Wednesday, October 21, 2015

Toughness Bonuses: When to take or Pass



One of my favorite things about playing Chaos Marines is their customizable options.  When working with marines and cultists Chaos has the option to buy an additional toughness with a mark of Nurgle.  The difficult part is determining when this is a good idea vs when should you add more models.  I am here with math to help you all figure things out.


I am going to focus exclusively on squads of models rather than special characters because you can't add additional characters in most cases.

The charts that I use talk about increased durability versus a particular strength of attack.  As long as the percent increase of durability is greater than the percent increase in cost of an additional model then a mark of nurgle is going to be more efficient for overall survivability than adding additional models.

Adding additional models does also increase the damage output for a unit, but that is a conversation for another time

Toughness 3: Cultists
Mark of Nurgle add a staggering 50% to the cost of each individual model, so in order for the upgrade to be worth the cost we need it to make our model at least 50% more durable.

StrengthDurability Increase
10%
2100%
350%
433%
525%
6+0%

So the only times where mark of Nurgle is worth the cost is when the attacks are strength 2 or 3.  Since most people aren't worried about these attacks it is almost always better to buy additional cultists rather than using the mark of Nurgle.

Toughness 4: Marines, Chosen, Terminators, Raptors, Possessed, Warp Talons

When we look at the toughness four models in the Chaos codex we see quite a few more options, and as a result some varying levels of effectiveness for the mark of Nurgle.  All toughness four models will get the same durability increase, but the increase in their points will vary.

StrengthDurability Increase
20%
3100%
450%
533%
625%
7+0%

This is more or less the same chart as was used for the cultists, but all of the strength values have increased by one.

Standard marines are relatively inexpensive, but mark of Nurgle will increase their points by 23%.  This means that a mark of Nurgle is going to be effective against any attack that is less than strength 7.  Chosen increase their cost by 16%, terminators by 19%, Possessed by 15%, raptors by 17% and Warp Talons by 13%; as long as you aren't getting hit by S7+ weapons a mark of Nurgle is mathematically worth the points.

I know some readers are thinking, "My terminators only get shot by plasma guns, how does this information help me?"  I will talk about shooting from mixed weapons in the next section.

Toughness 5: Spawn, Bikes

Once again we have the same chart as before, but since the starting toughness is higher the strength values have increased as well.

StrengthDurability Increase
30%
4100%
550%
633%
725%
8+0%

A mark of Nurgle for chaos spawn only increase their cost by 20%, so it is effective against anything but strength 8 and above.

Bikes pay 30% of their original cost for a mark of Nurgle.  This immediately means that it isn't as effective as adding additional bodies when the strength is 7 or above.  


Mixed Shooting:

Most of the time a unit gets shot it will have multiple types of incoming fire.  This could be from special weapons in a squad or it could be because they are taking fired from more than one squad.

Lets say I have a squad of terminators that I know is going to get shot up by marines with plasma guns.  A mark of nurgle will increase survivability from the bolters, but won't help with the plasma.  Here is how this gets calculated:

A squad of 10 guys with 2 plasma guns will have 80% of their shots from bolters and 20% of their shots from plasma.

80% of shots have 50% damage reduction and 20% of shots have 0% damage reduction.

0.8*0.5+0.2*0=0.4

So there is an overall damage reduction of 40%.  So it is still more efficient to purchase a mark of Nurgle before adding additional terminators.

For another example: A squad of bikes is likely to get shot by an ion cannon and smart missiles from a hammerhead.  The 8 smart missiles make up 73.7% of the shots and the ion cannon makes up 27.3%.

73.7% of the shots have a 50% damage reduction and 27.3% of the shots have a 25% damage reduction.

0.737*0.5+0.273*0.25= 0.432 or an overall reduction in damage of 43.2%.


Putting it all together:
When looking at a mark of Nurgle in most isolated situations, it is more efficient at increasing durability than adding additional models.  The increased survivability from the mark outweighs the increased survivability of adding more models to a unit.

In future articles I want to look at defense vs offense of adding bodies and marks of Nurgle to get a better overall perspective.

**Updated with the numbers for Raptors**

8 comments:

  1. This is an excellent break down. I've been curious about this as well as the mark of Tzeentch as well. I believe that is much weaker than a nurgle mark but +1 to invuln save seems useful for things like terminators who go from a 5++ to a 4++. Question is, should you opt for mark of nurgle instead?

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    1. Comparing mark of Nurgle vs Mark of Tzeentch is a bit of apples and oranges. Tzeentch only helps vs ap 2, but increases their survivability by 50%, so as long as at least 32% of the damage that they are taking is AP 2 then a mark of Tzeentch is worth it over additional bodies.

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  2. There are tons of intricacies, but it’s important to look at “worth” from an offensive perspective as well. For example, bikes add 33% toughness against S6 when you make them Nurgle but only cost 30% more. So strictly in terms of toughness you’re going to be better off on average by taking the mark instead of more bodies. But if that makes you take 5 bikers instead of 6 (or whatever the real list numbers work out to), you are losing offensive potential because you have less bodies in CC and less twin-linked bolters to fire on offense if you get the first crack at an enemy. So even if you know your bikes will probably only get attacked by S5 or S6 guns, it may still be worth it to load up on bodies instead.

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    1. The next article is going to be all about this.

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  3. Not to mention the joys of not having fearless units and watching them break and run because they lost too much % of their models.

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  4. Great article, I wonder if the rules designers have any grasp of this kind of stuff.

    Any chance of including the additional benefits of extra T for multiwound models. Instant death protection and the like.

    Thanks.

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    1. This is why I always take Nurgle on my Obliterators. Prevents ID from missile launchers, lascannons, marines with pfists, and so on. Very few things can ID something with T5.

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  5. Great article. There is something to be said for more bodies vs more durable bodies!

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