Heavy Weapons MathHammer

[jbaeza94]

All the below assume the model has moved and suffered a -1 to hit.

For D6, I will be using 3.5, since that is the average number

For D3, I will be using 2, since that is the average number

Formula is (Heavy X) x (To Hit) x (To Wound) x (Fail Armor Save) = Deaths/Unsaved Wounds per round of shooting.

(Model Wounds) / (Average Weapon Damage) / (Unsaved Wounds per Round of Shooting) = Rounds of Shooting to Kill (rounded up)

 

 

Assault Cannon VS

Dire Avenger (T3 SV4+)

                1.67 Deaths per Round of Shooting

Imperial Guardsman (T3 SV 5+)

                2.08 Deaths per Round of Shooting

Space Marine (T4 SV3+)

                1 Death per Round of Shooting

Terminator (T4 SV2+/5++)

                0.67 Unsaved Wounds per Round of Shooting   

                3 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.5 Unsaved Wounds per Round of Shooting     

                20 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.33 Unsaved Wounds per Round of Shooting   

                49 Rounds of Shooting to Kill

Cyclone Missile (Krak) VS

Dire Avenger (T3 SV4+)

                0.69 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.83 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.56 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.42 Unsaved Wounds per Round of Shooting   

                3 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.44 Unsaved Wounds per Round of Shooting   

                7 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.33 Unsaved Wounds per Round of Shooting   

                14 Rounds of Shooting to Kill

Cyclone Missile (Frag) VS

Dire Avenger (T3 SV4+)

                0.67 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                1.18 Deaths per Round of Shooting         

Space Marine (T4 SV3+)

                0.33 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.17 Unsaved Wounds per Round of Shooting   

                12 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.22 Unsaved Wounds per Round of Shooting   

                46 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.06 Unsaved Wounds per Round of Shooting   

                267 Rounds of Shooting to Kill

Grav Cannon VS

Dire Avenger (T3 SV4+)

                1.33 Deaths per Round of Shooting         

Imperial Guardsman (T3 SV 5+)

                1.33 Deaths per Round of Shooting         

Space Marine (T4 SV3+)

                1.11 Deaths per Round of Shooting         

Terminator (T4 SV2+/5++)

                0.88 Unsaved Wounds per Round of Shooting   

                2 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.56 Unsaved Wounds per Round of Shooting   

                9 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.44 Unsaved Wounds per Round of Shooting   

                19 Rounds of Shooting to Kill

Heavy Bolter VS

Dire Avenger (T3 SV4+)

                0.67 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.83 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.50 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.33 Unsaved Wounds per Round of Shooting   

                7 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.25 Unsaved Wounds per Round of Shooting   

                40 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.17 Unsaved Wounds per Round of Shooting   

                94 Rounds of Shooting to Kill

Heavy Flamer VS

Dire Avenger (T3 SV4+)

                1.56 Deaths per Round of Shooting         

Imperial Guardsman (T3 SV 5+)

                1.94 Deaths per Round of Shooting         

Space Marine (T4 SV3+)

                1.16 Deaths per Round of Shooting         

Terminator (T4 SV2+/5++)

                0.78 Unsaved Wounds per Round of Shooting   

                3 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.58 Unsaved Wounds per Round of Shooting   

                18 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.38 Unsaved Wounds per Round of Shooting   

                42 Rounds of Shooting to Kill

Lascannon VS

Dire Avenger (T3 SV4+)

                0.42 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.42 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.35 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.28 Unsaved Wounds per Round of Shooting   

                4 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.28 Unsaved Wounds per Round of Shooting   

                11 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.22 Unsaved Wounds per Round of Shooting   

                21 Rounds of Shooting to Kill

Missile Launcher (Krak) VS

Dire Avenger (T3 SV4+)

                0.42 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.42 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.35 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.28 Unsaved Wounds per Round of Shooting   

                4 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.28 Unsaved Wounds per Round of Shooting   

