SW Math-Hammer 201

[jjfelber]

CORRECTIONS!!! I Have noticed a large flaw in my Math-Hammer and do not yet have time to fix. Please look at this with thr following in mind. For some reason all the calculations are done at a Armor save of only 4+! :tu:, right? So the table and all the frag math will show that the frag is actually even worse than described.

Sorry!

 

 

Observation: While using my Longfangs I have the choice to shoot an enemy squad of Space Marines with either Krak Missiles or Frag Missiles. Which type of missile is better Vs. Space Marines? Frag or Krak

 

Hypothesis: Frags are better than Kraks at taking down a group of Marines, Kraks are better at taking down a small amount of marines or Marines in a full 2” Spread.

 

Experiment: Math-Hammer!!

 

The Math starts out pretty Simple. As with all weapons in Warhammer the equation is a follows.

(#of Shots)(Chance to Hit)(Chance to Wound)(# of failed Saves) = (# of wounds)

 

Krak Missiles are pretty straight Forward

(1)(0.6667)(0.8333)(1) = 0.5556 wounds per marine.

 

Frag Missiles are bit more abstract and we have to make some assumptions to make this work.

# of Shots = 1.85185

So How did I get that number?

One Missile can hit quite a few marines depending on how tightly the marines are clustered, and how far the shot scatters. So First things first, odds of direct hit (2/6 = .3333). That leaves the odds of scatter at .6667. But we all know you can roll a scatter and still get a direct hit with the 2d6-BS distance.

Which means, any roll of a 4 or lower on 2 dice is also a direct hit, or, 6/36=.1667. Now here is ASSUMPTION #1, if you roll a 5 on 2d6 the template only moves an inch, so I am also going to say a roll of a 5 is also a direct hit you may lose a model under the template but you may also gain a model. This will bring the total of a Direct hit after a scatter to 10/36=.2778. Multiplying this by the chance to roll a scatter gives you (.2778)(.6667)=(.185185). That number can be added to the odds of a direct hit to bring out Direct Hit total to .518518.

 

Now this is where it gets even trickier. Let’s say you roll a 6 or 7 on the 2d6 you may still have a few models under the template. So now we need to make some more assumption. ASSUMPTION #2, a direct hit has three models under it! ASSUMPTION #3, a scatter of 2 inches (6-BS=2) will now only have 2 models under it. So to do the same math as above, odds of a 6 on 2d6 is 5/36=.13889 Take that multiplied by the chance to roll a scatter gives you (.13889)(.6667)=.092593, But we need to multiply this by 2/3=.6667 because we are only hitting 2 models instead of 3. (.092593)(.6667)=.061728. That number can be added to the running total of odds of a direct hit to bring out “Direct Hit” total to .58025.

 

ASSUMPTION #4, a roll of a 7 on 2d6 or a scatter of 3 inches will only hit 1 model. Continuing to add to the running total, Odds of a 7 on 2d6, 6/36=.1667. That multiplied by the odds of rolling a scatter, (.1667)(.6667) = .1111. Now that multiplied by 1/3=.3333, because you are only hitting one model not three, (.1111)(.3333)=.037037. Add that to the running total of “Direct hit” and you get .61728. (Please note: I am NOT saying there is a 61.7% chance to get a direct hit) Now this may be a bit abstract and I hope you are all following. To get to the #of Shots fired by a single frag we have to multiply the .61728 by the original 3 models under the template for a product of 1.85185.

 

Now we can do our equation.

(#of Shots)(Chance to Hit)(Chance to Wound)(# of failed Saves) = (# of wounds)

(1.85185)(1)(0.5)(0.5)= 0.462963 wounds per marine

 

Analysis:

According to my math, Kraks are better at taking down Space Marines then I thought. They are actually better than frags, but how much Better? In the example above the Long Fangs are shooting at a squad of marines where the small template can at most hit 3 marines. On a scatter of 2 inches it only hits 2 marines, a scatter of 3 inches only hits one marine, and a scatter of 4-8 inches it hits nothing. Now, what if the marines are more tightly packed? At what point (not changing assumptions #3 and #4) do Frags become better than kraks? If we change assumption #2 to 4 marines under the initial template, and mess the math a bit on the scatter (2 out of 4 and 1 out of 4 instead of 2/3 and 1/3), we come up with:

(2.37037)(1)(0.5)(0.5)= 0.592593 wounds per marine

 

At 4 Marines under the initial template the Frag becomes better than the krak by a hair.

as that number increases the frag gets better. But as that number under Assumption #2 gets larger Assumptions #3 and #4 get more farfetched. The odds of hitting 2 marines after a 2 inch scatter is much worse if you can fit 6 marines under the template to begin with, this scenario only really happens if the enemy is disembarking a tank or being funneled.

