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Intense Mathhammer: 5th ed style
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Old 08 Oct 2008, 05:31   #1 (permalink)
Shas'Vre
 
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Default Intense Mathhammer: 5th ed style

So, I really shouldn't be up this late on Tau Online, but after a rough physics exam, I need something to do to take my mind of things.

Anyway, yesterday, while trying to make a 1500 point army list, I instead ended up doing the most intense bout of mathhammer I've ever done. It was a lot of fun, but I found a lot of scary things about my army lists that I hadn't realized, which is going to cause me to rethink a lot of things and/or play more to see how this all plays out practically.

So, the first thing I did was analyze my favorite unit, my deathrains. At 106 points, they put out 4 str 7 shots that hit 8/9 of the time (yay target locks). Now, normally they target rhinos, but with the new rules for killing vehicles in 5th edition, I had to see how they fared. The first time I do the mathhammer, I'll walk through each step in the thought process, but after that, I won't but the formula will be the same, so you guys should be able to bear with me.

First off, we have 4 shots that are at TL BS 4, and hit 8/9 of the time. Thus we get:

4 * 8/9

As I'm assuming the average scenario against a rhino, aka smoke launchers, we have to bring in the 1/2 chance of them ignoring our hit.

4 * 8/9 * 1/2

Now we'll go straight for the kill. 1/3 chance to pen. 1/3 chance to kill.

4 * 8/9 * 1/2 * 1/3 * 1/3 = 16/81

16/81 or 19.75%

Wow... In 4th edition, deathrains were definitely a lot more lethal. Now, of course killing a rhino is preferable, but immobilization can also help, so I'll include that as well.

4 * 8/9 * 1/2 * 1/3 * 1/2 + 1/6 * 1/6 = 18.25/81

That's ~22.5%.

Somewhat higher. The plus 1/6 * 1/6 is for glances, and this is the format I'll be using for the rest of the article, FYI.

Now, something I found out doing this (other than that missile pods are feeling neglected in 5th edition) has to deal with Ork trukks.

4 * 8/9 * 1/2 * 1/2 * 1/3 * 1/3 = 8/81 (9.87%)

An Ork trukk in cover has TWICE the survivability against this crisis team than a rhino. Of course, the extra 1/3 is for their stupid special rule, and if you include that on a 3-4 they still die (just Kareen! in a random direction), you get 16/81, equal to a rhino. An Ork trukk is EQUAL IN SURVIVABILITY to a space marine rhino. I'm not quite sure who should be insulted here, but hot damn... On the plus side, Orks rarely take to cover, so we have a good chance to double the chances of blowing them to hell, but still...

Oh, as a side note, I'm neglecting markerlights purposefully as they are better suited for increasing the BS of fire warriors for attacking enemy infantry. Plus, my army normally doesn't use them, and it adds far too many factors to include here :P

For completion, I'm going to include this deathrain unit against the new falcon, which is what they were originally designed for

4 * 8/9 * 1/2 * 1/6 * 1/3 * 1/3 = 8/243 (3.3%)

Ooh boy... Luckily, we've got railguns, so lets take a look at those.

[hr]

First off, railguns target the enemy heavy armour, so lets look at a railgun shooting at AV 14 and 13, both in cover. (As an aside, just double all chances of killing if you're shooting at a tank outside of cover. I know most of you got that, but just in case

Railgun (hammerhead) vs AV 14
1 * 2/3 * 1/2 * 1/3 * 1/2 + 1/6 * 1/6 = 1/12
(extra + 1/6 * 1/6 is for the chance of a glancing hit destroying the vehicle, thanks to AP 1)

So, for the record, a railgun has a 8.33% chance of killing AV 14 in cover. After doing these statistics, I start wondering how things die at all, and then I remember it's a dice game...

HH railgun vs AV 13

1 * 2/3 * 1/2 * 1/2 * 1/2 + 1/6 * 1/6 = 1/9

Somewhat better, but still ridiculous. I was hoping for something a little better, but that cover save is definitely rough.

