
  When exactly are Dark Lances better than Disintegrators?  
 
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Lord Johan Kabalite Warrior
Posts : 169 Join date : 20160721 Location : Coming to a realspace near you
 Subject: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 16:53  
 This was being discussed in the raider vs venom thread. It is a more generally interesting issue so I made its own thread for it. I wanted to solve this question analytically. It could be done with my old thread with its complex logicbased thingy or with Lord Splata's calculator, although the same caveat applies to both  they don't do d6s and d3s correctly. I wanted to develop some new formulas that will give more accurate results using step functions rather than logic. Please bear with me 'cause my math is rusty and I don't get to use it a lot at work these days. If you want the in depth explanation I spoilered it below.  math:

Here's some functions: 1. To wound roll You have this many chances out of six to wound. this is W roll =1+UnitStep(2X(Y+1))+UnitStep(XY)+UnitStep(X(Y+1))+UnitStep(XY*2) because 6 always wounds, if str > 1/2 toughness 5+ wounds, if str = toughness 4+ wounds, if str>toughness 3+ wounds, if str >= 2* toughness 2+ wounds Unitstep defines H(0)=1. It looks like below. 2. To wound probability is the above / 6 3. If damage = 2 then damage is min(W, D). If damage = d6 then damage is (1+min(w,2)+min(w,3)+min(w,4)+min(w,5)+min(w,6))/6. It looks like below. 4. The wounds multiplier vs AP is given by min(1(7SvAP)/6,1) which simplifies to min((SV+AP1)/6,1) and looks like this for Sv3+ with variable AP. 5. Then the entire expression for wounds at bs3+ is Dissie: 2/3 (to hit) * 3 (shots) * (1+UnitStep(10(Y+1))+UnitStep(5Y)+UnitStep(5(Y+1))+UnitStep(5Y*2))/6 * min(W,2) * min((SV+2)/6,1) DL: 2/3 (to hit) * (1+UnitStep(16(Y+1))+UnitStep(8Y)+UnitStep(8(Y+1))+UnitStep(8Y*2))/6 * (1+min(w,2)+min(w,3)+min(w,4)+min(w,5)+min(w,6))/6 * min((SV+3)/6,1) and we can table these for, say Sv3+ and 6 wounds and here is what that would look like. So that gives us the general equation to solve which is 2/3*(1+UnitStep(16(Y+1))+UnitStep(8Y)+UnitStep(8(Y+1))+UnitStep(8Y*2))/6*(1+min(w,2)+min(w,3)+min(w,4)+min(w,5)+min(w,6))/6*min((SV+3)/6,1) > 2/3*3*(1+UnitStep(10(Y+1))+UnitStep(5Y)+UnitStep(5(Y+1))+UnitStep(5Y*2))/6*min(w,2)*min((SV+2)/6,1) Let's consider first SV = 3 then it simplifies to (1+UnitStep(16(Y+1))+UnitStep(8Y)+UnitStep(8(Y+1))+UnitStep(8Y*2))/6*(1+min(w,2)+min(w,3)+min(w,4)+min(w,5)+min(w,6))/6 > 3*(1+UnitStep(10(Y+1))+UnitStep(5Y)+UnitStep(5(Y+1))+UnitStep(5Y*2))/6*min(w,2)*5/6 and further to (1+UnitStep(16Y1)+UnitStep(8Y)+UnitStep(8Y1)+UnitStep(8Y*2))*(1+min(w,2)+min(w,3)+min(w,4)+min(w,5)+min(w,6)) > (1+UnitStep(10Y1)+UnitStep(5Y)+UnitStep(5Y1)+UnitStep(5Y*2))*min(w,2)*15 unfortunately this was too complex for Wolfram Alpha still, so assumed w>=2 and solved instead as (1+UnitStep(16(Y+1))+UnitStep(8Y)+UnitStep(8(Y+1))+UnitStep(8Y*2))*(1+2+min(w,3)+min(w,4)+min(w,5)+min(w,6)) > (1+UnitStep(10(Y+1))+ UnitStep(5Y)+UnitStep(5(Y+1))+UnitStep(5Y*2))*30, w>=2, Y>0 which yields the following solutions 1. w>5, 5 < Y <= 8 2. w>5, 9 < Y <= 15 3. 3<w<=5, 5 < Y <= 7 4. 