 

Here is a table showing how changing Assumptions #1, #2, #3, and #4 change the resulting wounds per marine.

…A#1…A#2…A#3…A#4…WPM

……10……2 ……2 ……1 ……0.333

……10……3 ……2 ……1 ……0.463

……10……4 ……2 ……1 ……0.593

……10……5 ……2 ……1 ……0.722

……10……6 ……2 ……1 ……0.852

……10……7 ……2 ……1 ……0.981

……10……2 ……1 ……0 ……0.282

……10……3 ……1 ……0 ……0.412

……10……4 ……1 ……0 ……0.542

……10……5 ……1 ……0 ……0.671

……10……6 ……1 ……0 ……0.801

……10……7 ……1 ……0 ……0.931

……6 ……2 ……2 ……1 ……0.282

……6 ……3 ……2 ……1 ……0.394

……6 ……4 ……2 ……1 ……0.505

……6 ……5 ……2 ……1 ……0.616

……6 ……6 ……2 ……1 ……0.727

……6 ……7 ……2 ……1 ……0.838

……6 ……2 ……1 ……0 ……0.241

……6 ……3 ……1 ……0 ……0.352

……6 ……4 ……1 ……0 ……0.463

……6 ……5 ……1 ……0 ……0.574

……6 ……6 ……1 ……0 ……0.685

……6 ……7 ……1 ……0 ……0.796

 

 

 

 

Assumption #1 changes from the original idea, a scatter of 1 inch is still a direct hit, to a scatter of 1 inch is no longer a direct hit.

Assumption #2 changes depending on the number of marines under the template.

Assumption #3 changes between the template hitting 2 additional models to the template hitting 1 additional model on a scatter of one additional inch.

Assumption #4 changes between the template hitting 21additional models to the template not hitting any additional models on a scatter of one inch further than Assumption #3.

 

Conclusion:

According to the table for a frag to be better than a krak there has to be on average 4-5 models under a direct hit depending on the amount of models in the unit. Knowing that marine units rarely are above 10 models it is unlikely that a scatter of more than 3 inches will ever yield a hit. Frags also have an even more difficult to study perk. They have the potential to kill more models then you have Missile Launchers. A full unit of MLs firing kraks can only ever kill a max of 5 models, where if the LFs fired Frags they could potentially kill more than 5 models. I do not think this would change the table much but it is something to consider.

 

Quick note, when firing MLs at Terminators, Frags become much better than Kraks as the only reason kraks can compete with frags is that they are AP3. Take away the AP and they are pretty bad troop killers.

[breng77]

Seems pretty accurate except you also need to take into account that krak can double things out so if you are firing at say paladins krak is still better.

[jjfelber]

You are correct, That is another thing to keep in mind. I should have added that. The main part is for T4 W1 3+Sv. The Quick note is for T4 W1 2+Sv.

[Freman Bloodglaive]

Basically it comes down to, are they in cover or not.

 

If in cover then krak isn't going to make a huge impression, so going for frags forces them to make more saves which will result in more dead marines.

 

If they're in the open I'd krak them.

[Jaarl Stormfang]

In these sorts of mathematical assumptions it's best to reorganise it so that the assumption comes last. For example (using integers to keep it in comprehensible numbers).

 

To kill 5 marines takes 6 krak hits. Which takes 9 krak missiles shot.

To kill 5 marines takes 15 frag wounds, which is 30 frag hits.

 

 

So in order to match krak missiles, you would have to average more than 3 hits per frag shot. When you look at it this way you can quickly see that frags are obviously far inferior to kraks in taking out marines.

 

When cover is involved, I'd say it's a toss up, as it effectively halves the average number of frag hits you need in order to equal kraks.

[jjfelber]

Yes, and the math shows it even worse than and average of 3. The number is actually 4 and closer to 5.

 

I agree that I probably should have gone with whole numbers first, but scattering and model density are very important. To say Kraks are better than Frags at killing marines is largely untrue.

