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GAR
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PostSubject: Math Hammer for DE   Math Hammer for DE I_icon_minitimeWed Jul 20 2011, 15:06

Howdy all.

I have been giving some consideration to my Competitive Dark Eldar list and trying to get the most out of my units.

So while I was not aware of it, I had been doing mathhammer in my head for year now, picking out the odds and such.

I came across a series of threads by bringer of victory
http://nike40k.blogspot.com/

and it got me to thinking. While a lot of what he does is applicable for most armies, DE are a little bit different and I wanted to get some discussion going on some DE specifics.

To start, I want to emphaisze I am looking at this only from a competitive stand point. I could care less about any of this is my friendly games so please keep in mind, competitive perspective only.

Let me put forth the basics as I interpret them. I am going to write this all out so I can teach myself as well as clearly have everyone understand what I am doing and correct any mistakes.

if we have 5 dark eldar warriors with splinter rifles in rapid fire range we hae the following

5 models with 10 shots
we hit on 3s or better on 6 sided dice

resulting in 10 shots * (4 hitting results out of 6 possible results, we miss on 1s and 2s)

10 X 4 / 6 = 6.7 hits. I am going to round up for the sake simplicity because we can't actually rolled percentage of dice. I will adjust this later on the armor save. so 7 hits

from this, given splinter weapons, DE wound anything on a 4 or better

so we have 7 hits that wound on a 4 or better ( 3 possible wounding results on 6 possible results)
7 X 3/6 = 3.5, rounding up here as well to 4 wounds.

Now, since MEQ seems to be the dominant army type, lets assume this goes against marines

4 wounds against marines with a 3+ armor save

4 x 2/6 ( the marine will fail on 2 out of 6 possible results)

4 x 2/6 = 1.3 rounding down to 1 dead marine.

so the net basic result, with my basic assumptions and rounding to whole numbers comes out to one dead marine from shooting from 5 DE warrirors with splinter rifles in rapid fire.

The pure math for these results is
6.7 hits
3.3 wounds
1.3 casualties
so my assumptions are not far off from the actually numbers that are not rounded up or down.

Now that I have laid out my premise working model, where I am looking is the affect of haywire and lance weapon results against armor.

As a DE we need to get rid of armor threats. The blog I cited counts rhinos as destroyed and Landraiders as destroyed if I read it correctly.

personally, and this my be my failing, the only thing I really care about about is the lone immobilized result. All the other results either negate shooting ( stunned, shaken, wrecked or explosion) or reduce the number of shots ( weapon destroyed) to my precious skimmers or infantry.

If i can limit the affect of armor, to me, the rest of my army is free to zip around the battle field to isolate and eliminate my opponents army as quickly as possible.

So how exactly do we quantify the effect of glancing and penetrating results?
Do we even consider stunned and shaken as worthwhile?
Do we try to include the impact of power of the machine spirit?
What about extra armor?

I would put forth the target is effectively nullieifed in turn when it can no longer shoot. This could be raised to shoot or move depending on the vehicle and the passengers it is carrying.

Anyhoo, before I start plopping all kinds of math, I figured I would throw this out for consideration while I get the rest of my thoughts together on moving forward.

Thanks!

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeWed Jul 20 2011, 17:31

http://www.simhammer.com/node/7

Might be useful for you.

I personally consider stunned/shaken to be "as good as" dead for a turn...depending on the rules of the unit (extra armor, Fortitude, Spirit Stones, et al)

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeWed Jul 20 2011, 19:26

Thanks Thor665.

I'm not sure what is wrong, but I can't get anything to work. I keep getting user errors.


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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeWed Jul 20 2011, 20:04

Huh, actually looks like the site changed, I had it in my bookmarks as a useful link and posted it sight unseen. I have no idea what's up with the current site.

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeWed Jul 20 2011, 21:07

Howdy.

At this point I would like to continue on with my findings. I think when I am all done with this, I will have a decent database of information for the discerning DE player to use or disregard as each sees fit.

I am going to talk a little bit about Haywire.

What does haywire do?
Quite frankly as I have used them they are just one of the most awesome pieces of wargear we have.
What they do is for every hit, you roll 1d6. on the roll of a 1 nothing happens
on a 2 - 5 you do a glancing hit
on a 6 you get a penetrating hit.

What can units can have them.
Wyches as grenades
Bloodbrides as grenades
Treubron as grenades
Scourges as grenades and haywire blasters
Talos as a twin linked Haywire blaster

I might have missed one or 2 but that pretty covers units. ICs have a bunch of options for all manner of things so I have left them off of ICs

Let us begin with a review of attacking vehicles and Dreadnoughts in general.

