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Kantalla
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PostSubject: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 05:08

I have recently been doing some Mathhammering on how resilient our units are against a range of different weapons and thought the information might be of use to others.

The methodology is fairly straightforward:
For each unit (except the Archon) in our part of the Xenos 2 Index, I have come up with a typical unit configuration, worked out how many firings are required to destroy that unit, and then normalised that number based on cost of the unit.

Here is an example calculation:

A Succubus with Archite Glaive / Splinter Pistol against Bolter fire
Average damage  = 1 shot × 2/3 hit × 2/3 wound × 1/2 unsaved × 1 damage × 5/6 unsaved FNP = 5/27 wounds inflicted per firing
To kill the Succubus would require 5 wounds / (5/27 wounds / firing) = 27 firings
The number of firings was then normalised to kill the equivalent of 100 points, by dividing by the cost of the unit and multiplying by 100:
Bolter index against Succubus = 27 firings / 72 points × 100 = 38

Most calculations are fairly straightforward, but it can get complicated when there are weapons with variable multiple damage and multiple wound targets with FNP. I have calculated the odds of each wound outcome after feel no pain, and included that in the calculations, so a Grotesque that was wounded by a Lascannon would on average take 2.300 wounds after the D6 damage and FNP are accounted for.

This data could give some guidance on how vulnerable certain units are, for example, you want to place Mandrakes where they are not exposed to small arms fire if possible, and certain units that you might be more willing to throw in the face of the enemy, such as Urien Rakarth near a blob of Conscripts.

UPDATE:
I have expanded to include the Asuryani and the battlefield role. There are now a lot more entries, so I have broken the results into three tables:
1) HQ and Troops sorted by resilience against Bolters
2) Elites and Fast Attack sorted by resilience against Heavy Bolters
3) Transports, Heavy Support, Flyers and Lords of War sorted by resilience against Lascannons



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Archon Rixec
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 09:15

cool stuff. i'm amazed by the venom resilience! also, where would an archon be with his 2+ invuln? i would like to see added clawed fiends too... Wink
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Count Adhemar
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 09:20

I would imagine that if you take the Sslyth bodyguard rule into account, the Archon is our most resilient unit but then you look at the cost...

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Kantalla
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 09:52

Archons are messy because you could roll 13 saves in a row, or more likely, fail the first one. That random variation in the save is the reason I skipped including them. Working out Sslyth as bodyguards is fairly straightforward, but would need the Archon sorted to include anyway.

Clawed Fiends are hiding in there just after the Talos and Venom.

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Jimsolo
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 14:25

How is weapon profile accounted for? Each time a unit shoots a heavy bolter, does it count as one firing or three firings?
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Squidmaster
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 14:40

Got to appreciate a good bit of maths.

Very interesting to see the Chronos come outfairly decently considering it has no decent damage output of its own.
I'd love to see an output to resilience comparison.
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Burnage
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 15:14

Kantalla wrote:
Archons are messy because you could roll 13 saves in a row, or more likely, fail the first one. That random variation in the save is the reason I skipped including them. Working out Sslyth as bodyguards is fairly straightforward, but would need the Archon sorted to include anyway.

Clawed Fiends are hiding in there just after the Talos and Venom.

I don't see why that's messier than any other save? A Kabalite Warrior could, potentially, successfully save 13 times in a row with their 5+. They're unlikely to, sure, but it could still happen.

The Archon just needs an average of 6 successful wounds to lose their Shadowfield.
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Lord Johan
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 15:44

If you are interested I mathed out an expression for the Shadowfield in the nearby Shadowfield thread, page 1. (although the first reply to it was "no that wasn't enlightening')

He is right to say that they are messy, because their invuln save changes at some point from 2+ to none, right? But you don't know when, it is probabilistic. You could conceptualize that the Archon has a variable invulnerable save based on how many times he is making consecutive saves. The exact formula for it was (mathematica) s = (6^(-a) (7 6^a a + 6 5^(a + 1) - 5 6^(a + 1)))/a where s is the Archon's "ordinary" invulnerable save (what would be the equivalent normal invuln save for that many successive saves to have same probability of saving) and a is how many saves he is making.
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Diurach
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 16:55

Good lord man, top work. I love a spreadsheet and will certainly be making use of this!
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Eldur
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 18:22

Oh, thank you very much for this. This chart gives me a lot of ideas. Distraction Chronos, or even a distraction wave of Urien and two Chronos... if you focus your shooting phase on high dmg weapons first (or assault them quickly with bikes), that means you'll stay alive even more turns.