For completion, I'll include broadside railguns, and I'm assuming BS 3 because of A.S.S. usage

Broadside vs AV 14
1 * 3/4 * 1/2 * 1/3 * 1/2 + 1/6 * 1/6 = 13/128

Slightly better than a Hammerhead at ~10.2%

at AV 13

1 * 3/4 * 1/2 * 1/2 * 1/2 + 1/6 * 1/6 = 35/256

which comes to ~13.7% So a broadside is marginally better at killing tanks than a hammerhead, but we already knew that. However, let's continue to piranhas.

[hr]

In 5th edition, melta weapons at half range became the undisputed best tank killers in the game. Let's see just how well they do.

Piranha (with targeting array) at 6" vs AV 14

1 * 2/3 * 1/2 * 21/36 * 1/2 + 1/6 * 1/6 = 1/8

This is 12.5% Which is interesting, because it's only 2% points better than a broadside, and requires to be very close. What one should keep in mind, however, is that the close range required and the true LOS rules means that it is far more likely to negate the cover save, thus doubling the effectiveness of the attack, which is awesome.

At AV 13, we get

1 * 2/3 * 1/2 * 26/36 * 1/2 + 1/6 * 1/6 = 5/36

At 13.88%, melta weapons come out on top. Something to consider here, however, is that against Tau, melta weapons are generally far more effective, as they are inside the disruption pod's minimum range, and this effectiveness is doubled. That's a very scary prospect for us, so watch out.

[hr]

Lastly, we have our seeker missiles. They are very powerful weapons, capable of doing a great many things. Let's see how well they deal with rhinos.

1 * 5/6 * 1/2 * 1/2 * 1/3 = 5/72

This is 6.94%, which is okay at 10 points a missile. Three are better than missile pods, but not reusable, so it's a fair trade off. Of course, sticking seeker missiles on piranhas and getting the sides of predators is definitely worth the shot.

[hr]

I'll stop here for now, as I'm about to fall asleep. I'll post more up sometime soon.

Cheers!


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Old 08 Oct 2008, 23:37   #2 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

Nice post i would like to see some theoryhammer on pulse rifle on rhino action as well as mutiple Broadsides.
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Old 09 Oct 2008, 00:14   #3 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

Your math is fine, I just think efficiency is very important to keep in mind. Efficiency is much harder to figure out for tank killing because there is no "benchmark" or best, but you could do it "by points", that is to say, normalize the results according to the cost of the lowest option you want to compare things to.
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Old 09 Oct 2008, 20:08   #4 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

After this thread is done and the math is checked, it should get stickied.

Nothing beats having ALL the mathhammer figures done and ready for you when fine-tuning an army list.

Keep up the great work, Castris!
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Old 09 Oct 2008, 20:47   #5 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

I think your math is flawed, you are missing certain options. I've only checked this for the Deathrains vs Rhino, but I am suspecting it could be the same for the rest of your examples.

You want to immobilise or destroy the rhino, there's three possible ways to do this:

1. Penetrate --> Destroy
2. Penetrate --> Immobilise
3. Glancing --> Immobilise

Lets look at the math of each, following the format [# shots]*[chance of hit]*[cover save]*[chance to glance/penetrate]*[chance to immobilise/destroy] :

1. 4 * 8/9 * 1/2 * 1/3 * 1/3 = 16/81 = 19.75%
2. 4 * 8/9 * 1/2 * 1/3 * 1/6 = 8/81 = 9.88 %
3. 4 * 8/9 * 1/2 * 1/6 * 1/6 = 4/81 = 4.94 %

Added together you get 34.57 %.

