Anti-Tank Shooting Analysis

Here goes a similar analysis to the shooting weapon analysis against infantry, but this time covering vehicles. This is a shooting analysis, so ignores melee options, which our limited options might make you interested in checking out.

Damage against vehicles is more complicated than against infantry, so first I will explain my methodology with an example of a Heat Lance in melta range against a Dreadnought:

First we work out the odds of scoring at least a hull point against the vehicle
Unsaved hull points inflicted = shots × hit rate × armour penetration rate × unsaved rate
Unsaved HP = 1 × 2/3 × 26/36 × 1 = 13/27

Note for a melta weapon needing 6 to glance there are 5 combinations of two dice equal to six and 21 combinations of seven or higher, so 26/36 chance of glancing or penetrating the armour.

Then we work out the average number of hull points required to destroy the target.
Probability of penetrating hit following a hull point = pen hit combinations / (pen hit combinations + glance hit combinations)
p(PH|HP) = 21 / (21 + 5) = 21/26
The probability of an explode result following a hull point is therefore the last result multiplied by the explode chance. This is the probability of destroying the Dreadnought with the first damaging result.
p1 = 21/26 × 1/3 = 7/26
The probability of not destroying the Dreadnought with the first damaging result is therefore 19/26 and the probability of needing two damaging results is:
p2 = 7/26 × 19/26 = 133/676
And the probability of needing three damaging results is whatever is left over
p3 = 1 - p1 - p2 = 361/676
The average hull points required is the weighted average of the three probabilities:
Ave HP required = 1 × 7/26 + 2 × 133/676 + 3 × 361/676 = 2.26

We can then divide the average number of hull points required to destroy the Dreadnought with the average number of hull points inflicted by firing a Heat Lance to get the average number of firings required:
Ave Firings = Ave HP required / Ave HP inflicted
Ave Firings = 2.26 / (13/27) = 4.70

The analysis for almost all weapons shows that most weapons need 2.6 to 3 hull points to destroy a 3 hull point target, so explode results are not very common. I have ignored double immobilised results, because they are even more uncommon and make the math more complex for minimal difference in the results.

The only math step left is combinations of different weapons, and comparing options on a per 100 points basis. To combine weapons, I used a percentage killed approach, so a Heat Lance would on average kill 1 / 4.70 = 21% of a Dreadnought, so four Heat Lances (84%) a Blaster (12% using the same methodology) would combine for 96% killed. Then the same normalisation process as was used in the infantry analysis was applied (divide by the unit cost and multiply by 100) to identify the unit efficiency against the target.

Now for the interesting bit - the results!

I have considered six different targets for the various shooting options that can take out vehicles in the Dark Eldar Codex:
1) Dark Eldar Venom (low armour and HP, open topped with invulnerable save)
2) Rear Armour of most vehicles (AV10 / 3 HP)
3) Rhino with Smoke (AV11 / 3 HP / 5+ cover)
4) Dreadnought (AV12 / 3 HP)
5) Predator front armour (AV13 / 3 HP)
6) Land Raider (AV14 / 4 HP)

In general I have ignored cover saves (except for the Rhino). As we don't have ignores cover options, the efficiency order would be unchanged by adding cover saves.


So, after all of that analysis, the results probably will not provide too many surprises. Our best options against most targets are:
1) Heat Lance Scourges
2) Haywire Blaster Scourges
3) Kabalite Trueborn in a Raider with Dark Lance (no WWP character)
4) Dark Lance Ravagers

However, Scourges are generally reliant on Deep Strike meaning mishap risks (especially for Heat Lance Scourges) and not being effective turn one.

Trueborn score well, but with the FAQ ruling on Jink affecting passengers their marginal advantage over Ravagers is negated by being easier to destroy and shorter range.

The most reliable anti-tank option that can be effective from turn one is the Dark Lance Ravager, especially if you can sit them in cover with a good view of the battlefield. They are still decidedly average, they just happen to be the best option we have available.

Our flyers do OK, but if you want anti-tank from flyers, I would suggest a Crimson Death formation from Eldar to join your Dark Eldar list instead.

Disintegrators are effective against AV10, and if you want the most interesting results from the table, consider Mandrakes and Shredder armed Trueborn are among our best options against rear armour!

Excellent work. I'd love to see similar charts for other codexes to see how we compare.