For grenades, a vehicle that did not move or is immobilized is auto hit.
if the vehicle moves at all but less than 6 inches, you need 4s to hit
if the vehicle moved more than 6 inches then you need a 6 to hit the vehicle.

With grenades you get 1 attack on vehicles, which in low unit size is pretty bad. MSU huts DE here, but my combining units on the assault this can be easily remedied so I view that as not a significant issue, even when attacking vehicles moving more than 6 inches.

Dreadnoughts require a 6 to hit with grenades, unless they are stunned or immobilized, in which case they are hit on Weapon Skill. its important to remember this because if you have a IC, like a succubus leading and she manages to hit and then stun or immobilize, the rest of the unit attacking will benefit.

That being said, a typical Wych unit is on average 7 models strong. This gives us a base number of models to start. I know numbers vary from army to army, I typically run 8 myself, but this is I think a reasonable average.

Let us further assume that the wych unit is mounted. For this exercise it doesn't really matter other than they have a transport that can move them far enough to get the assault.

Assuming the vehicle in question has moved 6 inches or less, we need 4s or better to hit.

Therefore we have 7 attacks needing 4s or better to hit.
We get 3.5 hits so lets round down for this exercise.
3 hits on a vehicle.

Now, we roll 1 die for each hit to determine effect. Here is where it starts getting a little weird in doing the math.

Looking at the averages, we should get a reasonable spread of results, 1 result should be 1 or 2, 2nd result should be 3 or 4, and 3rd result should be 5 or 6. Each die rolled is completely independent but I think we can reasonably work with this.

For this lets assume we get 3 glance results.
The glance results, with the glance modifier ( -2) to the die roll will nominally be the same as the roll for haywire result. I am going to assume we get a 1, 3 & 5, which results in 2 crew shaken and a weapon destroyed. So the vehicle can still move, but cannot shoot.

The alternative is to go with a 2, 4 and a 6. Which means we get a crew stunned result, a crew shaken result and immobilized. No movement, no shooting, which is still good.

What we can discern from numerous iterations of this is that for one set of dice rolls, to effectively wreck or render a vehicles wrecked, we need 9 hits assuming we have a vehicle with 2 weapons. I assume no penetrating hit for this exercise, so just from glancing, if we immoblize it and destroy 2 weapons, it is effectively wrecked.

or if we double immoblize and destroy one weapon, it is still effectively a wreck.

Since from glancing we only get a 1 in 3 shot at immobilizing or weapon destroyed, you need to roll 9 dice on the glancing table to take out any sort of armor.

Mathematically it should look like this

7 attacks need 4s
7 x 1/2 = 3 hits
3 hits needing 2-5 and/or 6s
3 X 5/6 = 2 glancing hits + 1 glancing hit or 1 penetrating hit
for 3 glancing hits we get either a weapon destroyed or immobilized plus crew stunned
for 2 glancing hits and a penetrating hit we get a crew stunned, either a weapon destroyed or immobilized and then a 1 in 3 chance to destroy the vehicle.

So now how do we quantify all of this so it makes sense in simple language ( My personal favorite since I can't use big words very well).

Basically when using haywire grenades in an assault, you will likely need 9 dice rolling to take out a vehicle assuming nothing but glances. We can further say that assuming 1 in 6 is a penetrating hit and an additional 1 in 6 is a no effect, then with 7 models assaulting, 3 or 4 hitting, then the 4th die is hard to quantify but you have a 4 in 6 chance of getting a glance and that glance could get you the extra weapon destroyed or immobilized result you are looking for.

In short it makes it hard to destroy a moving vehicle in one assault phase. That being said, the following turn the vehicle should not be moving and then the dice rolling should be enough to take out the vehicle.

The numbers I have are in dice rolls

7 attacks
3.5 hits
2.3 will glance
0.6 will penetrate
from glances 0.8 will weapon destroy or immobilize
from penetration, 0.2 will destroy.

I think this makes sense, I'm not a statician, but I do know how to work out the math for basic probablity using fractions. Like I said, working out haywire effects is quite a challenge given the range of results but I hope I am off to a good start. More to come as I work out more math and I would welcome anyone who knows this better than I ( Which I assume is most everyone) do to please contribute.

Thanks!



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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeWed Jul 20 2011, 21:07

It's hard to quantify vehicle damage because it's highly dependent on the following

The nature of the vehicle (tank/apc/hybrid)
It's position on the board/its range
whether it has already achieved its goals

so for example

a Leman Russ that can't fire is worth counting
an imobilised result against a LR with the flamestorm cannon is good (you can avoid it)
a Rhino that dumped off it's passengers is only worth killing to get the KP

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeThu Jul 21 2011, 09:40

Can someone please recommend a good website that has a Math Hammer calculator. The one posted previously in this thread is no longer valid.