                11 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.17 Unsaved Wounds per Round of Shooting   

                27 Rounds of Shooting to Kill

Missile Launcher (Frag) VS

Dire Avenger (T3 SV4+)

                0.58 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.78 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.29 Deaths per Round of Shooting         

                4 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.15 Unsaved Wounds per Round of Shooting   

                14 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.19 Unsaved Wounds per Round of Shooting   

                53 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.05 Unsaved Wounds per Round of Shooting   

                320 Rounds of Shooting to Kill

Multi-Melta VS

Dire Avenger (T3 SV4+)

                0.42 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.42 Deaths per Round of Shooting         

                3 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.42 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.28 Unsaved Wounds per Round of Shooting   

                4 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.33 Unsaved Wounds per Round of Shooting   

                9 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.21 Unsaved Wounds per Round of Shooting   

                21 Rounds of Shooting to Kill

Plasma Cannon VS

Dire Avenger (T3 SV4+)

                0.83 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.83 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.56 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.44 Unsaved Wounds per Round of Shooting   

                3 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.42 Unsaved Wounds per Round of Shooting   

                12 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.22 Unsaved Wounds per Round of Shooting   

                37 Rounds of Shooting to Kill

Plasma Cannon (Supercharged) VS

Dire Avenger (T3 SV4+)

                0.83 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Imperial Guardsman (T3 SV 5+)

                0.83 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Space Marine (T4 SV3+)

                0.69 Deaths per Round of Shooting         

                2 Rounds of Shooting to Kill

Terminator (T4 SV2+/5++)

                0.83 Unsaved Wounds per Round of Shooting   

                2 Rounds of Shooting to Kill

Rhino (T7 SV3+)

                0.56 Unsaved Wounds per Round of Shooting   

                9 Rounds of Shooting to Destroy

Land Raider (T8 SV2+)

                0.33 Unsaved Wounds per Round of Shooting   

                25 Rounds of Shooting to Kill

[Interrogator Stobz]

:tu: ;)

 

Thanks for bringing this here :D

 

Any chance of adding Heavy Flamer calcs in there?

 

 

 

Stobz

[RayJ]

Looks like your big weapons (missiles and lascannons) aren't factoring in multiple damage on failed saves against rhinos and land raiders. That calculation is very important in those cases.

[jbaeza94]

Looks like your big weapons (missiles and lascannons) aren't factoring in multiple damage on failed saves against rhinos and land raiders. That calculation is very important in those cases.

yes that is true. i dont know of a true way to calculate it. On a Damage d6 you should count as 3.5 and a Dd3 as 2, that is the average number on the dice. what i can put in is the average it would take to kill the vehicles, such as 9 multimelta shots to down a a rhino (3 shots for one unsaved wound, doing 3.5 per unsaved wound)

[jbaeza94]

Thanks for bringing this here

Any chance of adding Heavy Flamer calcs in there?

Stobz

Stobz, i added in the Heavy Flamer for you.

[Interrogator Stobz]

So a HF will kill a Landraider quicker than a Multimelta, lolz.

 

Thanks for the maths Brother :tu:

[jbaeza94]

So a HF will kill a Landraider quicker than a Multimelta, lolz.

Thanks for the maths Brother

lol not quite. A HF causes more unsaved wounds vs a LR, but the Multimelta does more D per wound. 43 HF shots vs 22 MM shots. Well, on average.

[Interrogator Stobz]

Ahah, you have not added the new Damage mechanic into your equations.  

 

Any chance of doing that? It makes a hell of a difference in the end as to which weapon is best or not for each job.

[jbaeza94]

Ahah, you have not added the new Damage mechanic into your equations.  

 

Any chance of doing that? It makes a hell of a difference in the end as to which weapon is best or not for each job.

i did, but only for multi damage weapons. ill add it in for all of them.

[Interrogator Stobz]

Man, I'm a nag aye?

You're too cool though, thanks heaps

The lesson in red is that you might as well ignore vehicles in 8th, just wait and kill the squishy contents when they get out.

