Advantages of a Death Guard Marine

Question: how much better is a plague marine in comparison to a normal marine? How can this be evaluated? Are they worth the extra points?

Statistic of Merit.

I'll define the statistic of merit as being the "number of standard shots required to kill", where a standard shot is one bolter round fired by a space marine. I choose this as being the standard shot as it is the type of round most commonly encountered in the game. Perhaps I'll look in to other rounds & alien races at a later date (e.g. las-guns fired by Imperial Guard; etc.).

Removing the fancy mathematical language, I like to think of this statistic as a measurement of the "hardiness" of a model, or how long it'll last on average.

Baseline.

Let's start by considering a standard space marine. He's got 1 wound, a toughness of 4 and a save of 3+ from his power armour. How many standard shots does it take to remove him?

Well, an opposing space marine firing a bolt round will hit on 3+, or 66.7% of the time. Therefore, he needs to shoot 1.5 times to hit his target once.

A bolt round (Strength 4) will wound our unfortunate space marine 50% of the time. So our standard shooter will need to fire 3 times at the space marine to cause a wound.

But, with a 3+ save, our space marine is only going to be removed from play a third of the time. So, our standard shooter will require an average of 9 shots to accomplish this task. Or put another way, when declaring fire with a marine on another marine, we have a 1-in-9 chance of a kill shot.

Plague Marine.
Our Death Guard plague marine has an incredible (for troops) toughness of 5, a 3+ armour save from his power armour and the "feel no pain" special rule.

As with our baseline example, it'll take 1.5 shots to hit the plague marine. No changes there.

Wounding the plague marine is harder though. It'll require 4.5 shots on average to land a wound compared to 3 against the baseline marine.

Given the power armour, we're now looking at an average of 13.5 shots to cause a (preliminary) un-saved wound. But with the feel no pain special rule, it'll take an average of 27 standard shots to remove the plague marine from the game. That is rather impressive to say the least.

The ratio of 27 to 9 standard shots means that our plague marine is 3 times hardier than an average marine! Without even looking up the numbers, I know that the points value of a plague marine is certainly not 3 times that of an ordinary marine.

But -- that is not the end of the story. A plague marine is 23 points compared to 16 (or 15) points for a standard marine. So, how many extra standard shots does a difference of 8 or 7 points make? Or put another way: how does an imaginary 23 point standard marine stack up? Let's take the worst case scenario that a standard marine is 15 points (a typical Chaos Space Marine). Those 15 points generate 1 standard shot, so 23 points generates 1.53 standard shots. Is this enough to remove the plague marine's advantage? To figure this out, I divide the hardiness derived above, 27, by the points-weighted number of shots, 1.53. This comes out as a points weighted average of 17.6 shots being required to kill a plague marine, shot by our imaginary 23 point standard space marine. This is still about double the hardiness of our standard marine.

So to answer the question posed at the beginning, they are most certainly worth the extra points.

Close Combat Hardiness.

I'm also going to define a close combat hardiness. This works exactly as above, but instead of firing shots, I'm going to consider a space marine striking an opponent in close combat. Here, the question is slightly modified: "How many attacks must a space marine make to remove a given model?"

Against another marine, 2 attacks are required to generate 1 hit. Only 50% of those hits will cause a wound, so 4 attacks are needed to give 1 wound. Two-thirds of those wounds will be saved, so 12 attacks are necessary to remove a space marine.

In comparison, our Death Guard marine is going to be wounded less often due to his higher toughness. Again, 2 attacks will lead to an average of 1 hit. However, this time one third of them are going to wound. That implies 6 attacks per wound. Two thirds of wounds will be saved, so 18 attacks will generate 1 un-saved wound on average. With feel no pain, this rises to 36 standard attacks from a space marine being required to remove the plague marine. You'll notice that this is a factor of 3 greater once more. Don't leave home without the power fist or melta gun.

Caveats.
Of course, there are problems with a pure Death Guard army list that are not folded in to our statistic of merit. Namely, since they're more expensive per model, they don't pump out as many shots as other marine armies (less models on the tabletop). The loss of one plague marine can also be rather significant. The loss of an entire squad from a vindicator shot or plasma rapid fire is a terrible blow. Remember that the Death Guard are an highly elite army and we must construct army lists & manoeuvre accordingly. The statistic of merit outlined here is of little consequence if no further thought is applied.

Finally, I think that this computation must be repeated for an imaginary 23 point ork ... I've got a feeling they're going to turn out rather well under this analysis. But, I'm not certain how to fold in the different weaponry & associated ranges just yet. I wonder how the designers go about assigning points values?