Quote:
Originally Posted by wind777
Nice post i would like to see some theoryhammer on pulse rifle on rhino action as well as mutiple Broadsides.
Assuming you want to score an immobilised, the math for one pulse rifle at more than 12" is (assuming the rhinio has no cover save):

BS3: 1 * 1/2 * 1/6 * 1/6 = 1.39% --> roughly 72 pulse rifle shots to immobilise
BS4: 1 * 2/3 * 1/6 * 1/6 = 1.85% --> roughly 54 pulse rifle shots to immobilise
BS5: 1 * 5/6 * 1/6 * 1/6 = 2.31% --> roughly 43 pulse rifle shots to immobilise

For broadsides, the chance to wreck, destroy or immobilise (counting only the TL railgun) is:

BS3: 1 * 3/4 * ( 5/6 * 2/3 + 1/6 * 1/3) = 45.83%
BS4: 1 * 8/9 * ( 5/6 * 2/3 + 1/6 * 1/3) = 54.32%
BS5: 1 * 35/36 * ( 5/6 * 2/3 + 1/6 * 1/3) = 59.41%

[size=10px]Edit by FT: I merged your two posts together as double posting is strongly discouraged here. But I did give you a karma point for helping out .[/size]
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Old 09 Oct 2008, 23:09   #6 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

Quote:
Originally Posted by Anders
You want to immobilise or destroy the rhino, there's three possible ways to do this:

1. Penetrate --> Destroy
2. Penetrate --> Immobilise
3. Glancing --> Immobilise

Lets look at the math of each, following the format [# shots]*[chance of hit]*[cover save]*[chance to glance/penetrate]*[chance to immobilise/destroy] :

1. 4 * 8/9 * 1/2 * 1/3 * 1/3 = 16/81 = 19.75%
2. 4 * 8/9 * 1/2 * 1/3 * 1/6 = 8/81 = 9.88 %
3. 4 * 8/9 * 1/2 * 1/6 * 1/6 = 4/81 = 4.94 %

Added together you get 34.57 %.
Thanks, Anders. I'm going to go through the original work on this, and redo certain things. However, this clarifies a few things for me, and they will get reflected in the main post, and subsequent ones.

The rest of this won't be posted until, at the earliest, tomorrow. I've got far to much Calculus homework to do, and my folks are coming to visit me, so I have to spend time with them (and have a good bitch about the new marines with my little brother )

Cheers!
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Old 10 Oct 2008, 03:47   #7 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

Hmmm castris, you should talk to Dr Wu about this. He'd love to help, since he's into all of the mathammer stuff.
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Old 10 Oct 2008, 06:13   #8 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

I* am good at mathammer but this may take me a while. The two deathrains work however smoke launchers in 5th basically make most weapon ineffective against them. One weakness with just this data is it assumes you are in range. This is why the deathrain appears inefficient while in reality and actual game play his utility is greater as he will get more shots off fast. The thing is its hard to assume your opponent has cover. agianst the non cover is just doubles. the thing is smoke launchers are only one turn. Another reason that does not happen is if you have the first turn and are shooting the deathrain gets. imoblizing the enemy may help on rhino as it renders the scoring rhino ineffective. So one half of the time if you get the first turn 34 (seizing the initive cancels out) percent chance to kill the rhino before he strikes the one half here replaces the cover save. Then there is the 34 percent chance to kill it on the second turn. However unless your opponent stupidly places his rhino in front of you. however you cannot assume that the 11/12 of the time that you do not sieze the initive your opponent will place the rhino directly in front of your or other tank you want to take out. Yes you also did forget the immobiliznign for the rhino on penning. Remeber theese kind of staics apply to your vehicles and their disruption pods. so for that unit deathrains is actualy more eefficient than the figures first suggest. Same with broadsides and hammerheads although hammerheads can manevuer making cover less important.
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Old 11 Oct 2008, 05:06   #9 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

I hate to break it to you, but some of your calculations aren't quite correct; in this case I'm going back over your Deathrain vs. Rhino argument (specifically, the first part where we are trying to destroy it outright).

To begin with, you're incorrectly calculating how shooting 4 shots affects the probability. Also, you've not taken into account that three Immobilised and/or Weapon Destroyed results will also give you a Wrecked result.

For any given shot, the chance of scoring an outright destructive hit is 8/9 * 1/3 * 1/2 * 1/3 = 4/81 (hit, penetrate, cover save, damage table). Whilst taking 4 shots, the chance of scoring an outright destructive hit is: 1 - (1 - 4/81)[sup]4[/sup] which approximates to an 18.3% (3sf) chance.