3<w<=5, 9 < Y <= 15 there are no solutions for w = 1 so the assumption was justified. Then let's consider Sv4+. we can assume w>=2 since this is a situation where lance is worse. it's now (1+UnitStep(16(Y+1))+UnitStep(8Y)+UnitStep(8(Y+1))+UnitStep(8Y*2))*(1+2+min(w,3)+min(w,4)+min(w,5)+min(w,6)) > (1+UnitStep(10(Y+1))+ UnitStep(5Y)+UnitStep(5(Y+1))+UnitStep(5Y*2))*30*6/5, w>=2, Y>0 and solutions are 1. w>4, 5<Y<=7 2. w>4, 9<Y<=15 Finally Sv2+. Here it's modifying from above (1+UnitStep(16(Y+1))+UnitStep(8Y)+UnitStep(8(Y+1))+UnitStep(8Y*2))*(1+2+min(w,3)+min(w,4)+min(w,5)+min(w,6))*5/6 > (1+UnitStep(10(Y+1))+ UnitStep(5Y)+UnitStep(5(Y+1))+UnitStep(5Y*2))*30*6/5*2/3, w>=2, Y>0 and solutions are 1. w > 23/5, 5 < Y <= 8 2. w > 23/5, 9 < Y <= 15 3. 57/20 < w < 23/5, 5 < Y <= 7 4. 57/20 < w < 23/5, 9 < Y <= 15 these can be put as 1. w > 4, 5 < Y <= 8 2. w > 4, 9 < Y <= 15 3. 2 < w < 5, 5 < Y <= 7 4. 2 < w < 5, 9 < Y <= 15 seems like a result that you should check so let's do a table of results. Results 12 can be seen to be true comparing tables for w6 and sv3+. Let's check the difference sv2+ for dissie and DL at 4 wounds. Substituting, it is 2/3 * (1+UnitStep(16(Y+1))+UnitStep(8Y)+UnitStep(8(Y+1))+UnitStep(8Y*2))/6 * (1+2+3+4+4+4)/6 * 5/6  2/3 *3 * (1+UnitStep(10(Y+1))+UnitStep(5Y)+UnitStep(5(Y+1))+UnitStep(5Y*2))/6 * 2 * 2/3 and then we do a table for it with Y from 1 to 16. And sure enough this is positive only at Y=6 and Y=7 and Y > 10 to 15. If you're good at math, I would be grateful for your help in checking this! Images: 1. Wound roll function, S5 2. Wound roll function, S8 3. Damage d6 function 4. Armor save function, at sv3+ and ap value = a 5. Dissie cannon damage as function of toughness at sv3+ 6. Same for Dark Lance 7. The difference of Dark Lance and Disintegrator cannon expected wounds for a W4 Sv2+ target as a function of toughness
Conclusion: Dark Lances are better at dealing unsaved wounds than Disintegrator Cannons exactly when the following criteria are met: 1. The target has 2+ armor, more than 4 wounds, and a toughness of 6 to 8 or of 10 or more. 2. The target has 2+ armor, exactly 3 or 4 wounds and a toughness of 6 to 7 or of 10 or more. 3. The target has 3+ armor, more than 5 wounds and a toughness of 6 to 8 or of 10 or more. 4. The target has 3+ armor, 4 wounds or more and a toughness of 6 to 7 or of 10 or more. 5. The target has 4+ or higher armor, more than 4 wounds and a toughness of 6 to 7 or of 10 or more. In all other cases Disintegrator cannons are better. Invulnerable saves weren't considered because they affect both in the same way. Thoughts? Edit1: "more than 4 wounds > 4 wounds or more" on #4 because that's what's implied by the inequality. Also 57/20 < x means x > 2 on tabletop.
Last edited by Lord Johan on Thu Aug 17 2017, 21:37; edited 1 time in total 
   Skulnbonz Wych
Posts : 567 Join date : 20120713 Location : Tampa
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 17:47  
 You cannot simply say that and have it be true. There are so many other factors that you have not even considered. Three Ravagers, all tripple dissies over dark lances.
That is 90 points of upgrades that you do not take into account for the rest of the army. That is 6 blasters for your kabalites, that is a venom, that is almost a raider. That is almost 10 khymerae.
You cannot and do not factor in the protection a venom gives troops, the manuverability and the firepower in your above analysis. Adding 6 blasters to the "dark lance" side would tilt the scales a bit.
