Pi is a Lie!

I have just seen the light and now feel compaired to share this with you. 

Pi is a lie!

Termagants, a study of weapon load outs.

    So I pick up playing Tyranids this year, and I was debating how to assemble my Termagants. This led me to look at the pedigrees before I play the ponies, so to speak. Really I was looking to play with R, think about writing an iPhone app (still thinking doing that), and the end doing my number crunching in Excel. The opponent de jure was Vanilla Space Marines, because that will probably be what I am fighting the most.

The Setup

So to start I found what the odds for a single model to kill (T4 with 3+ armour) for each weapon chooses I was considering Devourers, Fleshborer, and Spinefist.  That was the thought part, because Spinefist are twin linked, but this is more for another day.  After you have the chance to kill for one attack, then it a simple matter of Binomial Theory to make the following graphs, but first the chance to get one kill.

Vs. T4 w/ 3+ armour

Devourers = 8.3% = {½ (hit) * ½ (wound) * 1/3 (fail armour save)}
Fleshborer = 8.3% = {½ (hit) * ½ (wound) * 1/3 (fail armour save)}
Spinefist = 8.3% ={ ½ (hit) * 1/3 (wound) * 1/3 (fail armour save)} + { ½ (miss) * ½ (twin linked) * 1/3 (wound) * 1/3 (fail aromur save)}

    So attack for attack, they are statically equal, but Devourers get three attacks per model at 10 points apiece, and the spine fist get the same odds as a Fleshborer (5 points), but at a one point more. Note that the calculation on the spine fist makes things a bit more interesting.   To make the comparison fair I went to a close to 100 pts worth of model as I could get it, end up with 102 points worth of SpineFist. That comes to ten models with

The Graph and Results

 

Kills	Devourers	Fleshborer	Spinfist
0	7.35%	17.55%	22.78%
1	20.05%	31.91%	35.21%
2	26.43%	27.55%	25.61%
3	22.42%	15.03%	11.64%
4	13.76%	5.81%	3.70%
5	6.50%	1.69%	0.88%
6	2.46%	0.38%	0.16%
7	0.77%	0.07%	0.02%
8	0.20%	0.01%	0.00%
9	0.04%	0.00%	0.00%
10	0.01%	0.00%	0.00%

    Well there the results, and against such a high toughness unit, the Spin fist just does not cut it.  While they are more likely to kill one model then a Fleshborer, the Fleshborer is less likely to get no kills and more likely to kill in each category higher than one.  But the king here is the Devourer in pure killing ability. It would take 150 points (30 models) worth of Fleshborers to get the same odds, but this might not be a bad thing as it would make the unit last longer, when they start taking casualties. Devourers also have two more advantages going for them, they shoot 18”, unlike the 12” of the Fleshborers and Spinfists, as well force a moral check on the receiving unit.

Conclusion:

    Devourers win on laying down the fire, but if I was going to press forward and not hold ground a large blob of Fleshborers would be my pick, and this is just how I put my bugs together.
I still think Spinfist could be an interesting choice, but just not against such high toughness targets, due to their lower strength.

Closing Thoughts:

• This is what I want to see when someone talks about Math Hammering, don’t tell me the odds for one attack to kill, tell me the chances of how many kills the unit will give out.  This takes in to account how many are attacking as well as how good they are at it.
• If you like this and want to see how these bio-weapons will do against you favorite piece of flesh, let me know, I have it automated in Excel would take me all of five minutes to make you a pretty graph of your liking.
• Plan on doing much more of these, so I am open to suggestion of what you want to see, X vs. Y sort of thing.
• Still owe you a math talk on binomial theory, but that is in the pipes works and will be coming.  Probably after my vacation this summer.