[jbaeza94]

Man, I'm a nag aye?

You're too cool though, thanks heaps

The lesson in red is that you might as well ignore vehicles in 8th, just wait and kill the squishy contents when they get out.

haha no way Stobz, i just want it to be as easily understood as possible. Think of me as GW and you as my play tester. i write something, you tell me whats wrong, so i fix by adding more information, culminating in way too much information, leaving you even more confused then when you started lol. In all seriousness though, i may just get rid of hits and wounds, and just leave unsaved wounds and shots to kill, to make it easier to read, what do you think?

But i agree, vehicles are really tough and hard to kill. you need to dedicate allot of firepower to it. this is good for VenDreads, especially since they regain a wound every turn. I just hope tyranids arent this hard to kill.

[Ezzeran]

Man, I'm a nag aye?

 

 

 

 

The lesson in red is that you might as well ignore vehicles in 8th, just wait and kill the squishy contents when they get out.

This is generally what I've been leaning towards too. I'm not even sure it's worth engaging most vehicles, at least not with these weapons.

 

Other things I'd be curious about are Predator autocanons and twin autocannons. Mortis dreads return, perhaps? Heavy 8 Str 7 D2 on a Ven dread might be a decent way to go.

 

Ezz

[Interrogator Stobz]

Yep; either ave kills of MEQ,TEQ,GEQ,DAEQ etc. per round, or number of rounds firing a weapon (shots is ambiguous too) to kill a vehicle. 

 

I'd add it as a summary at the bottom (so math can be checked), maybe in a table. And is the CY Krak correct vs. LR? 14 seems low.

[jbaeza94]

Yep; either ave kills of MEQ,TEQ,GEQ,DAEQ etc. per round, or number of rounds firing a weapon (shots is ambiguous too) to kill a vehicle. 

 

I'd add it as a summary at the bottom, maybe in a table. And is the CY Krak correct vs. LR? 14 seems low.

Rounds of firing sounds like a much better word choice. thanks. ill condense it all by weapon type, thanks man. I'll call it my 8th edition, everything simplified. lol

 

And 14 Cyclone is correct. 16 wounds / 3.5 Damage per unsaved wound = 4.57 wounds needed to kill it. 4.57 wounds/ .33 wounds per shot = 13.85 or 14 Shots

[jbaeza94]

Hey Stobz, check it out now. everything is by weapon type and generally less cluttered. is it to your liking? lol 

[Interrogator Stobz]

Haha, lol.

 

Looks really cool; I'll have to trust your maths, but it seems like LRCs will survive all battle midfield shooting 37 times per turn. Two for the Win.

[Wyzariel]

Haha, lol.

 

Looks really cool; I'll have to trust your maths, but it seems like LRCs will survive all battle midfield shooting 37 times per turn. Two for the Win.

I was thinking of a cheese list that has Azrael in the middle of a formation of Land Raider Crusaders, with a techmarine inside each one of them... The LRC's will have 4++ from Azrael and can re-roll all failed to hit. They will also conveniently block all line of sight to Azrael.

[Teetengee]

Also, these are going to underestimate actual time to death, because as far as I can tell jbaeza isn't accounting for excess wounds from damage being discounted. Won't usually matter, but for things like lascannons that deal d6 damage per shot, it becomes much more significant.

On the other hand, I imagine a lot of weapons won't be moving before firing, which will help things.

[Ezzeran]

All of this is confirming my worst fears:

 

ALL HAIL OUR GUARD TANK COMPANY OVERLORDS! XD

 

Ezz

[jbaeza94]

Also, these are going to underestimate actual time to death, because as far as I can tell jbaeza isn't accounting for excess wounds from damage being discounted. Won't usually matter, but for things like lascannons that deal d6 damage per shot, it becomes much more significant.

 

On the other hand, I imagine a lot of weapons won't be moving before firing, which will help things.

Can you explain excess wounds from damage being discounted?