Comparing Dark lances and Dissies is more than mathhammer. It is what you have to give up in your list to afford the dissies than cannot be taken into account.
And frankly, dissies DO NOT IN ANY WAY add enough to a list to compensate for their higher cost. My tournament list has 20+ dark Lances. That is 200 points.
yeah, I think I will pass on that for the .0002% difference.
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   Mppqlmd Hekatrix
Posts : 1137 Join date : 20170705
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 17:59  
 I'm pretty sure changing half/a third your DL into dissies would be a very good buy, even considering the points increase. First, it's a tremendous gain in antiMEQ and anti TEQ power. Secondly, mixing DL and Dissies increases your antitank power. Why ? Because D2 is reliable. If you have both dissies and DL, you can alternate so that you always start your targets with DL, and finish them with dissies once they drop to 2/4/6 wounds (if they get to 1/3/5/7 wounds, use missiles to even the numbers). I have found it to be the most reliable way to crack vehicles. 
   Lord Johan Kabalite Warrior
Posts : 169 Join date : 20160721 Location : Coming to a realspace near you
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 18:05  
 That's definitely a good point about the cost. You should have more reasons to take disintegrators than the supposed advantage vs. Sv2+ W4 T8  that advantage was 1 wound for every 18 disintegrators you took, so probably not worth 180 points. You should probably think about it more that you are not losing in this particular capacity if you take dissies.
What was interesting, to me, is that once any tank is down to 4 wounds your dissies are statistically better vs. it than your lances (unless it has 2+ armor and T67, then this happens at 3 wounds). Also, they are better vs. T9 regardless of armor.
It's a very interesting issue. 
   Hellstrom Sybarite
Posts : 471 Join date : 20141124 Location : South Central England
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 20:29  
 Great maths. I prefer dissies because they are close enough damagewise to Lances when shooting armour, but they are an absolute miles better at killing everything else. What if you opponent arrives with no vehicles? Lances are pretty terrible then. 
   Skulnbonz Wych
Posts : 567 Join date : 20120713 Location : Tampa
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 20:52  
 And what if your opponent arrives with nothing but leeman russes? Your dissies are pretty terrible then.
This back and forth can go on forever, i am just stating, that in a competitive environment, Lances are better for greater damage output potential, greater strength, greater AP value and less cost.
Shoot some dissies at an Imperial Knight who is shooting back and see how "great" they are.
For dissies to be used, they would have to be the same or (preferably) LESS than a dark lance in cost.
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   Jimsolo Dracon
Posts : 3063 Join date : 20131031 Location : Illinois
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 21:02  
  @Skulnbonz wrote:
 And what if your opponent arrives with nothing but leeman russes? Your dissies are pretty terrible then.
Not really. They're STILL a pretty decent weapon. Even factoring the points discrepancy in, Dark Lances are good against vehicles and mediocre against everything else. Dissies are still good against vehicles and absolutely phenomenal against MEQ, TEQ, and GEQ. The ONLY area that Dissies aren't the superior choice is medium to heavy vehicles. At this tier, the Lance is a little bit better. At the other end of the spectrum, where the lance is a huge waste of points, the dissie is miles better. The dissie seems like the clear winner in this edition, at least to me. If you've already got a bunch of AP 3 and 4 stuff in your army, and a lot of massed shots (giving you the ability to put some hurt on hordes or elite infantry) and you don't have any antivehicle, you might consider using lances instead. But in every other instance, I think the smart money is on the disintegrator. 
   Mppqlmd Hekatrix
Posts : 1137 Join date : 20170705
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 21:35  
  @Skulnbonz wrote:
Shoot some dissies at an Imperial Knight who is shooting back and see how "great" they are.
Well, you should try. I've exploded Baneblades, Leman russes and Land Raiders with a force that consists mostly of dissies. 
   Hellstrom Sybarite
Posts : 471 Join date : 20141124 Location : South Central England
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 21:43  
 I agree. I run 3 units of DL Scourges, 6 Dissie Ravagers and 3 Dissie Razorwings. Never had a problem with getting rid of Vehicles. 