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeThu Jul 21 2011, 11:56

http://math-hammer.appspot.com/

Not good (it's for WFB) but may work for 40k... wound-based models at least.

You may also check this, it's in MS Excel (.xml).

http://www.warseer.com/forums/attachment.php?attachmentid=25740&d=1185316617

I'm gonna look for Vehicle one.

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeFri Jul 22 2011, 07:33

Thanks for sharing all this GAR, it's a very interesting and useful thread that I am enjoying reading greatly.

Looking forward to more.

Cheers.
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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeTue Jul 26 2011, 17:48

Howdy.

So to continue on my thoughts and analysis on Mathhammer for DE.

I went back and read the original blog and he has an FAQ up where he clarifies some sticky issues.

For rhinos and landraiders, he determines that a penetrating hit is equivalent to a wrecked result. I disagree with this, because otherwise our weapons would be much more effective than they actually are. So with that in mind, my results will appear to be far worse, but I go the extra step to consider the vehicle damage roll.

Also, he uses percentages instead of fractions. It is stated that there are a number of reasons why he does this. In my case, I use dice possible results( Fractions) instead of percentages because we roll dice and deal with dice results, not percentages. Not a big deal, but it does make a slight difference in the results.

With that said, I want to look at Scourges and make a comparison to Truebron.

Scourges, equipped with haywire blasters.

if I read it correctly, 5 scourges equipped with shard carbines and haywire blasters will get us the following results against MEQ

3 shooting carbines
carbines are assault 3 poison at 18 inches
from this we get
9 shots X 4/6 possible hitting results = 6 hits
2 haywire blasters x 4/6 possible hitting results = 1.3 hitting results
as I have done before I will round the hits up and later we will round the casualties down.

so we have 8 hits, all wounding on 4+ against power armor
8 wounds x 2/6 failed armor save results = 2.6 failed armor saves
we round this down to 2 failed armor saves and 2 dead marines

if we evaluate Scourges with blasters
3 shooting carbines
carbines are assault 3 poison at 18 inches
from this we get
9 shots X 4/6 possible hitting results = 6 hits
2 blasters x 4/6 possible hitting results = 1.3 hitting results
as I have done before I will round the hits up and later we will round the casualties down.

so we have 8 hits, 6 wounding on 4+ against power armor, 2 wounding on a 2+ with no armor save
6 wounds x 2/6 failed armor save results = 2 failed armor saves
2 blaster wounds with no armor save = 2 more failed armor saves
net 4 dead marines
however it is worth noting, that because we rounded up the hits and there is not real rounding down of the failed armor saves, it is reasonable to consider the initial roll, and we could consider that we would get 3 to 4 actual casualties.

Trueborn vs infantry
There are a number of players who take the 5th trueborn to keep the numbers up for Ld checks. I don't do this, and as it seems a waste of points, for this exercise I will leave it out.

Also, there are a number of players who take 3 man units with blasters. I have done this, but it is as common as the 5 man units, so I leave this out.

Where I will begin is a 4 man trueborn unit with 4 blasters. I am not going to include a venom transport in this, but it can be easily added later as the results for it are fairly simple.

4 trueborn with blasters
4 shots x 4/6 possible hitting results = 2.7 hits
we will round up to 3 hits
3 hits x 5/6 possible wounding results = 2.2 wounds
we will round down to 2 wounds, results in 2 dead marines.


The results thus far for shooting against MEQ in the open are

5 scourges with haywire blasters = 2 dead marines
5 scourges with blasters = 3-4 dead marines
4 trueborn with blasters = 2 dead marines


Now, looking at armor
5 Scourges with 2 haywire blasters
the shardcarbines have no effect on armor, so we ignore them

2 haywire blasters x 4/6 hitting results = 1.3 net hits
we round up to 2 hits
for these 2 hits we roll a D6 each
2 x 5/6 possible results = 1.6 glancing or penetrating results
we will assume that we get 2 glancing results
since it is a glance, we have 4 possible results that will stun or shake a vehicle and 2 results that will immobilize or destroy a weapon.
lets assume we shake it, no shooting, and we get a weapon destroyed.

5 scourges with 2 blasters
2 blasters x 4/6 hitting results = 1.3 net hits
we round up to 2 hits
from this we need a 4 to glance or a 5 or 6 to penetrate.
we assume we get 1 penetrating hit
rolling 1 die with 6 possible results of which it is not really possible to predict any expectation other than an immobilized result, for most vehicles, is less than ideal.