I don't see any mention of ranges here, but based on a cursory examination of the results, my first guess would be that you simply assumed each unit would get the ideal range for the weapon they were equipped with. Is that correct?

Betray - yes I have assumed the weapons are in range and for melta weapons within 1/2 range. The outputs do need some thought in terms of how practical the top scoring options are, which is why I mentioned the issues for Scourges and Trueborn when compared to Ravagers.

Count - not too hard to add in other codex units for comparison if you have specific units in mind. If you wanted say all the Eldar, Corsair, Harlequins, Marines, etc then it is a massive undertaking. As a quick spoiler Dark Eldar feel sad when seeing Scatter Laser Windriders and Hornets, let alone Fire Dragons and Wraithguard.

Kantalla wrote:

The outputs do need some thought in terms of how practical the top scoring options are, which is why I mentioned the issues for Scourges and Trueborn when compared to Ravagers.

I noticed that you said that, and agreed with your take on pretty much all of it, which is why my response to your post was uncharacteristically short from me!

I wasn't trying to attack your results or anything, just making sure I understood the information you presented, which I thank you for!

No wonder I'm so depressed whenever I try and figure out AT in a pure DE list.

Kantalla wrote:

Count - not too hard to add in other codex units for comparison if you have specific units in mind. If you wanted say all the Eldar, Corsair, Harlequins, Marines, etc then it is a massive undertaking. As a quick spoiler Dark Eldar feel sad when seeing Scatter Laser Windriders and Hornets, let alone Fire Dragons and Wraithguard.

Yeah, I figured Aspect Host Fire Dragons would be pretty much top tier and Hornets are ridiculously good for their points. Might be nice to see a (small) selection of other codex units that are typically used for AT as a comparison. So, Centurion Devs, Fire Dragons etc.

Just out of curiosity here, what about Scourges with Blasters? I'm assuming that option isn't considered because Haywires are available, which are of course fantastic against vehicles but lack the potential to punch soft targets.

Scourges with Blasters score the same as Trueborn in a Dark Lance Raider. They are inferior to Haywire Blasters against every armoured target and have shorter range. They are of course superior against infantry, but I wouldn't personally recommend them.

I have been putting together a comparative list for Eldar to see the difference in efficiency, and potentially get some options for improving our anti-tank punch. D-Weapons are messy mathematically, so I have made some simplifications to them (assuming they always get 2 hull points if they don't explode or devastating hit the target). I have included Haywire Blaster Scourges and Dark Lance Ravagers on the Eldar list to see how our best options compare:

Eldar have some really strong options available, and with Battle Brothers we can access them without any significant issues, and still remain essentially a Dark Eldar army. Here are some formation options if you don't take an Eldar CAD or Allied Detachment:

1) Aspect Host - Fire Dragons (either WWP character or Wave Serpent) and Warp Spiders
2) Hornet Swarm - 3 Pulse Laser Hornets will overkill some targets, but anything with a cover save will not have excessive overkill
3) Fist of Vaul - 2-3 Warp Hunters are a bit more efficient than Ravagers, and shouldn't overkill too often
4) Wasp Phalanx - Up to 6 individual Wasps - excellent at shredding light vehicles
5) Crimson Death - 3 Flyers with a cover save and better efficiency than our Ravagers

Or if you take an Allied Detachment or Eldar CAD, there are a lot of good options available (but you might start to get tempted to phase out the Dark Eldar).

What do the actual numbers in this last chart represent? Like 172 for aspect host fire dragons vs venom. What is the 172?

If you're talking about Eldar Craftworlders you're talking about another army. And if you want an army dedicated to anti-tank, you want the Queens of Melta. When I roll anti-tank hard, I roll Sisters in Immolators. Give them a Beastmaster as a proxy for a Canoness to make it fluffy (mon-keigh are beasts, right?) and drown em in twin linked melta.

TeenageAngst wrote:

If you're talking about Eldar Craftworlders you're talking about another army.

He knows that. The point was to compare to another army we were battle brothers with, and so could ally with easily.

Very nice work!
But also very disheartening to see how good the Eldar units really are. I knew they had the edge but this isnt just the edge, its the whole damn sword they got!

