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I have seen umpteen arguments about the efficacy of a unit. To be honest some factors are very hard to measure on a numerical basis like the ability to move and fire or the impact that the ability to deep strike should have on the cost of a unit. and one factor that many people typically misjudge is the cost of the unit compared to its ability to kill enemy troops. To mitigate this I have been using a system that levels the point cost of the unit whom you are applying math hammer too.

1st. Determine how many shots/attacks it takes on average to kill an enemy unit. I usually use MEQ because they are the most common troop in the current meta. (# of attacks)(% chance of hitting)( % chance of causing a wound)(% chance of an armor save preventing the wound).

This is pretty standard.

2nd. Divide the average cost of the troop that you are examining by the percent chance that you will inflict a kill on the enemy.
(cost of individual from unit)/ (% chance of inflicting a kill on MEQ).
This tells you the number of points you need to spend on this unit type per kill that you can expect it to inflict on average.

As an example
plague marine vs MEQ in melee (2A)(.5)(.75)(.33)= .2475 marines killed per Plague marine in melee. (24/.2475) = 96pts CPK
Chaos Space Marine with extra CCW (2A)(.5)(.5)(.33)=.1615 marines killed per CSM in melee. (15/.1615) = 92pts CPK
Berzerker vs MEQ in melee (2A)(.66)(.5)(.33) = .2178 marines killed per Berzerker in melee. (21/.2178) = 96pts CPK

So you have to spend the same number of points roughly on CSM as you do Plague marines, as you do berzerkers to produce one kill on a MEQ. There are of course innate advantages that all three units have over one another however, CPK(cost per kill) analysis is a better yardstick to use for determining the efficacy of a unit than just looking at how many kills that unit inflicts on average.

It's interesting, but I still find some issues with it. I'll say, quite simply, that I do use mathammer, but the system still functions from a core issue that causes it overall problems: points are not an accurate value of unit efficacy. Though CSMs in the above example kill marines for the cheapest cost in melee, combat alone is not a measure of a unit's effectiveness. Tactically your plague marines (if I recall correctly) are the most resilient. If your opponent is packing tons of high output, high damage weapons, they can easily out-value other troops.

Whereas if you have sufficient mobility and the enemy is largely ranged, the Khorne bezerkers sky rocket in price.

Though this is interesting, at it's core it can only weed out very inefficient units (in most cases) which are often weak and easily identifiable. Thus you leave yourself in a position where you have to choose among X number of choices. Given the effort required, and the variables of what you fight, how they are equipped, what vehicles they're in, whether you attack first or not, etc., etc., the system doesn't seem overall useful.

Not that it isn't cool, and a neat way to compare various troops. I just don't think it solves enough problems to still justify the system on a wide scale.

User Labmouse42 has already done what is arguably the best way of determining a units durability called Resilience-per-point (RPP). And it uses similar reasoning to what you have, it might be worth taking a look to help you refine your idea.
http://www.simhammer.com/node/9

Isn't this just the standard calculation that everyone already does? I don't see what you've really added to it.

@ Peragrine.
It looks to me like he is using its effectiveness and comparing it to the cost.
If i am understanding this correctly....
a regular marine fighting a plague marine in melee will be (1A)(.5)(.33)(.33)(.66) = .0359 and then (18/.0359) = 501 pts.

So you are saying that the marine player would have to have 500pts of marines to ensure an average of 1 dead plague marine in melee.

500/18 = 27.7 marines to kill one plague marine in melee.
:? tests this theory. (27.7)(.5)(.33)(.33)(.66)= .99 dead plague marines. Hmmmmm?

I think this is why sennacherib plays nurgle.

@ orkninious - you are correct my freind, though this is NOT why i play plague marines. I just like nurgle.
@Krelinus - I'm not sure but it looks like the table that Labmouse42 came up with is the defense oriented version of my system. together they would make a nice compliment.

I don't math hammer like that, because honestly it doesn't just work like that. This game has dice, so you bet the average, and win an average amount - 66.7%(you use your math hammer). Another way to look at the game, is point exchange rates, point weights on the table, points on the table, points in small exchanges (unit vs unit smack) - example 700pts of tau suits shoot and kill 250pts of Ork bikers. Factoring in what the unit can absorb in terms of damage against an average will make you a better player then any math analysis can generate. Then again i recap, you can bet the 66.7%

Math is a helpful tool, but its not the end all/be all of the game. I'm a big fan of mathhammer, but the game isn't really balanced enough for a cost-per-kill breakdown for one, especially across Codexes for two. For three, you can't really look at it on a per model basis accurately. The number of available attacks greatly affects how many hits/wounds/failed saves your unit is going to have. The further into the equation you go (calculating hits vs calculating wounds vs calculating unsaved wounds), the larger the effect the initial number of attacks has.

The size of the unit and number of attacks each model has will be changing your numbers a lot. Plus, some units have different models that are a required part of it (Sergeants, Champions, Exarchs, etc) with a different number of base attacks, and possibly other abilities. Also you missed the fact that Plague Knives are Poison 4+ and so wound MEQ the same as any other MEQ wielded CCW.