4 Trueborn
4 blasters x 4/6 possible hitting results = 3 hits
3 hits x 3/6 glancing or penetrating hits
we assume 1 failed penetration, 1 glance and 1 penetration
rolling on the glancing table, we are more likely to get a stunned or shaken result
rolling 1 die with 6 possible results of which it is not really possible to predict any expectation other than an immobilized result, for most vehicles, is less than ideal.

In brief summary

VS MEQ
5 scourges with haywire blasters = 2 dead marines
5 scourges with blasters = 3-4 dead marines
4 trueborn with blasters = 2 dead marines

Vs Armor 12
5 scourges with 2 haywire blasters = stunned and weapon destroyed or immobilized
5 scourges with 2 blasters = 1 stunned glancing result or 1 penetrating hit
4 trueborn with 4 blasters = 1 stunned glancing result and 1 penetrating hit

So what do we have here. I want you all to know I don't have a pre-conceived notion of what the results should be, I am just going through the math with all of you and we can make our own conclusions from the results as I have shown.

What I get from this is, from a purely firepower standpoint is that the trueborn are somewhat better than the scourges in both shooting MEQ and against armor.

The best a 5 man Scourge unit with blaster can hope for a is the golden BB with a penetrating result and a wreck or explosion, which does happen, but is not very likely

The best a 5 man Scourges unit with 2 haywire blaster could hope for is 2 glances that will both get lucky and destroy 2 weapons, since we are considering armor with 2 weapons only.

The best a 4 man trueborn unit could hope for is 2 penetrating results and one of those wrecking the vehicle.

All in all I think a 4 man treuborn unit is slightly superior to a 5 man Scourge unit with haywire blasters. My assessment is that because the blasters need a 4+ to glance or penetrate where as a haywire blaster only needs a 2 or better.


To be fair though, some of the additions that are obvious are the trueborn need a transport, a venom the most likely choice. The venom or raider will afford them some protection from small arms fire.

The scourges don't have a transport option, but are able to deep strike and come with jump packs. So they will be able to move 12 all the time everytime.

So what are my thoughts, if I had to make 1

4 trueborn with blasters mounted on a venom with dual splinter cannons and nightshields are slightly superior to a 5 man unit of scourges with haywire balsters.

One thing I have not talked about is a 1o man unit of scourges with haywire blasters, which is pricey, but I think is superior to a 5 man trueborn unit. More haywire, greater poison shooting and the ability to get almost anywhere on the table via deep strike make the 10 man unit a much greater threat in my opinion. The consideration for this is the points that go into this unit.

In the end, the payer will have to decide if they want to sink that may points into a 10 man unit. You could Vect for less, and it is arguable as to whether or not he is better.

My hope is that the numbers will help the discerning player to make a informed choice based on what they want to take in their list. Or at the least help each of us to figure out what each unit should be able to do and then go from there.



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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeTue Jul 26 2011, 21:27

Nice to see the numbers.
I do think a lot of your rounding is...skewing the numbers. To my mind 1.3 should round to 1, not to 2 as you did. Your results are giving advantage to some unit shooting situations because of that.

I'll also add 'best case' with Haywires is not popping weapons, but rather getting stunned and shaken results - at least for my money and what I want them to do.

Thanks for the work.

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeTue Jul 26 2011, 21:36

Thor,

thanks for your input. I highly value your comments as you have helped me a lot in developing my DE to be competitive and not the local store whipping boy.

That being said, what I have done in the rounding is round the hits and wounds up while rounding the number of failed saves down. Having the spreadsheet with the unmodified numbers it does not make much of a difference, 10ths of a point or individual results. I find things get a little wonky when translated into percentages since we are dealing with die rolls and the results thereof.

The biggest guess is the effect of Haywire but I think I have gotten it down to a number if dice rolls you need to statistically get a wrecked or effectively wrecked result.

I have taken into account the stunned or shaken results, those tend to dominate the haywire effects, but where I add to it is that with more dice, we get weaponed destroyed and immobilized results, which given enough dice can wreck a vehicle.

Pretty much in summary, assuming nothing but glance results, we need 9 dice rolls to wreck a vehicle.

it changes a bit with penetrations, but those are as likely as "no effect" rolls so I cancel each out to keep it simple.

Thanks much for your thoughts.

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeTue Jul 26 2011, 21:56

Yeah, the vehicle part is tricky, especially since the goal of the shooting is so different depending on the vehicle in question. I usually just mathhammer for hits and use vague hope for results.