   Lord Johan Kabalite Warrior
Posts : 169 Join date : 20160721 Location : Coming to a realspace near you
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 21:55  
 To be fair the difference can be significant vs. intact T67 vehicles at Sv3+. It can reach up to 4 wounds for every 9 cannons in favor of DL vs. Dissie. The difference is less significant for T8 vehicles according to my math corresponding to 1 extra wound for every 18 weapons advantage for DL. Caveat: I was very tired, tried to copypaste the right thing. I put the Mathematica string and tables in spoilers.  math:

Dark Lance wounds  Dissie Wounds, T6 or T7, Sv3+, W= wounds remaining on target Table[2/3×4/6 (1/6 (1 + min(w, 2) + min(w, 3) + min(w, 4) + min(w, 5) + min(w, 6)))  2/3×3×2/6 min(w, 2)×5/6, {w, 0, 7}] Dark Lance wounds  Dissie Wounds, T8, Sv3+, W= wounds remaining on target
In this use case the DL is superior as is known from earlier threads. This is also its singular best use case vs dissie. You can expect the absolute difference to be less wherever else it has an advantage. 
   Lexer Hex Slave
Posts : 4 Join date : 20170128 Location : New York
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 23:14  
 I do think there's something to say about the three rerolls you get and having increased damage hinging on fewer rolls. The offensive power of a unit with many dissies is less affected by the ability to reroll one of them than an equivalent unit with lances.
As the number of attacks increase, of course I would expect it to approach the limit of the math without rerolls considered. And as you mentioned earlier obviously no benefit to increased damage if your target can't soak it up. _________________ White Dwarf: 23,000 slaves Red Giant: 65,000 slaves Black Hole In Jar: priceless

   Mppqlmd Hekatrix
Posts : 1137 Join date : 20170705
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Thu Aug 17 2017, 23:24  
 This is quite true, the DL benefit from rerolls. The dissies, on the other hand, are less random and will mostly perform the way you expect them to perform.
If you run only dissies you don't have good ways to dump your CP. If you run only DL, you don't have enough CP to reroll every single bad dmg roll. I mix them. And i'm happy. 
   Barrywise Sybarite
Posts : 441 Join date : 20121114 Location : Illinois
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 04:27  
 Your math was incrediblely insightful. I'm only 1/2 of the way through and I love it. Thank you. 
   Meavar Wych
Posts : 658 Join date : 20170126
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 07:21  
 So I think we can say some lances are usually smart (unless you expect a lot of people without vehicles with t6 , remember against t6/7 tanks you deal assuming full health 1.4 times more damage with a lance. That means taking 2 lances and 1 dissie is equavalent to 4 dissies against most vehicles. Looking at hellstrom who has 3*4 dl and 6*3+3*2dissies (a total of 26 dl/dissies) I completely agree having them all dark lances is silly. But any time you shoot a dissie at a t6/7 4+ wound vehicle you are just lost 10 points and x% effectiveness. Sure you can compensate for this by having a lot of dissies and still kill them. Also a lot of vehicles are barely dangerous anymore when they have <3 wounds left. Also the above stats also did not take into account that the lance spread is different then the dissies. Yes a dissie does more damage on average to a 3 wound vehicle (assuming no 2+ save) but has only half the chance of killing it outright (0.29 vs 0.148). 
   Count Adhemar Dark Lord of Granbretan
Posts : 6785 Join date : 20120426 Location : London
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 07:27  
 I'm thinking of adding a 4th Ravager to my fleet (currently 2 x DL, 1 x Dissie) and now I'm utterly confused as to which weapon to equip it with! _________________ You have been weighed, you have been measured, and you have been found wanting. In what world could you possibly beat me? 
   amishprn86 Klaivex
Posts : 2004 Join date : 20141004 Location : Ohio
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 09:40  
 As dedicated AT, when you need 3/4+ to wound with chances of more damage compare to 5+ to wound for 2D, when you are using your Reroll each phase on the DE b.c you play Harlequins and you need to break tanks as fast as you can. 
   FuelDrop Wych
Posts : 878 Join date : 20150621
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 09:44  
 Good news everyone! I talked to GW and they have said they are going to deal with Darklances replacing Blasters as infantry/Scourge weapons of choice! Effective next Errata, Darklances will be vehicle exclusive! Isn't that neat?!?  Spoiler:

Not really, though at this point I doubt anyone would be surprised.

   LordSplata Kabalite Warrior
Posts : 150 Join date : 20170614 Location : Sydney
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 10:24  
  @Skulnbonz wrote:
Shoot some dissies at an Imperial Knight who is shooting back and see how "great" they are.
