Tuesday, August 23, 2016

Mathammering Xenos Deathlocks

Preamble.
Today's post applies a bit of mathematics to the usage of Xenos Deathlocks that we discussed in the Horus Heresy Review on the Blackshields Rules. In brief, Xenos Deathlocks (which we will abbreviate to XD's from herein) are a type of weapon that some of the renegade space marines wielded in 30k when they went outside their command structures because of the Heresy. I really like this idea and concept. Hence, regardless of the outcome of the mathammer below, I really want to see people play these on the desktop just because they're cool. No other reason! In fact, you can see that I already convert some of my miniatures along these lines any way (with a slightly different narrative within the Alpha Legion of using reversed engineered technology).


Basics.
The Xenos Deathlocks are S=5, AP5 with assault 2 weapons. They have a half decent range for assault weapons at 18 inches as well, which is very nice -- nay attractive even, especially compared to a bolter at a similar range. But there's a price to pay for this -- not only in the points cost. They have the Lethal Exposure rule. Firing this weapon causes the unit using them to roll 2d6. If the roll is less than the number of shots fired by the unit, then one wound is taken with no armour save possible. (Overwatch is exempted from this).

So why take them at all given how downright deadly they look on paper? The answer is in the Deathlock rule. In the spirit of Volkite weapons, a unit that got hit and wounded by a XD weapon must take a leadership test modified (negatively) by the number of wounds suffers (fearless and stubborn units don't apply modifiers). Failure causes an extra 1d6 wounds that can have normal saving throws. 

So is this potentially amazing weapon worthwhile?

A trivial case.
Let's suppose a squad sergeant has a XD. He is targeting some space marines (of course!). On average, he scores 1.33 hits (from 2 shots), and of these, causes 0.89 wounds. A "typical" 3+ save in the 30k environment will reduce this down to 0.30 unsaved wounds (rounded). 

Its trivial here to see that the lethal exposure test is passed: one can never roll under 2 on 2d6, so the sergeant is always going to be safe.

How many extra wounds will the target unit take though? We will treat the enemy squad as having Ld=9 for this purpose. Hence the Ld test is taken at 8.70 for the 0.30 unsaved wounds caused already. Rounding, a roll of 8 or less therefore happens 72.2 per cent of the time. Or putting it another way: fails 27.8 per cent of the time. 

We will use this number to multiply by the 1d6 extra wounds to come up with an outcome. The average 1d6 roll is 3.5. Thus, 27.8 per cent of 3.5 extra wounds is 0.97. 

The target squad is allowed a saving throw which reduces this down to 0.32 extra wounds. That makes a total of 0.30 + 0.32 = 0.62 wounds from the two shots every turn. This is therefore rather powerful!

Complex cases.
Things get much more complex here when we have more than one shooter. Plus, there's the potential to take wounds of your own from the firing squad. In the table below, I summarise the outcomes, using the basic logic presented above in the trivial case. The final two columns are the number of lethal wounds suffered by the shooters, and the difference between the last two columns (or: how many wounds ahead the shooters are!). 

N(XDs shooting in a squad); N(Unsaved Wounds); Lethal?; Difference.
1; 0.62; No; 0.62
2; 0.92; 0.08; 0.84
3: 1.21; 0.28; 0.93
4; 1.68; 0.58; 1.10
5; 1.97; 0.83; 1.14
6; 2.27; 0.97; 1.30
7; 2.75; 1.00; 1.75
8; 3.05; 1.00; 2.05
9; 3.35; 1.00; 2.35
10; 3.64; 1.00; 2.64

As can be seen, there are a few critical turning points.

The first one is illustrated in the trivial case. There, there's no lethal wounds suffered as there's not enough shots fired for them to be lethal.

The next jump is around 6 shooters where the difference shoots up. The spread between 2 to 5 shooters is only 0.3 wounds, but the range from 2 to 6 is 0.46 wounds -- an increase of a factor of 1.53.
The jump from 6 to 7 shooters is also a big one thanks to the twin effects of increasing the number of unsaved wounds coupled with keeping the lethality relatively static. From therein, the difference increases steadily more or less; (although there is another minor jump at 11 shooters for the interested reader). 

Conclusion.
The best number of shooters for XDs is arguably 1. There's no risk to the shooter of dying from the shot. Plus they're still effective.

Beyond that, plump for 6 or 7 depending on the points available due to the rational transaction between wounds caused versus wounds taken from shooting. From therein, up to 10 shooters, the increase is linear. 

I hope this has been helpful. And I hope its accurate (I am human, and I do make mistakes, so please be kind in your comments if I have and you point them out! Thanks!). 

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