Forum adverts like this one are shown to any user who is not logged in. Join us by filling out a tiny 3 field form and you will get your own, free, dakka user account which gives a good range of benefits to you: No adverts like this in the forums anymore. Times and dates in your local timezone. Full tracking of what you have read so you can skip to your first unread post, easily see what has changed since you last logged in, and easily see what is new at a glance. Email notifications for threads you want to watch closely. Being a part of the oldest wargaming community on the net. If you are already a member then feel free to login now.

Has anyone done a statisticaly analysis of this yet, for the highest hit rate?

Heres some numbers i ran :

Assuming the target's base is 2 inches long and you place the initial point 6 inches away :

A roll of 6 and 8 on the artillery dice are guaranteed hits. That is 1/3 of the time.

A roll of 10 is an overshoot, and a misfire fails. 1/3rd of the time.

A roll of 4 requires at least a 2 on the bounce to hit. 1/6 chance of getting a 4, 5/6 chance of getting 2-10. 14% of hitting (1/6 * 5/6)

A roll of 2 requires at least a 4 on the bounce to hit, 1/6 chance of getting a 2, 2/3 chance of getting 4-10. 11% chance.

So roughly 55% chance to hit if you place the point 6 inches away.

From what my friend usually does it goes 8 or 9 inches off the back of the targets base (furthest point of the model).

So that is shooting at characters and well knights so hope this helps.

Yep 8 inches from the back of the model, or most front ranking model, that way if you get an 8 it still lands on them.

Depending if you shoot at a big long block I would say put it like 4 to 6 inches from the front then again I havent used a cannon cannon is.... its been a while but ya that should still work.

Logically speaking wouldnt 10 inches from the back of the base be the best point?

You have 0% chance to overshoot. Any undershooting you do has a chance of being nullified by the bounce roll.

Well 10 inches is a good idea the problem tho is if you roll a 2 and a 4 then well it kind of sucks if you roll a 2 and a 4 for 8 inches then if its cave them you are more likely to hit it it was explained to me and it made sense sorry i cant regurgitate that atm because I dont remember.

Also if shooting at chariots or bigger models then different "rules" apply (by rules i mean where the best place to put your template initial hit).

Against the giant spider from the front put it off 2 inches and no matter what you will hit it unless you misfire.

I think re-rolls also play a factor in this- so if you have a Master Engineer or some such, that probably skews it.

I personally always guess 10" from the back of a monster's base. This changes if I'm firing at a unit I hope to skip through, but usually only goes below 8" from the back of the first base if it's a particularly deep unit.

The other issue there is that I'm often trying to force a look out sir on some poor shmoe in the first rank, so overshooting is less valuable.

I know what you mean other than taking out scary things and lords what else do you use a cannon for you have magic and mortars or stone throwers to take care of hordes (stone throwers were meant for the half pints and mortars are meant for empire just in case clarification was needed).

But ya usually its not really a problem and if you are shooting a unit 8 ish inches should be good seeing as you then dont have anything else to shoot haha.

Things get a little bit tricky when the numbers are uneven.

For example if the base is 3 inches long...you can only put it 6 or 8 inches away(no roll of 7 on the artillery dice). If you put it inches away a roll of 10 will overshot by 1 inches, so 8 is still your best bet.

Best odds on a 2" deep target is 10" from the back of the base (so 8" from the front).

When you're rolling 2 dice to resolve cannons you have 36 possible outcomes.
If the 1st die is a misfire, it doesn't matter what the 2nd die is (6/36 of the combos).
Other than the misfire, you're only going to miss when the total doesn't include a 8-10.
That's rolls of:
2,4,6 and misfire
2,4 and 2
4 and 4

66.7% hit chance.
Best odds.
Aiming closer to the target adds overshoot issues, along with short and stick (2nd die misfire) and hits less often.

As others have pointed out though, other factors do come into play. Is it bad to over shoot? Do you want to force a Look Out on someone in the front rank?
And, in the case of skaven warp lightning, what's the strength of the hit and where does the template end up.

-Matt

That sounds about right haha
usually you are just going for the guy or a monster.

Sort of off topic can you get a look out if you are on horse?

I always go with 6 inches from the front of the model. 6 is the average number that will come up on the artillery dice, then you can always bounce through to hit it. Bear in mind if you are aiming at a hydra or something like that a roll of a 10 sould still hit it if you are going strait at it IIRC.

The artillery dice does not have an average number. Either misfire, 2, 4, 6, 8 or 10 have perfectly equal outcomes.

cowpow16 wrote:
Sort of off topic can you get a look out if you are on horse?

If they are in a unit of 5 RnF cav, yes. Least from my understanding.