When I first saw the list with only DE units, then I thought I would give the Ravagers another chance.. I like the model and have used them a lot earlier.. But it takes 4 of them to take out a Land Raider (ok not the most common vehicle)! Or 1 units of Fire Dragons.. at 1/4 the cost.. a bit surprised at how good the FD are for their price, they need transport but still!!

I'm a fan of Corsair Reavers with melta. 10 Reavers with 4 meltaguns and jetpacks in a Sky Burners coterie will reliably deepstrike in melta range, melt whatever they shoot at, and then end up 18-20 inches away with their two jump moves. They're obsec and with a baron or void dreamer with shadowfield, even if their jumps don't get them to safety they can weather a round of shooting after they arrive. Just need Forgeworld to start selling the Corsair bits again so I can convert up a bunch of Kabalites...

BetrayTheWorld wrote:

What do the actual numbers in this last chart represent? Like 172 for aspect host fire dragons vs venom. What is the 172?

The numbers represent a "Kill Percent per 100 Points".

That means in the example of Fire Dragons vs a Venom, that 100 points of Fire Dragons have 172% of the shots they need (on average) to kill a Venom. The Fire Dragons at 120 points therefore would have 172% × 120/100 = 206% of the shots they would need on average.

Or more depressingly perhaps, a DL Ravager against a Rhino with 5+ cover has 27% × 125/100 = 34% of the shots to kill the Rhino. So, if you have six Ravagers in an army list, against Rhinos with smoke, you would expect to kill about two of them in a turn.

Hmm, I think I'd prefer to see it with the percentage chance of actually killing it, rather than % of shots needed on average. Makes it sort of laborous to read, and doesn't really give a clear idea of what you can expect from the unit.

Personally I like the points efficiency version rather than the kill percentage number, so you can legitimately compare a cheap unit like a Shuriken Cannon Vyper with an expensive unit like a Wraithknight. However, if you would like the other way around that is easy to present too:

Raw Percentages

Hmm...something is wrong with your calculations. I'm not sure what it is, as I haven't investigated, but you shouldn't be able to get over 100% chance to kill.

With squadrons you can sometimes go > 100% and still make perfect sense. However, the percentage isn't exactly a chance to kill an undamaged target.

The "Kill Percent" is more accurately the proportion of the average number of shots required to kill the target. On average it would take 2.25 Scatter Lasers to destroy a normal vehicle shooting at rear armour. 3 Windriders with Scatter Lasers therefore have 3/2.25 = 133% of the average shots required.

I took that approach, as it makes it fairly easy to add different types of weapons together, and also means you can add units together fairly easily too, so a Ravager and Scourges on average can destroy a Dreadnought in one round of shooting.

Warning math heavy post below, read at your own risk of bordem

Once you've calculated your probabilities of an individual shot glancing / penning a given vehicle the best method is binomial distribution for calculating odds of actually destroying it.

Calculations for 3 hull point vehicles

Three glances:
=IF(NumShots>2,BINOM.DIST.RANGE(NumShots,ChanceOfGlanceOrBetter,3,NumShots),0)
Explode:
=IF(WeaponAP<3,BINOM.DIST.RANGE(NumShots,ChanceOfPen*((3-WeaponAP)/6),1,NumShots),0)
Double Immobilized:
=IF(D3>1,BINOM.DIST.RANGE(NumShots,ChanceOfPen*(1/6),2,NumShots),0)

Total Destroy Calc:
1 - (1-ThreeGlances)*(1-Explode)*(1-DoubleImmobilized)

HeatLance Scourge unit vs. a Rhino 53.74% (in melta range)

if anyone cares for the Math for Glance or better (Melta, haywire, and Lance are 0 or 1 values):

ChanceNum=6+(5*Melta)-(MAX(AV*(1-Lance),MIN(12*Lance,AV))-WeaponStrength)+1
GlanceOrBetter = MAX((ChanceNum/(6+(5*Melta))),(HayWire*5/6)) * HitRate * TargetFailSaveRate
ChanceOfPen = GlanceOrBetter * =MAX(IF(ChanceNum>1,(ChanceNum-1)/ChanceNum,0),(Haywire/6))

On heatlance scourges it's also safest to place the initial deep striker within 1" of a target vehicle that has a 9" void around it, 1/3 chance to not scatter, then if you do scatter in the direction of the vehicle there is only a 1/6 chance of the scattering being less than 5" (you'll over shoot the vehicle safely), if you scatter back there is only a 1/6 chance that the scatter will be greater than 9" (so you can still be in melta range).