Taking two of your examples:

plague marine vs MEQ in melee (2A)(.5)(.75)(.33)= .2475 marines killed per Plague marine in melee. (24/.2475) = 96pts CPK
Chaos Space Marine with extra CCW (2A)(.5)(.5)(.33)=.1615 marines killed per CSM in melee. (15/.1615) = 92pts CPK

Both of these units can have a minimum of 4 models + a Champion version. For CSM, you get 4 CSM w/ Bolt Pistol and CCW plus a Champion w/ Bolt Pistol and CCW for 83 points. For Plague Marines you get 4 with Bolt Pistol and Plague Knife plus a Champion with Bolt Pistol and Plague Knife for 120 points. Both units have 11 attacks, 16 on the charge. Re-do the math vs MEQ:

11 Attacks * (3/6) * (3/6) * (2/3) == 1.83 Unsaved Wounds

Plague Marines: 120 points minimum / 1.83 == 65.5 CPK
Chaos Space Marines w/ BP + CCW: 83 points minimum / 1.83 == 45.3 CPK

Since this is vs MEQ, you should also factor in Veterans of the Long War:

11 Attacks * ((3/6) + ((1/6) * (3/6))) * (3/6) * (2/3) == 2.14 Unsaved Wounds

Plague Marines: 125 points minimum / 2.14 == 58.4 CPK
Chaos Space Marines w/ BP + CCW: 88 points minimum / 2.14 == 41.1 CPK

For just plain old CSM (without the extra CCW) this would turn into 1.17/1.36 Unsaved Wounds and CPK of 64.3/58.8 depending if they had VOTLW or not.

So your CPK numbers are double what they should be or as near enough as makes no difference. This is a game of Units. For the most part, individual models don't make actions so you have to do your calculations on a per unit basis. Otherwise your numbers quickly go wrong. You're shorting your Plague Marines 0.4 kills, even with your generous boost to their To-Wound roll.


Anyways, it can be useful to look at these numbers. But its useless to compare them to units not in the Codex. I'm not saying you were saying to do that sennacherib, but there are some who might assume you could do that. Its irrelevant to do so since if something isn't in your Codex, you don't have it as an option. Seems a silly comment, but its an important one to note. Some enemy units can potentially be more efficient at killing enemy models than a unit you have. Either you have an older Codex and it doesn't matter because you only have one choice regardless, or a combination of units in your own Codex working together can lead to you being more efficient (see Codex: Tau Empire).

But when analyzing a unit compared to other in-codex units or the same unit with different options, it can be a little enlightening. For example, this makes me think that paying for the extra CCW in a vanilla CSM squad is well worth the time! For an extra 8 points the 5 man unit is increasing its chance to kill MEQ in an assault by ~53.5%. That's useful information to know.

It also helps to have some perspective in what you are actually getting. Those Plague marines for example. 120pts vs 83 pts doesn't buy you any added killing power. The extra 43 points (and loss of Initiative vs MEQ) is getting you Toughness 5, Fearless, and Feel No Pain. On top of that durability you are getting the option to take double Special Weapons without having to take 10 models. That's what makes Plague Marines interesting to take, considering just to get Toughness 5 on CSM it is costing you 15 Points, nearly half the increased point cost between the 5 man CSM and the 5 man Plague Marine units.


Blah I'm starting to ramble now! My point I was trying to make was that CPK is good to look at when comparing units in a single Codex, but to keep perspective and that there's a lot more to how efficient a unit is than just how much they throw out there. Also, you have to look at Units, not Models if you want an accurate number.

I actually wrote a program that did all of what you suggested and took it one step further. The program would tell me how long a unit of a certain size would take to kill a unit of marines that were X size. who would win and in how many rounds of combat.
(Turned out that a 10 zerker unit would wipe out a whole unit of marines on the charge).

The Value that I find in CPK analysis is the side by side comparison that it yeilds. You do have to make some mental gymnastics for factors such as durability, feel no pain etc. However. In the long run i think it is especially illuminating for case by case comparisons. I fully agree with your opinion cowmonaut, that a multivariate system like 40k is difficult to precisely analyze. Yet people will do math hammer and often neglect the price of the unit in their calculations. Thus, CPK.

I'm a big fan of math-hammering, and anyone who looks over my past posts will see that.

However, I think part of the problem here is that we're trying to reduce something down to a single metric. I think comparisons (such as cost per kill) can be useful, but first you need to determine the role you're trying to fill. Otherwise your metric can be misleading.

For example, on a CPK metric, bloodletters in CC will score exceptionally well against marines. Plague Marines will fare much worse, despite, from a whole of game perspective, being better.

I think the real value of math-hammer is comparing two things that are (at least as far as the analysis is concerned) being considered for the exact same role. Are broadsides or hammerheads more likely to kill a given enemy tank (ie annihilation barge with jink) in one shot? How do markerlights change that?

A metric like CPK is great if you know you're always fighting enemy x, and that you'll always have y models in combat. But as soon as other factors kick in (such as different iniatives, and shooting, and situations where alpha strike is quite important (ie getting at least 3 glances on a given tank)) then more advanced techniques are required to actually give a useful metric of comparison.