Here's a table that shows, assuming you don't roll a misfire on the first roll, the probability of a spot x inches away from the target getting hit by the cannon shell;

2 20.00%
3 16.67%
4 36.67%
5 30.00%
6 50.00%
7 40.00%
8 60.00%
9 46.67%
10 66.67%
11 50.00%
12 50.00%
13 33.33%
14 33.33%
15 20.00%
16 20.00%
17 10.00%
18 10.00%
19 3.33%
20 3.33%

Basically, it says 'there is a chance of a shell falling short of a certain point on the field, and a chance of it landing over that point, if neither of those two things happen then the shell will travel through that point, therefore the probability of such is x%' For instance, if you put the shell 6" short of the target, then a roll of 8 or 10 will fly over that spot (40% chance if we remember we're excluding misfire), while a roll of 2 followed by a roll of misfire or a roll of 2 (6.67% overall) or a roll of 4 followed by a misfire (3.33% overall) will see the shell fall short of that spot. This means there's a 50% chance of the shot not hitting that point, therefore there's a 50% chance of it hitting that spot.

So does that mean the best spot to aim is 10" short of the target, because that's the mostly point of the cannon shell landing (66.67%)? Well, not quite, because it depends on the depth of the enemy unit. Thing is, while a low roll on the first dice roll will always see cannon shell's threat range wasted as the shot travels into the enemy unit, a high roll on either or both of the dice will see some the cannon shell's threat range wasted as the shell exits the enemy unit at the back. But this second risk is reduced if the enemy has a lot of ranks. The more ranks the enemy grows in depth, the closer you can be willing to place the cannon ball to the front of the enemy, as the risk of overpenetration is reduced against the risk of underpenetration.

It's hard to explain, but the end result of all that is that the maximises the expected number of casualties is always 10" short of the centre of the enemy unit. That's the trick, judge the distance from the centre of enemy unit, not the front.

Then, lastly, just to show that this can't be worked out entirely through maths, you have to weigh all of that against the advantage of getting lucky and sniping a character with a failed Look Out Sir! (which means that even though you might be mathematically better off shooting a little closer threatening you want to increase the likelihood of hitting the front rank, more than the likelihood of hitting another back rank). If an enemy unit carries a particularly valuable character, then you might want to pull your distance back by a couple of inches, improving your chance of hitting the front rank, at the cost of hitting back ranks you're not so concerned about.

That doesnt make sense. It is impossible for the artillery dice to roll an uneven number. The chances of hitting the target with the initial point being 3 or 4 inches away should be the same.

If the initial point is 4 inches away you will overshoot on a 6, 8 or 10. You will undershoot on a 2 but can bounce hit it. You will always hit on a 4.

The same thing applies if the initial point is 3 inches away. A 6, 8 or 10 still overhsoots. 2 still underhsoots but can bounce hit it and you still guaranteed a hit on a 4.

Also it doesnt make sense to measure from the center instead of the rear.

sebster's numbers are correct. The uneven numer of inches could actually be any value between the even number of inches (so the probability to hit a target 9" away from the initial guess is actually the same as any distance between 8" and 10").

sebster wrote:It's hard to explain, but the end result of all that is that the maximises the expected number of casualties is always 10" short of the centre of the enemy unit. That's the trick, judge the distance from the centre of enemy unit, not the front.

This isn't entirely true. The distribution of the probabilities isn't symmetrical (for example, probability to hit 4" over the initial placement is a lot higher than the probability to hit 16" over the initial placement). For this reason, the depth of the enemy unit matters when determining the optimal initial placement. Calculating the optimal placement would probably not lead to any large changes though (nothing larger than .5" I guess), so 10" before the centre of the enemy unit is probably the best estimate.


As far as wanting to force Look out Sir's goes: taking a look at the table posted by sebster, an initial placement of 10" in front of the Character will give the highest chance to force a look out sir. However, initial placement of 8" in front of the Character will still give a fairly high chance to force a look out sir, while having a higher probability of hitting the ranks behind the Character.


Warplightning Cannon considerations are a lot more complicated, as you would have to include the Thougness and Armour Save of the unit into the equation as the distance rolled on the artillery dice also influences the Strength of the shot. Also, the endpoint causes more damage (small blast) against units with multiple models.


Automatically Appended Next Post:

Question wrote:The chances of hitting the target with the initial point being 3 or 4 inches away should be the same.

No they shouldn't. Any cannon balls that roll 2" on the first dice roll and do not roll a misfire on the second will pass both 3" and 4". However, any cannon balls that roll 4" on the first dice roll will not hit a target 3" away, while they do hit a target 4" away...

Question wrote:That doesnt make sense. It is impossible for the artillery dice to roll an uneven number. The chances of hitting the target with the initial point being 3 or 4 inches away should be the same.

You're misreading the table. It isn't showing the probability of hitting the target if you pick 3" short of it, it's showing the odds of a cannon ball affecting a spot 3" from where you pick, and that spot alone.

If the initial point is 4 inches away you will overshoot on a 6, 8 or 10. You will undershoot on a 2 but can bounce hit it. You will always hit on a 4.

The same thing applies if the initial point is 3 inches away. A 6, 8 or 10 still overhsoots. 2 still underhsoots but can bounce hit it and you still guaranteed a hit on a 4.

