
  AntiTank Shooting Analysis  
 
Author  Message 

Kantalla Wych
Posts : 723 Join date : 20151221
 Subject: AntiTank Shooting Analysis Sat Aug 27 2016, 14:13  
 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(PHHP) = 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 antitank 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 antitank 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! 
   Count Adhemar Dark Lord of Granbretan
Posts : 7070 Join date : 20120426 Location : London
 Subject: Re: AntiTank Shooting Analysis Sat Aug 27 2016, 17:27  
 Excellent work. I'd love to see similar charts for other codexes to see how we compare. _________________ You have been weighed, you have been measured, and you have been found wanting. In what world could you possibly beat me? 
   BetrayTheWorld Trueborn
Posts : 2665 Join date : 20130404
 Subject: Re: AntiTank Shooting Analysis Sat Aug 27 2016, 23:53  
 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? _________________ 
   Kantalla Wych
Posts : 723 Join date : 20151221
 Subject: Re: AntiTank Shooting Analysis Sun Aug 28 2016, 00:32  
 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. 
   BetrayTheWorld Trueborn
Posts : 2665 Join date : 20130404
 Subject: Re: AntiTank Shooting Analysis Sun Aug 28 2016, 03:34  
  @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! _________________ 
   Woozl Kabalite Warrior
Posts : 150 Join date : 20150103
 Subject: Re: AntiTank Shooting Analysis Sun Aug 28 2016, 19:34  
 No wonder I'm so depressed whenever I try and figure out AT in a pure DE list. 
   Count Adhemar Dark Lord of Granbretan
Posts : 7070 Join date : 20120426 Location : London
 Subject: Re: AntiTank Shooting Analysis Sun Aug 28 2016, 21:58  
  @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. _________________ You have been weighed, you have been measured, and you have been found wanting. In what world could you possibly beat me? 
   Ikbih Slave
Posts : 3 Join date : 20160824
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 10:02  
 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. 
   Kantalla Wych
Posts : 723 Join date : 20151221
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 10:52  
 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. 
   Kantalla Wych
Posts : 723 Join date : 20151221
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 11:15  
 I have been putting together a comparative list for Eldar to see the difference in efficiency, and potentially get some options for improving our antitank punch. DWeapons 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  23 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). 
   BetrayTheWorld Trueborn
Posts : 2665 Join date : 20130404
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 16:35  
 What do the actual numbers in this last chart represent? Like 172 for aspect host fire dragons vs venom. What is the 172? _________________ 
   TeenageAngst Incubi
Posts : 1556 Join date : 20160829
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 16:37  
 If you're talking about Eldar Craftworlders you're talking about another army. And if you want an army dedicated to antitank, you want the Queens of Melta. When I roll antitank hard, I roll Sisters in Immolators. Give them a Beastmaster as a proxy for a Canoness to make it fluffy (monkeigh are beasts, right?) and drown em in twin linked melta. 
   BetrayTheWorld Trueborn
Posts : 2665 Join date : 20130404
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 16:42  
  @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. _________________ 
   goofydk Hellion
Posts : 49 Join date : 20130531 Location : Copenhagen
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 17:28  
 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!! 
   JamesB Slave
Posts : 1 Join date : 20160829
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 20:07  
 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 1820 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... 
   Kantalla Wych
Posts : 723 Join date : 20151221
 Subject: Re: AntiTank Shooting Analysis Mon Aug 29 2016, 21:03  
  @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. 
   BetrayTheWorld Trueborn
Posts : 2665 Join date : 20130404
 Subject: Re: AntiTank Shooting Analysis Tue Aug 30 2016, 01:31  
 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. _________________ 
   Kantalla Wych
Posts : 723 Join date : 20151221
    BetrayTheWorld Trueborn
Posts : 2665 Join date : 20130404
 Subject: Re: AntiTank Shooting Analysis Tue Aug 30 2016, 17:20  
 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. _________________ 
   Kantalla Wych
Posts : 723 Join date : 20151221
 Subject: Re: AntiTank Shooting Analysis Tue Aug 30 2016, 21:09  
 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. 
   Seshiru Sybarite
Posts : 405 Join date : 20120703
 Subject: Re: AntiTank Shooting Analysis Tue Aug 30 2016, 21:45  
 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*((3WeaponAP)/6),1,NumShots),0) Double Immobilized: =IF(D3>1,BINOM.DIST.RANGE(NumShots,ChanceOfPen*(1/6),2,NumShots),0)
Total Destroy Calc: 1  (1ThreeGlances)*(1Explode)*(1DoubleImmobilized)
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*(1Lance),MIN(12*Lance,AV))WeaponStrength)+1 GlanceOrBetter = MAX((ChanceNum/(6+(5*Melta))),(HayWire*5/6)) * HitRate * TargetFailSaveRate ChanceOfPen = GlanceOrBetter * =MAX(IF(ChanceNum>1,(ChanceNum1)/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. _________________ The worst sort of protection is confidence. The best defense is suspicion.

   BetrayTheWorld Trueborn
Posts : 2665 Join date : 20130404
 Subject: Re: AntiTank Shooting Analysis Tue Aug 30 2016, 21:57  
  @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 mathwise 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! _________________ 
   Kantalla Wych
Posts : 723 Join date : 20151221
 Subject: Re: AntiTank Shooting Analysis Wed Aug 31 2016, 09:09  
 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? 
   fisheyes Wych
Posts : 843 Join date : 20160218
 Subject: Re: AntiTank Shooting Analysis Wed Aug 31 2016, 14:56  
 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. 
   Seshiru Sybarite
Posts : 405 Join date : 20120703
 Subject: Re: AntiTank Shooting Analysis Wed Aug 31 2016, 16:42  
  @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 _________________ The worst sort of protection is confidence. The best defense is suspicion.
Last edited by Seshiru on Wed Aug 31 2016, 20:45; edited 1 time in total 
    AntiTank Shooting Analysis  

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