 

When Cover is involved it again needs to check scattering and model density. But the models really have to be sparse for kraks to be better than frags

[jjfelber]

I just noticed the math is a bit flawed showing the frag is better than it actually is. Please be advised. I will attempt to fix later. Sorry Guys!

[Jaarl Stormfang]

Yes, and the math shows it even worse than and average of 3. The number is actually 4 and closer to 5.

 

I agree that I probably should have gone with whole numbers first, but scattering and model density are very important. To say Kraks are better than Frags at killing marines is largely untrue.

 

I have to disagree here. Firstly, the number isn't 4 or 5, it's just over 3 as my very easy to follow maths shows. 30/9 = 3.33. So frags will equal krak kills if you average 3 and a third hits per frag missile. Averaging even 3 hits per frag missile is very difficult.

 

Next, it is not largely untrue to say that kraks are better than frags at killing marines. In fact it is largely true. It is sometimes untrue - in particular when cover is involved (but even that's debateable)

[jjfelber]

To kill 5 marines takes 15 frag wounds, which is 30 frag hits.

 

So in order to match krak missiles, you would have to average more than 3 hits per frag shot. When you look at it this way you can quickly see that frags are obviously far inferior to kraks in taking out marines.

 

Now to be clear, when I say it is largely untrue, that kraks are better than frags I mean that the blanket statement is untrue, because there are many situations when frags will be MUCH better than kraks. Quick Example. Your dread destroys a Rhino with a Melta, ten marines disembark. The marines are so tightly packed you can hit 7+ marines with a direct hit. If you used Kraks in the situation you would be making a mistake. That is one of the points I am trying to get across. Model Density matters. So just using a blanket statement "Kraks are better than Frags" is false.

 

 

Your simple math is also correct, but how many shots does it take to average 3 hits per shot?

[Jaarl Stormfang]

Ok, that's cleared it up. I agree about blanket statements and, if you can get 7+ models with each blast you are going to average way more than 3 hits per frag fired, so in that case go for frags.

 

I dont understand your last question. It's an average so it's independent of the number of shots fired.

[jjfelber]

I dont understand your last question. It's an average so it's independent of the number of shots fired.

 

That's what my long spiel was about. You say 3.33 frag hits per missile, but your math also says 6 frag hits should yield 1 dead model. So how many missiles must be fired to yield 6 frag hits?

 

My math, going off of assumptions #1-4, shows a single frag shot will yield 1.852 frag hits. So to kill a single marine, where the template is a direct hit on 3 models (A#2) you would need 3-4 shots.

 

We are saying the same thing here, just in different ways.

[Jaarl Stormfang]

I dont understand your last question. It's an average so it's independent of the number of shots fired.

 

That's what my long spiel was about. You say 3.33 frag hits per missile, but your math also says 6 frag hits should yield 1 dead model. So how many missiles must be fired to yield 6 frag hits?

 

 

My point is you don't need to know the answer to this question. You're trying to estimate it using assumptions that are very situational.

 

Instead, if you leave the estimation till the end like I did by working out how many hits you need per frag shot, then it becomes a much more real world understandable conclusions. Ie.

 

Vs Marines

No cover: Frags are better if you can average more than 3.33 hits per shot (normally you can't)

4+ cover: Frags are better if you can average more than 1.66 hits per shot (i'd say its a push)

 

Your method has merit, but by it's nature is very inaccurate. I say leave the estimation up to the user, working from those two rules I've labelled above. It gives the user guidelines, so they can look at them, look at the situation on the battelfield (ie, spread out unit in the open, or densely packed rhino survivors in cover) and pick frag or krak based on that.

 

 

EDIT* But as you say, we are saying the same things ultimately. Frags need dense packing to be better than kraks. If our conclusions were different I'd be worried!

[breng77]

Another note on Frags, is sometimes they are situationally more useful due to the face that they have a bigger upside.

 

What I mean by that is if you are shooting 4 missile launchers at 5 marines, even if you can only catch 2 marines in the blast, the frag missile has the possibility of killing all 5 marines (i.e. it can cause 10 wounds) so if you need to wipe out a squad (maybe that squad is fearless) the frag gives you the possiblity that this can happen, the krak can only ever kill 4 marines. Now the situations in which this might be needed are not many, nor is it likely that you will kill more marines with the Frag missiles, only that it is possible.