In addition to this, the chance that you score an Immobilised or Weapon Destroyed result is 8/9 * (1/6 * 1/2 * 1/3 + 1/3 * 1/2 * 1/3) = 2/27. Therefore the chance of NOT getting an Immobilised or Weapon Destroyed result is 25/27. As we are rolling 4 dice, there are a total of 16 outcomes (2[sup]4[/sup] = 16). Out of these 16 outcomes, only 4 outcomes give us 3 Immobilised/Weapon Destroyed results and only a single outcome gives us 4 Immobilised/Weapon Destroyed Results (assuming Y = Immobilised or Weapon Destroyed result and N = otherwise, we need YYYN, YYNY, YNYY or NYYY for three, or YYYY for four, hence 4 and 1 outcomes, respectively, out of 16 outcomes).

Therefore, using the formula P[sup]a[/sup] * Q[sup]b[/sup] * c, where P is our chance of success (2/27), Q is our chance of failure (25/27), a is the number of Immobilised/Weapon Destroyed results we want, b is the number of Immobilised/Weapon Destroyed results we do not get (and a + b = 4, since we're rolling 4 dice) and c is the number of occurrences (4 when a = 3 and 1 when a = 4), we get the following:

(2/27)[sup]3[/sup] * (25/27)[sup]1[/sup] * 4 = 0.151% (3sf) (yes, that's one fifteenth of a percent)
(2/27)[sup]4[/sup] * (25/27)[sup]0[/sup] * 1 = 0.00301% (3sf) (three hundredths of a percent)

However, if 3 Immobilised/Weapon Destroyed results are rolled, there is a chance that the fourth roll will be an outright vehicle destroyed roll - since we're looking at adding all of these percentages up, we need them all to be mutually exclusive, so we need to deduct the chance of rolling a vehicle destroyed from that first value. This is calculated by multiplying 0.00151 by 77/81 (i.e. the chance of it NOT being an outright vehicle destroyed result), giving us 0.143%[sup]see note below[/sup].

Ergo, the chance of destroying a Rhino, in cover or using Smoke Launchers, with no additional weapons, is 0.183 + 0.00143 + 0.0000301 = 0.185 (3sf) = 18.5% (3sf) chance of destroying it outright.

Whilst the calculations to add the chance of 3 or 4 Weapon Destroyed/Immobilised results are a little tricky, and add a nearly negligable percentage to our chances, between the fact that you have neglected to consider all possible damage outcomes and the initial error in calculating the chance of an outright destructive hit makes me wonder if there's anything else forgotten in the rest of your calculations.

[hr]

Note: This calculation may or may not be entirely correct; it's 5am right now and I kinda need some sleep. Nonetheless, regardless of whether this specific calculation is correct or not, my points that not all variables have been taken into account, and that the OP's calculations are not 100% accurate are still valid.
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Old 11 Oct 2008, 10:58   #10 (permalink)
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Default Re: Intense Mathhammer: 5th ed style

@ Masked Thespian

You are calculating propabilities, whereas we have been calculating statistical averages. Both have their uses. But the major difference is that, say you have 50x2 Deathrain suits, by use of propability you will have a (without having done the math) 98-99 % chance of killing (at least one) rhino - whereas the statistial average approach will tell you that on average, 50x2 deathrains will kill ~16 rhinos.

I just wanted to make that clear for any reader, the difference between the two calculative approaches.

propability = 1 - (1 - propability of a shot "wounding)^(number of shots) - gives a number between 0 and 1 - the propability of your cumulative shots "wounding"
statistical average = (number of shots) * (propability of a shot "wounding") - gives a number between 0 and infinite - the average number of shots "wounding"

Personally, I find the statistical averages more useful - I dont need to know that my 12 rapid firing firewarriors have a 98% chance of killing a guardsman in the open, I'd rather know that they will, on average, kill so-and-so many guardsmen.
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