EDIT: and khymerae are the other sIde of resilience, doing well against plasma and lascannons. If only I could use all that information on the battlefield... IT'S TESTING TIME

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Kantalla
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 19:17

Jimsolo wrote:
How is weapon profile accounted for? Each time a unit shoots a heavy bolter, does it count as one firing or three firings?
I use the term firings to mean essentially each selection of a weapon. So a Heavy Bolter firing is 3 shots for example.

For the Rapid Fire weapons I assumed the shots from the profile (i.e. out of half range).

Archons are mathematically interesting to include, but so unreliable, because of when that Shadowfield fails that I wanted to leave them out. Will consider whether to revise that.

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Jimsolo
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 19:25

So the numbers should double if you're looking at bolters or plasma guns within their rapid fire range?

EDIT: Half, rather?
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Kantalla
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Wed Sep 27 2017, 21:28

Correct on the rapid fire weapons. Half range would double their damage, which would halve the shots required to kill 100 points in the table.

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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 04:41

Yeah this is great work. I really like the idea of normalizing this vs points. It really helps give a good idea of what is overcosted (at least from a resilience standpoint). I knew Reavers were expensive, but this really helps to paint the picture pretty clearly. I was personally always concerned about the offensive output, but now seeing this, I'm also concerned about their defensive abilities too!

I want to 2nd the notion of comparing this to damage output! I'd LOVE to see that. It would give a great overall picture.
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|Meavar
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 05:54

I like it but I am not really understanding it I think. I tried a few but get vastly different results.

For instance let's look at the trueborn:
The plasma and assault cannon are very similar.
assault cannon s7 leaves a 6+ save but 2 wounds for the 6++
PLasma s7 no save but a 6++
an assault cannon should have 2 times as many shots being heavy 2 so should halve the value
but it goes from 9.1 to 1.8
Actually the assault cannon looks of completely.
wracks (where both the heavy bolter and assault cannon wound on a 3+ shows better values for the assault cannon why the heavy bolter has more shots).

Succubus vs lasgun
1 shot × 2/3 hit × 1/2 wound × 1/2 unsaved × 1 damage × 5/6 unsaved FNP = 10/72
5 wounds => 36 firings
36 / point cost 72 *100 => 50 in your tabel it says 100 (at first I thought maybe it is rapid fire but taking rapid fire into account makes it 25 not 100)
Although it would work if you used conscripts instead of veterans. I assumed you used a standard 3+bs to compare weapons to each other.
If you did not you should mention who wields each weapon. A lascannon on a moving guard vehicle hitting on 5+ would give vastly different results then a lascannon held by a space marine, or as mentioned above the lasgun by the conscript, veteran or standard guard.
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|Meavar
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 05:54

I like it but I am not really understanding it I think. I tried a few but get vastly different results.

For instance let's look at the trueborn:
The plasma and assault cannon are very similar.
assault cannon s7 leaves a 6+ save but 2 wounds for the 6++
PLasma s7 no save but a 6++
an assault cannon should have 2 times as many shots being heavy 2 so should halve the value
but it goes from 9.1 to 1.8
Everywhere the s8 -3 ap 2 wounds supercharged plasma does worse then the assault cannon most of the time much worse, while the stats are better.
Actually the assault cannon looks off completely.


Succubus vs lasgun
1 shot × 2/3 hit × 1/2 wound × 1/2 unsaved × 1 damage × 5/6 unsaved FNP = 10/72
5 wounds => 36 firings
36 / point cost 72 *100 => 50 in your tabel it says 100 (at first I thought maybe it is rapid fire but taking rapid fire into account makes it 25 not 100)
Although it would work if you used conscripts instead of veterans. I assumed you used a standard 3+bs to compare weapons to each other.
If you did not you should mention who wields each weapon. A lascannon on a moving guard vehicle hitting on 5+ would give vastly different results then a lascannon held by a space marine, or as mentioned above the lasgun by the conscript, veteran or standard guard.
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Kantalla
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 06:02

|Meavar wrote:

assault cannon s7 leaves a 6+ save but 2 wounds for the 6++
Are you thinking Autocannon instead of Assault Cannon? I used the Assault Cannon Heavy 6 S6 AP-1 D1 there.

Quote :
Succubus vs lasgun
...
Although it would work if you used conscripts instead of veterans. I assumed you used a standard 3+bs to compare weapons to each other.

If you did not you should mention who wields each weapon. A lascannon on a moving guard vehicle hitting on 5+ would give vastly different results then a lascannon held by a space marine, or as mentioned above the lasgun by the conscript, veteran or standard guard.
I did indeed use Conscripts as the bearer of the Lasguns, so they are at BS5+, and everything else is on a BS3+ platform. Should have stated that as you say.

