just think of it as if your BS is two steps higher. This will of course need to be explained clearly.

I'm curious about doing some modelling for the v-formation and the open circle as well. I just know that it will involve a _lot_ of annoying calculations, since the marker, the bases and the deviation are circular. My out-of-my-ear opinion would be that both the V and the open circle would risk taking slightly more hits than the line(for a few golden deviations), but take up far less space sideways on the table, and thus be better able to concentrate firepower and assaults, and be far more likely to be able to take advantage of cover and stay out of LoS.

On the other hand, a wide line will allow you to strategically remove casualties from one end (unless you have extra equipment on a few), and thus move your focus towards the other end... Hmm, I feel myself slipping a bit sideways :-)

I'll see if I can do some math or at least approximations on the V and Circle. And I'll make sure to include a note about how the blast marker must be exactly over the middle of a model for these calculations to be applicable, and indeed for following the rules. Sloppy center placing makes the most difference when units are tightly packed or placed at exact distances, for the Unshapely Blob, the effect is probably minimal unless you abuse it on purpose.

Hmm, V-deviation. Where would I have to place the blast to optimize... If I base the first calculation on placing the blast over the model in the point of the V. I'm too tired for this right now, it's 03:30 in the morning here in sweden. So I'll just go to sleep and think about this while I'm on the train tomorrow.

Mellon wrote:
Minigun, you might be right that a more compact guide with only the results would be good. I don't think there is a need to have a separate list with chances of being within 2". It's much easier to just think of it as if your BS is two steps higher. This will of course need to be explained clearly.

I don't want your awesome information to get hidden away behind a wall of text and sometimes it helps to know your audience and their attention span (or lack thereof).
One element you might want to consider is the effect of twin linking. I'm not sure there are many TL'd Blast weapons (I can only think of the Havoc Launcher) but if there are enough other ones, it might be a good addition.

My out-of-my-ear opinion would be that both the V and the open circle would risk taking slightly more hits than the line(for a few golden deviations), but take up far less space sideways on the table, and thus be better able to concentrate firepower and assaults, and be far more likely to be able to take advantage of cover and stay out of LoS.

I believe that would be correct. My guess is that its a way to mitigate the effect of the blast weapon while not stringing your troops all over the board.

Thanks for doing this, certainly worth the read.

minigun762 wrote:I'm not sure there are many TL'd Blast weapons (I can only think of the Havoc Launcher) but if there are enough other ones, it might be a good addition.

Any blast from an Eldar unit being guided by a Farseer, or 2 Fire Prisms linking up for a stronger blast is what I can add.

Also Cyclone missile launchers, and griffon mortars.

Devxcil wrote:Also Cyclone missile launchers, and griffon mortars.

Since when are CML TL'd? I thought they just fire twice?

minigun762 wrote:
Since when are CML TL'd? I thought they just fire twice?

My mistake! I misremembered. For some reason twin-linked became "two shots" somewhere in my mind while reading up on the SW codex.

I appreciate the work you have done here, but 1 thing bothers me.

A base is 25 mm. An inch is 25.4 mm. A 3 inch template is 76.2 mm across, meaning if bases are stacked in a line then you can hit 5 bases in a line with a 3 inch diameter.

More than this, if you are in a base to base hexagon, like in deepstrike, then you hit 19 25mm bases with a single small blast template. A bit more than the 6-7 you claim are hit LOL!

AKA, Lash of submission into a clump, then 3 plasma cannons from oblits = up to 57 potential s7 hits!

thebetter1 wrote:Some of these formations can be completely thrown off by placing the blast marker slightly off the center of the model. Watch out for that.

When I'm worried about blasts, I usually position my models in circular formations. This usually means that a large blast can only hit 3 models, and it mostly eliminates the problems caused by arranging in a line with 2'' gaps.

I think this remark is important enough to be emphasized. Blasts do not have to be placed centered over a model, the center just has to be entirely over the base, giving you considerable wiggle room on 25 mm bases, and even moreso on larger bases and vehicles.

A lot of interesting posts here, and all of them makes simulating things much harder... And I can't help but smile at the challenge :-)

DevianID: Are you sure about that? The red measure-sticks that is delivered with the Assault on Black Reach box does actually use what my gaming group refer to as "GW-inches". That means they are numbered at 25mm intervals, not proper brittish inches of 25.401 mm. I must admit that I've taken for granted that the blast markers are also measured in this strange "GW-inch", wich matches the base size etc. However, I do not keep my blast markers at home so I can't measure one at the moment. IF GW does indeed measure their blast markers by proper inches, I really need to redo some calculations. And thank you for the mention of Lash, it does definitely deserve a mention when it comes to placing blasts.

Willydstyle. OMG! I'd missed that completely. I've played it "center over a model" ever since that rule was first implemented in 4th ed (I think it was?). It makes for a whole different set of statistics when it comes to placing blasts.

Minigun: Thank you for mentioning TLing blasts. That needs to be added. Should be pretty simple: P(hit) = 1-P(miss)^2 But it needs to be elaborated upon. I should have seen that one coming btw. The old Tyranid codex had MCs that could carry TLed blastweapons, and I've done some rough math that generally indicated that there as no point in having them. And a very good point about attention span. I tend to forget that a lot of people actually find math boring and don't really care about why the statistics looks like they do. They would rather read the finished numbers and spend their time playing the game :-)

I've done some clever (if I may say so) math during the trainrides this weekend, and while I have not yet gotten to a solid theory for calculating the statistics, I think I'm on the way to crafting one. For the statistically inclined of you, the idea is to calculate the risk to be hit, as a formula dependent on how far you are from the targeted model. There will be 1" wide concentric circles that each carries a risk of being hit. This is proper because the deviation is in comlete inches, not fractions. Each (25mm-based) model will be assumed to be placed in one of these circles. I will calculate the risk of the scatter arrow to point near enough for the blast to touch your base: (blast width+base width)/circle width. I will do some cheating, such as taking an average of blast width for the circle it is placed in and the neighbouring circles, rather than doing the proper sin/cos/whatever formulas, and I'll do similar simplifications for the base width. I doubt I'll manage more than two digits of precision on these calculations.

I think that it will be possible to solve this formula to make a printable sheet that looks a bit like a circular target for shooting practice. Wich if printed on transparent plastic can be centered over your intended target to easily calculate the chance to hit each other model in that unit. Different sheets could be produced for different BS. There could be a table like: "Each model that is mostly in the range 5"-6" from the target model adds an average of 0.12 hits".

It should also be possible to make an excel (or rather an Open Office calculus)-sheet where you can enter coordinates for where the models in the unit is placed, what model you are targeting and then the sheet will calculate number of hits. Although I'm not sure it is worth the time.