 

If you mean how long it takes to remove all wounds with multiple damage weapons, then it is accounted for. For d6 damage I used 3.5, which is the average number of damage it will do. For d3 I used 2, which is the average. It's easiest seen with the cyclone krak missile vs land raider. 14 rounds of shooting to kill a 16 wound model.

 

This is what you meant right? Or did I totally miss the mark lol

[stuka06]

What he means, I think, is that a lasercanon will indeed do 3.5 damage, but only to a single model, so 2 lasercanon wounds, will still only kill 2 terminators, not 3, etc.

[jbaeza94]

The math is for the probability of unsaved wounds.

For example,

grav cannon does 1.11 unsaved wounds vs space marines. although the weapon does 2 damage on average, it still only kills 1 marine for every time its fired. so to wipe a squad of 10, it'd be a little under 10 shots, despite d3 damage.

 

 

Rounds of Shooting to Kill, is how many times you would need to fire that weapon to kill a single model.

 

 

EDIT: i dont know how else to write the list, but i am not trying to say excess damage rolls over. i guess to fully understand the list above you will need a grasp of how the damage mechanic works.

[Teetengee]

 

Also, these are going to underestimate actual time to death, because as far as I can tell jbaeza isn't accounting for excess wounds from damage being discounted. Won't usually matter, but for things like lascannons that deal d6 damage per shot, it becomes much more significant.

 

On the other hand, I imagine a lot of weapons won't be moving before firing, which will help things.

Can you explain excess wounds from damage being discounted?

 

If you mean how long it takes to remove all wounds with multiple damage weapons, then it is accounted for. For d6 damage I used 3.5, which is the average number of damage it will do. For d3 I used 2, which is the average. It's easiest seen with the cyclone krak missile vs land raider. 14 rounds of shooting to kill a 16 wound model.

 

This is what you meant right? Or did I totally miss the mark lol

 

Let's say I have a weapon that fires once, fully ignores an enemy's armor, and does d3 damage per shot. I hit and wound 50% of the time (not that that is really possible in the 40k system, but let's just say so for a sec).

 

Each time I fire the weapon, I do an average of 2 wounds to the target, if they target has three+ wounds left to take.

(1 shot*1/2 hit chance*(1+2+3)/3 wounds per shot=1*.5*2=1 wounds per shot)

 

Let's say a target starts with 3 wounds. We would expect three firings of the weapon would on average take out the target. This isn't quite correct.

 

Each time I fire, I see the following probabilities:

1/2 chance of no wounds

1/6 chance of 1 wound

1/6 chance of 2 wounds

1/6 chance of 3 wounds

 

However, that is only true if the target has 3 wounds left to lose. Overkill doesn't contribute to my averages.

2 wounds left:

1/2: 0 wounds, 1/6 1 wound, 1/3: 2 wounds

1 wound left:

1/2: 0 wounds, 1/2 1 wound

 

 

So against a target with 3 wounds remaining, I average 1 wound per attack. Against a target with 2 wounds remaining, I average 5/6 wounds per attack. Against a target with 1 wound remaining, I average 1/2 wound per attack.

 

Therefore, here is a tree for analyzing number of shots necessary:

1/6 chance of dead from 3 wounds in 1 additional shot

1/3 chance of dead from 2 wounds in 1 additional shot

1/2 chance of dead from 1 wound in 1 additional shot

1/6 chance of dropping from 3 to 1 wounds in 1 additional shot

1/6 chance of dropping from 3 to 2 wounds in 1 additional shot

1/6 chance of dropping from 2 to 1 wound in 1 additional shot

 

 

Therefore, if you have 1 wound left on the target, you have 1*(1/2)^1+2*(1/2)^2+3*(1/2)^3+...=2 shots on average to kill.

 

If you have 2 wound left on the target, you have (3*1/6+1*1/3)+(4*1/6+2*1/3)*1/2+(5*1/6+3*1/3)*(1/2)^2+...=8/3 or 2.667 shots on average to kill.