I'm not quite through reading this thread yet, which I'm enjoying very much, thanks OP, but I had to comment on this and the OP's comment on not taking into account invulnerable saves. Funnily enough this is the exact time when they REALLY makes a difference! Dissies are better against imperial knights! Try it out on my calculator, the invulnerable save makes the dissies 2 equivalent to the 4 on the lance. Basically against targets with invulnerable saves dissies are always better. Wound shenanigans aside. 
   Count Adhemar Dark Lord of Granbretan
Posts : 6785 Join date : 20120426 Location : London
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 10:30  
  @LordSplata wrote:
 @Skulnbonz wrote:
Shoot some dissies at an Imperial Knight who is shooting back and see how "great" they are.
I'm not quite through reading this thread yet, which I'm enjoying very much, thanks OP, but I had to comment on this and the OP's comment on not taking into account invulnerable saves.
Funnily enough this is the exact time when they REALLY makes a difference! Dissies are better against imperial knights! Try it out on my calculator, the invulnerable save makes the dissies 2 equivalent to the 4 on the lance. Basically against targets with invulnerable saves dissies are always better. Wound shenanigans aside.
On a weapon for weapon basis yes, Dissies are better than Dark Lances against Knights (0.89 wounds per firing vs 0.77). When you take into account the points cost, they become worse (0.59 v 0.77). _________________ You have been weighed, you have been measured, and you have been found wanting. In what world could you possibly beat me? 
   Lord Johan Kabalite Warrior
Posts : 169 Join date : 20160721 Location : Coming to a realspace near you
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 10:35  
 That is actually true. I didn't consider this in OP as it reads but there is this special case: A 5+ invulnerable save makes DL effective AP only 3.
In this case, the term 5/6 will be eliminated from both sides of the inequality. Which means you will use the 4+ table to determine whether DL is better. Meaning vs. 3+ 5++ T8 Dissie cannon can be expected to do more wounds. and DL is better only if there are more than 4 wounds AND toughness is 6 or 7, or 10 to 15.
The exact amount of how many more can be found with Splata's calculator for large numbers of wounds (it, and my table become exactly accurate at 6 wounds or more) and for small numbers you could run the DL and dissie expressions in this post.
The same exception will apply in case of 2+ 4++.
Thanks Splata!
Edit: Looks like Adhemar posted the exact difference above. 
   mynamelegend Hellion
Posts : 96 Join date : 20150405
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 10:36  
  @Count Adhemar wrote:
 On a weapon for weapon basis yes, Dissies are better than Dark Lances against Knights (0.89 wounds per firing vs 0.77). When you take into account the points cost, they become worse (0.59 v 0.77).
Take the cost of the Ravager into account as well and the difference gets a lot smaller. (DLs 75.75 points per wound, Dissies 76.78 points per wound) If you ask "would I pay a 1.35% price increase per wound caused, against Imperial Knights, to massively increase my efficiency against a vast number of other targets?", the answer will probably be "Yes". 
   Kantalla Sybarite
Posts : 461 Join date : 20151221
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 10:55  
 I'm finding my preferred HQ is a Farseer with Doom lately, and that swings the advantage toward Disintegrators (and Mandrakes become really good).
Excluding Doomed targets, usually Dark Lances are better against most vehicles/monsters and Splinter weapons are better against infantry types. Disintegrators are a nice versatile option that is effective against both though. 
   LordSplata Kabalite Warrior
Posts : 150 Join date : 20170614 Location : Sydney
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 11:06  
 Good catch Count, they still don't have the points advantage, even after you add in the cost of a Ravager, but on a raider they remain the most points efficient choice, as well as the most damaging.
Not that raiders are the most points efficient choice for damage...
Edit: and RWJF's are almost equivalent for points vs a knight
Last edited by LordSplata on Fri Aug 18 2017, 11:19; edited 1 time in total 
   FuelDrop Wych
Posts : 878 Join date : 20150621
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 11:10  
  @LordSplata wrote:
Not that raiders are the most points efficient choice for damage...
If you want points efficient damage you came to the wrong army, son. Go talk to obliterators if you want points efficient damage. 
   Lord Johan Kabalite Warrior
Posts : 169 Join date : 20160721 Location : Coming to a realspace near you
 Subject: Re: When exactly are Dark Lances better than Disintegrators? Fri Aug 18 2017, 11:33  
 That may be  but if possible, I would like to keep this thread to discussing the specific issue of Disintegrators vs Dark Lances, please. 
   
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