Something the numbers don't tell you though is how you can actually make use of those advantages, heatlance scourge is a great example of being one of the most effective vehicle killers out there it's not very useful for a lot of games when all you want to do is get your opponent out of transports early on before they drive them across the field, not blow them up on your side of the table.

Kantalla wrote:

With squadrons you can sometimes go > 100% and still make perfect sense. However, the percentage isn't exactly a chance to kill an undamaged target.

That's what I was talking about. Not changing it away from the "kills per 100 points" model or anything. Just changing it so that the numbers accurately represented the percentage chance to kill an undamaged target. Such a calculation, while certainly more difficult math-wise to calculate, is of far greater practical value, is all I was saying.

Example: Knowing that a unit of Haywire Scourges has roughly a 79% chance to destroy an undamaged venom, including a 16% chance of it exploding is, at least in my opinion, more valuable information than just calculating an arbitrary number on a chart that's only practical purpose is to rank said item on the chart.

Don't get me wrong. Your method is fine for this chart, and I'm sure it's an accurate representation of rankings. I was just hoping to put the chart to more practical, everyday use by using it as a quick reference for things like I demonstrated above. No big deal, though!

Betray - I understand what it is you are after now. It will take a bit of work but I will try to get that sorted out over the next week or so. I can see there is some value in a chart of destroyed chance.

I was aiming for a slightly different measure, as I wanted to know what the most efficient use of points for killing tanks was. I think I have captured that reasonably well, and for my own use I find the outputs very valuable, and not arbitrary in the slightest.

The key limitation of a destroyed chance table is that explode results are reasonably uncommon, so most vehicles need to be shot at with multiple weapons, or multiple units in order to destroy them. A unit that takes a hull point or two off the target is still really valuable, but could be underestimated by a destroyed chance chart.

As an example, consider Scourges against a Dread:
With Haywire Blasters there is a 2/3 × 5/6 = 5/9 chance of a hull point and 0 chance of explode
Destroy chance is 40%

With Heat Lances there is a 2/3 × 26/36 = 13/27 chance hull point and 2/3 × 21/26 × 1/3 = 7/39 chance explode
Destroy chance is 55% explode + 27% chance to wreck = 82%

I think that overstates the advantage of Heat Lances substantially.

Seshiru - is there a good way you can think of to deal with different weapons on the same unit? If we were looking at say a Falcon with Pulse Laser, Scatter Laser and Shuriken Cannon, each potentially with its own odds of hull point, immobilise and explode, how would you get the odds of a double immobilise for example? Is it the odds of each weapon getting two immobilises, plus the odds of one each, plus the odds of each of three combinations of one from two weapons and zero from the other?

Once again, great job Kantalla. Did you include for the double immobilized resulting in a HP?

Regardless, I believe the purpose of these charts was to see the relative usefulness of our AT units. I can clearly see what units are good vs high AV units, and what is ok at low AV.

I would be interested to see how high some heat lance reavers score on the charts.

People, please keep in mind that these eldar units are widely considered to be the best in the game. Comparing DE anything to a wraithguard hauling around D shouldent be surprised.

Kantalla wrote:

With Heat Lances there is a 2/3 × 26/36 = 13/27 chance hull point and 2/3 × 21/26 × 1/3 = 7/39 chance explode
Destroy chance is 55% explode + 27% chance to wreck = 82%

So the chance of neither of those things happening is (100%-55%)*(100%-27%) = 32.4%
making the chance of either one of those things happening is 67.6%

Kantalla wrote:

Seshiru - is there a good way you can think of to deal with different weapons on the same unit? If we were looking at say a Falcon with Pulse Laser, Scatter Laser and Shuriken Cannon, each potentially with its own odds of hull point, immobilise and explode, how would you get the odds of a double immobilise for example? Is it the odds of each weapon getting two immobilises, plus the odds of one each, plus the odds of each of three combinations of one from two weapons and zero from the other?

I had not considered this, probably a bayesian network would do it.
I'll try something and see what I can come up with

EDIT - had a mistake in handling 2D6s properly that Betray caught, will follow up with the correct handling for double immobilized on 2D6 once I fix my functions