 

If you have 3 wounds left on the target, you have (1/6)*(11/3+3+1)+(1/2)*(1/6)*(14/3+4+2)+(1/2^2)*(1/6)*(17/3+5+3)+...=32/9 or 3.556 shots on average to kill.

 

 

Therefore, in truth there is an overhead due to overkill chances that causes direct calculations of average damage/shot to underestimate the true expected number of shots to kill a target. The actual numbers require summing some infinite series (though typically going out only a few iterations will be sufficient for most hand calculations). You will not that in the case of the example weapon above, the expected number of required shots to kill a target does not necessarily go down by 1 each time you reduce the target by the expected damage number of wounds. This is because the probabilities change as we know that the chance of killing it already didn't happen.

 

 

This error increases the more damage a weapon has the chances of dealing per shot relative to the wounds remaining in the target. A 20 wound vehicle doesn't deviate from the estimate provided by just expected damage on a single shot d3 damage weapon until determining how many wounds will be remaining after the 7th shot, for instance.

[jbaeza94]

Therefore, here is a tree for analyzing number of shots necessary:

1/6 chance of dead from 3 wounds in 1 additional shot

1/3 chance of dead from 2 wounds in 1 additional shot

1/2 chance of dead from 1 wound in 1 additional shot

1/6 chance of dropping from 3 to 1 wounds in 1 additional shot

1/6 chance of dropping from 3 to 2 wounds in 1 additional shot

1/6 chance of dropping from 2 to 1 wound in 1 additional shot

I understand this.

 

Therefore, if you have 1 wound left on the target, you have 1*(1/2)^1+2*(1/2)^2+3*(1/2)^3+...=2 shots on average to kill.

 

If you have 2 wound left on the target, you have (3*1/6+1*1/3)+(4*1/6+2*1/3)*1/2+(5*1/6+3*1/3)*(1/2)^2+...=8/3 or 2.667 shots on average to kill.

 

If you have 3 wounds left on the target, you have (1/6)*(11/3+3+1)+(1/2)*(1/6)*(14/3+4+2)+(1/2^2)*(1/6)*(17/3+5+3)+...=32/9 or 3.556 shots on average to kill.

 

I don't understand this. Can you just explain what each number stands for? Im just not sure where some of the numbers come from. I'm sure I'll understand it with a label.

 

 

I'm sure you followed my math. It seems to be over simplified, with a larger margin of error, but I have a feeling it's close. Let me know. Here's how I figured how many shots to kill.

1 damage weapons was just wounds/unsaved wounds. So a rhino vs assault cannon is

10/0.50 = 20 rounds of firing to kill.

D3 damage weapons, I did wounds/2 (d3 average)/ unsaved wounds. Rhino vs grav.

10/2/0.56=8.93, rounded up to 9. So 9 rounds of shooting.

D6 is the same thing but with 3.5 instead. Lascannon vs rhino

10/3.5/.28 =10.20, rounded up to 11.

 

My logic is this. I have a 10 wound model, if my weapon averages 2 damage per unsaved wound (d3), then it should take about 5 unsaved wounds kill it. If my weapon causes an unsaved wound .56 of the time, then that means I need to fire it 8.93 times to achieve 5 unsaved wounds. I can't fire .93 times, so its just get rounded up.

 

 

Like I said its not perfect, very Barney style. But I'm sure it's a pretty good approximation of how long it would take.

 

Edit: but hey, get me on the same page as you, and ill definitely update the whole thing.

So if you could:

Label your math problem, With what each thing stands for, and insert an actual example from above (grav vs rhino would be good, multiple damage vs multiple wound, and a .56 chance to wound.) You could do it here or message me. Thanks

[Darkangeldentist]

Very useful guide jbaeza94. For the sake of completeness could you please add the plasma storm battery to the list of weapons. It's profile is quite markedly different from a plasma cannon with D6 shots and damage values of 2 & 3. Many thanks in advance.