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PostSubject: Re: Math Hammer for DE   Math Hammer for DE I_icon_minitimeThu Jul 28 2011, 15:58

Howdy.

To continue of my discussion of working the numbers to evaluate how a Dark Eldar army will perform on the averages I will put forth my list from WargamesCon along with how it worked out.

Dread Pirate Garness Wargamescon DE List [/tr]
Unit DMS DM CC DS AV11 DS AV12
Succubus 0.1 1.5 0.4 0.4
Haemonculus with Liquifier gun 3.3 0.3 01 0.0
Haemonculus with Liquifier gun 3.3 0.3 01 0.0
4 Trueborn w blasters 3.1 0.4 0.3 0.2
Venom w/ Dual Splinter cannons 1.3 0 0 0
4 Trueborn w blasters 3.1 0.4 0.3 0.2
Venom w/ Dual Splinter cannons 1.3 0 0 0
7 Bloodbrides, Syren with Agonizer 0.8 2.6 0.2 0.2
Raiders w/ DL .6 0 .1 .1
5 Warriors w blaster 1.7 0.3 0.1 0.1
Venom w/ Dual Splinter cannonss 1.3 0 0 0
5 Warriors w blaster 1.7 0.3 0.1 0.1
Venom w/ Dual Splinter cannonss 1.3 0 0 0
5 Warriors w blaster 1.7 0.3 0.1 0.1
Venom w/ Dual Splinter cannonss 1.3 0 0 0
5 Warriors w blaster 1.7 0.3 0.1 0.1
Venom w/ Dual Splinter cannonss 1.3 0 0 0
5 Warriors w blaster 1.7 0.3 0.1 0.1
Venom w/ Dual Splinter cannonss 1.3 0 0 0
8 Wyches, Hekatrixwith Agonizer 0.9 2.2 0.2 0.2
Raider w/ DL 0.6 0 0.1 0.1
3 Wracks 0.0 0.3 0.0 0.0
Venom w/ Dual Splinter cannonss 1.3 0 0 0
5 Scourges w haywire blaster 3.2 0.3 0.2 0.2
Ravager w/ DL 0.8 0 0.4 0.3
Ravager w/ DL 0.8 0 0.4 0.3
Ravager w/ DL 0.8 0 0.4 0.3
Total per turn 39.1 17 3.7 2.8

So now that we have looked at all the numbers as I have them figured, let me explain some things in a little more detail.

My vehicle wrecked results, as compared to the Bringer of Victory, butt an actual wrecked or destroyed result from penetration. The BoV site uses penetration as the cutoff. Therefore because I go a step further, my actual wrecked or destroyed results are much lower, but more accurate. If I was to go just off penetration my numbers would be much higher.

Additionally I have accounted for wrecked results from the haywire effect of our grenades and weapons. They are really low, but do result in some meaningful number because with a enough hits, a vehicle can be effectively wrecked though immobilized and weaponed destroyed results.

Secondly, my close combat numbers are doubled. Why you ask? Because there are 2 Close combat phases in each turn and I butt they will be fighting in both out turn and our opponents turn.

Based on these numbers. and how my list has performed over tha last 2 months and probably 30 or so games, it is pretty spot on. My list shoots like there is no tomorrow, and anything not in a transport gets hosed pretty bad.

Close combat is not this lists strong suit, but given I use my wyches and bloodbrides to crack open vehicles that are not destroyed from shooting or to block units coming out of transports, it don't really need the superkilly CC phase. Furthermore, the wyches are big enough to surround transports and by blocking exits, kill all the infanty inside a transport. How you would reflect this I don't know, but I usually am able to take out a unit just from blocking exit points. it leaves the wyches somewhat exposed, but a wreck vehicle is good for cover.

I am not saying this is the end all be all list, or that shooting is the way to go. What I have done is ladi out my list and looking at the numbers I can agree that based on those results, this is how my list actually performs overall.

In a nutshell, my list loves foot lists, and is not to fond of heavy mech, not big surprise considering DE codex. However, I did get a chance to play a leafblower list, and while it was a Dawn of War mission, the haywire grenade attacks wreaked havoc on the chimeras. In one multiassult phase, 5 out of 7 chimeras were either destroyed, stunned or immoblized off of some good dice rolls as well as a manticore. Looking at my numbers, that should not happen, and my dice were rolling really hot in the butt. Conversely, my shooting with 8 trueborn, 2 raiders and 3 ravagers did not result in a a single glance or penetration, Treu this is out of the norm and statistically this should not happen, but that is why we roll the dice. Very Happy

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