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Barrywise
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 06:05

See, I was attempting to do this piece meal and figure out where our army stands. You stole my thunder, gonna start calling you Percy Jackson (The Lightning Thief) or something.

Thor is already taken, might call you Zeus.

Jokes aside. This is prime, and I love you for saving me work. I'd love for the Splintermind podcast to take a peek at this and compare specific slots. Like compare how the troops stack up or something. Or transports and their personal experiences so far.

Still need that Exalt button...

edit: on second look, sweet jesus those grav cannons

Also, my man Urien literally doesn't die. What a dude.

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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 07:25

Kantalla wrote:
|Meavar wrote:

assault cannon s7 leaves a 6+ save but 2 wounds for the 6++
Are you thinking Autocannon instead of Assault Cannon? I used the Assault Cannon Heavy 6 S6 AP-1 D1 there.

Quote :
Succubus vs lasgun
...
Although it would work if you used conscripts instead of veterans. I assumed you used a standard 3+bs to compare weapons to each other.

If you did not you should mention who wields each weapon. A lascannon on a moving guard vehicle hitting on 5+ would give vastly different results then a lascannon held by a space marine, or as mentioned above the lasgun by the conscript, veteran or standard guard.
I did indeed use Conscripts as the bearer of the Lasguns, so they are at BS5+, and everything else is on a BS3+ platform. Should have stated that as you say.

Ah ok that explains a lot why my math did not add up.
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 07:41

I dont fully understand the numbers, a Cronos is 445 with a Lasgun, its that 445 points of lasguns? I dont know what the numbers mean other than the higher number = better?

I say this b.c a Raider takes 90 shots of Boltguns to kill and a Venom takes 72 and i dont know how a Venom is higher score than a raider on your chart?


Nevermind i see what you did, miss read.

You normalized the difference, like a Raider takes 25% more damage but costs 43% more. I still don't understand what your numbers means tho. Like what does the 445 number mean on the cronos for lasguns?

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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 08:54

The unit appears to be "100 firings to kill per point" so 445 means you must fire 4.45 lasguns (at bs 5+ single shot range) to kill 1 point's worth of a Cronos without upgrades. Because a Cronos without upgrades is 102 pts it would then take 1.02*445 =appx 454 such lasguns to do 1.02*445*1/3*1/6*1/3*5/6 =appx 7 pts of damage and kill the Chronos.

The main issue as is pointed out is that you have to agree with the unit upgrades and it is not explicit here who is doing the firing, e.g. it would be different if those were guardsmen or veterans. But that of course makes it simpler looking and more attractive, and importantly the order of resilience, but not the number, will stay the same despite different dudes firing the weapon at different ranges so if you only care about the order of resilience and not the number then that is applicable to all firers of such weapons
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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 10:51

amishprn86 - The numbers are the "firings required to kill 100 points of XX unit". It was the best way I could find to normalise things across a range of different units.

Lord Johan - you can disagree with the upgrades - maybe you always take the Spirit Vortex on your Cronos Razz - but in most cases the points wont change massively, and it is reasonably easy to convert the numbers if you want a different configuration. Or if there is a configuration you would especially like to see I can add to the table.

The firer does matter slightly in terms of the order of resilience. For units with Hard to Hit (Flyers / Venom / Mandrakes) they reduce a Conscript from 5+ to 6+ (damage reduced 50%) but a Space Marine from 3+ to 4+ (damage reduced 25%). For everything else though, the order will be unchanged as you say.

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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Thu Sep 28 2017, 11:22

These are great numbers and all, nice to see.

Im not trying to undermine what you did in anyway, nor want to change the subject, but this is a good time to also add value in survivability vs damage out put.



If you Venom let say always stay alive for 4 turns and your Raider for 3, how much damage difference does the raider put out compare to a venom? How much is it per turn? If a Raider costs 43% more but is doing 67% more damage per turn, then isnt that better point for point?

Then how much is the units inside and what are they doing to add to this as well?



On a side note (this was on Bols forums)

Back in mid 7th, i saw (I couldnt save it for some reason) a person basically did a large scale version of what you did, but also added damage out put vs GEQ, TEQ Vehicles etc... and had those numbers combine in a way to give a unit score rating (he also had some rules/artifacts/formations to add to the score), and claimed to have had the "best" list in 40k went on to win a bunch of tournaments until the St. Celestine/DA combo came out due to new releases.

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PostSubject: Re: Drukhari resilience (now includes Craftworlders)   Sun Oct 01 2017, 04:37

I am working on the damage output to go with the resilience data, and am most of the way through that.

In the mean time, I have expanded the original post to include Craftworlders, as resilience has a lot less options and complexity to work through. From a resilience point of view we actually do OK, although obviously we have a lot less options.

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