You won't hit a spot 3" from the target if you roll a 4 on the first roll. That accounts for the difference between 3" and 4".

Also it doesnt make sense to measure from the center instead of the rear.

Of course it does. Because by only measuring from the rear, you're not accounting for the possible waste of over-penetration (where a shot lands in the midst of the unit, and then wastes much of it's potential damage by blowing past the back rank).


Automatically Appended Next Post:

Airmaniac wrote:This isn't entirely true. The distribution of the probabilities isn't symmetrical (for example, probability to hit 4" over the initial placement is a lot higher than the probability to hit 16" over the initial placement). For this reason, the depth of the enemy unit matters when determining the optimal initial placement. Calculating the optimal placement would probably not lead to any large changes though (nothing larger than .5" I guess), so 10" before the centre of the enemy unit is probably the best estimate.

Ah yes, you're right. I didn't take a close enough look at my own figures, and assumed they'd be largely symmetrical, when they're not. Still, like you say, it probably doesn't make that much of a difference.

As far as wanting to force Look out Sir's goes: taking a look at the table posted by sebster, an initial placement of 10" in front of the Character will give the highest chance to force a look out sir. However, initial placement of 8" in front of the Character will still give a fairly high chance to force a look out sir, while having a higher probability of hitting the ranks behind the Character.

Yeah, 10" from the centre of the unit if you want to target infantry, 8" from the front if you want to maximise your chance of sniping a character seems a pretty good rule of thumb.

Warplightning Cannon considerations are a lot more complicated, as you would have to include the Thougness and Armour Save of the unit into the equation as the distance rolled on the artillery dice also influences the Strength of the shot. Also, the endpoint causes more damage (small blast) against units with multiple models.

I'll leave that to someone else to figure out...

I've got shooting solutions for skaven, given unit size and unit toughness; where to fire to maximize damage.
After working out the math, I came to the conclusion that those things are stupidly under-priced, and way to good even with less than ideal aiming points.

-Matt

owever, any cannon balls that roll 4" on the first dice roll will not hit a target 3" away, while they do hit a target 4" away...

Except that all bases are at least 1 inches long, so if you pick a point 3 inches away from the front you will still hit the target same as if you picked 4 inches.

Question wrote:Except that all bases are at least 1 inches long, so if you pick a point 3 inches away from the front you will still hit the target same as if you picked 4 inches.

First up, the most common base size is 20mm, which less than an inch.

Second up, you're confusing the principle the calculations demonstrate with other detail. If you want to remodel the maths with a complete range of base sizes adjusted to inches to determine the exact number of models hit by each roll then you can. But the result will be the same, you should fire the shell 10 inches short of the centre of the enemy unit.

To make it messy, you're also very unlikely to be firing head on at a unit, you're most likely going to be firing at an angle across the bases.

-Matt

I almost always place 6 inches away from the target as on an average you will roll just enough to land either on top of the first guy or right in front of him. Its even better when your aiming at a large target like one of the new Shpynx models, your almost guaranteed a hit from the front or almost any angle from starting 6 inches out

You should fire 10 inches short of the rear, not the center.

Question wrote:You should fire 10 inches short of the rear, not the center.

I already explained your mistakes, and why it was best to aim for the centre. And then you just come back and repeat your initial claim again.

He did make it quite clear a couple posts ago this thread is pretty much done since what we have the math the different situations that pretty much sums up this thread.

I cant think of anything else that needs to be covered.

sebster wrote:

Question wrote:You should fire 10 inches short of the rear, not the center.

I already explained your mistakes, and why it was best to aim for the centre. And then you just come back and repeat your initial claim again.

Except that you are wrong.

10 inches from center of a 2 inch base. Rolls 6, bounces 2, misses by 1 inch. If it was 10 inches short from the rear of a 2 inch base, roll 6, bounce 2, you would hit it and would still have 0% chance to overshoot.

He did the math up above showing what the chances are depending where the initial point of impact is.

This math changes with certain things with larger models like the spider its 2 inches from the front so unless you misfire or it gets stuck it will hit it.

Point being it has been explained and dosnt need to keep being discussed.

Personally put it 10 inches just short of the back of the base unless I want to take out a line of infantry.
It works most of the time.

The math is there and he did the math what is there left?

HawaiiMatt wrote:I've got shooting solutions for skaven, given unit size and unit toughness; where to fire to maximize damage.
After working out the math, I came to the conclusion that those things are stupidly under-priced, and way to good even with less than ideal aiming points.

-Matt

I hate to be "That Guy", but it makes me glad the skaven book was just done...

That said, I usually started about 10" off the FRONT of the unit I'm shooting at when using a Warp Lightning Cannon. I have a decent track record of landing the template right in the middle of a unit, including wiping out a unit of Knights Errant that were within 7 or 8 inches of my cannon when it fired. That was a tense shot...

Dont worry you are not "that guy" they had a new book comming adn I do enjoy playing against their new book more.

Those cannons are great Took out my Hellcannon with a str 3 shot

Very nice luck steam