Tuesday, October 16, 2012

Coming Back from the Brink, pt.10: Shoot Tau Thrill

Play to Kill
Greetings Gentlereaders!

Today, we're going to talk about the main battle  tank of the Tau army, the Hammerhead gunship.  Specifically, I'll be breaking down the ion cannon vs. the railgun option  I have never run an ionhead, but sixth edition has inspired me to look into more options.  Let's take a look at this awe-inspiring tank and how it may find a new niche in Tau.

The main battletank of the Tau Empire offers a mobile, versatile and highly lethal firing platform for a high price tag.  I has armor thirteen in the front, twelve on the side and ten in the rear.  When outside of twelve inches, the hammerhead has a 3+ cover save with a disruption pod if it moves.  With a multitracker it can fire two weapons while moving twelve inches a turn.  The hammerhead comes with a  targeting array built in, netting it ballistic skill four, and cannot take a second.  The ability for the hammerhead to take a blacksun filter allows it to ignore the increasingly frequent night fighting of the 41st millenium.  The hammerhead can do it all in style.

Most hammerheads are usually 'railheads' because the railgun was the weapon option of choice for Tau cadres.  The railgun brings both the solid shot just like the broadside, but also provides Tau their primary blast weapon a strength six armor penetration four large blast.  This was Tau's best answer to either mass medium infantry or gants with Feel No Pain while offering the strength ten solid shot.  This versatility was very powerful and still is, though without a target lock the hammerhead can become an anti-infantry gunship with the option to fight other tanks rather than being a tank designed to fight other tanks (e.g. lascannon predators).  In fifth edition, there was little argument for the ion cannon turret, but now there may be more.

I'll be keeping an ion you!
A fellow blogger, Old Shattered Hands, put out a deployment tactica that illustrates alternative strategies for Tau cadres, especially the hammerhead that I think would be enlightening.  The ion cannon sacrifices strength, armor penetration, and range for rate of fire.  Clocking in at strength seven, armor penetration three and three shots at sixty inches, the ion cannon is also forty points cheaper than the railgun.  When the hammerhead costs a minimum of 110 points, the upgrade to the railgun is a 36% increase in price that may not be worth it now.  Let's take a look at how each weapon matches up, both against vehicles and against infantry. Math Alert!

TL;DR: The ion cannon isn't as bad as it looks.

Let's start with shooting at vehicles.  To calculate which is better we need to consider the expected value of each round of shooting.  The railgun's expected value is the same as it's probability as it only has one shot; however the ion cannon's expected value is thrice its probability.  So let's compare the probabilities to strip a hull point [P(glance) + P(penetrate)]P(to hit).

Probability Railgun          Ion Cannon
vs. AV 10  0.667             1.333
vs. AV 11  0.667             1.000
vs. AV 12  0.556             0.667
vs. AV 13  0.444             0.333
vs. AV 14  0.333             0.000

Looking at the above table you can see that if you are trying to strip hull points off of a vehicle to kill it you should take the ion cannon unless you expect to be fighting leman russ or land raiders en masse.  This is with the condition that you should be taking at least one team of broadsides.  In some cases you can't afford to wait for the hull point to wear down vehicles.

Pictured: Target-Rich Environment
Let's look at the probabilities of killing a vehicle with a salvo, so the odds of getting a penetrating hit multiplied by the probability of one of those  penetrating hits getting a kaboom result.  Here is where the railgun shines, as it beats the ion cannon at every armor value, which was all that mattered in fifth edition and why the railgun was my choice of weapons.  Against armor value ten, the railgun should kill the target one third of the time while the ion cannon has a 0.168 expected value of doing so.  As the armor increases to eleven the railgun maintains a 0.278 while the ion cannon only has a 0.111.  Against armor value, twelve the railgun has a somewhat impressive 0.222 chance to kill in a single hit while the ion cannon has only 0.057.  Above this the ion cannon can't kill in a single shot, but the railgun maintains a one sixth chance of killing an armor thirteen target and a one ninth chance.  To summarize, the railgun is a much better weapon to kill a target in a single shot, while the ion cannon can be relied upon to provide more consistent damage to light and medium armor.

Against non-vehicle targets there more dissimilar targets then there are when vehicles are concerned.  Let's start with monstrous creatures as they are most similar to tanks.  The probability for a railgun to wound does not change, no matter the target, though it does for the ion cannon.  Where a railgun wounds on 2+ and can inflict instant death to anything short of toughness six, an ion cannon can only inflict instant death on targets that are toughness three or less and wound roll a wound on a 5+ against some targets.  Let's consider the probability of wounding a wraithlord:  a railgun has a 0.556, while ion cannon has a 0.222.  But remember the ion cannon has three shots and thus an expected value of 0.667.  Against a carnifex, or non-armored shell Tyrant the probabilities are 0.556 and 0.444, respectively and the expected value bumps the ion cannon to 1.333 expected wounds to the railgun's 0.556 expected.  Again, the ion cannon's volume of fire wins out.

The real difference in performance between the two comes based on the armor save of the target rather than its toughness.  Against a tyrannofex the railgun still can expect 0.556 wounds, but the ion cannon's   expectation drops to 0.222 wounds.    The railgun would have it's output drop against a dreadknight with its 5+ invulnerable save, but it would still outshine the ion cannon by 66.7% (0.370 compared to 0.222).

Where's the kaboom?
Now let's look at the chances to kill multiwound models that are less than toughness six.  If you are facing units like paladins or thunderwolf cavalry the ability to cause instant death is a great bonus the railgun has over the ion cannon, but it really doesn't matter.  Let's consider the probability of getting a wound with a railgun and an ion cannon on the thunderwolves (0.556 each) and probability of each getting a wound on a paladin (0.370 vs 0.093).  Counting the instant death against thunderwolves as two wounds, as it would cause that unless you snipe a character without an invulnerable save, we still get an expected value of 1.11 vs 1.67 in favor of the ion cannon.  Even counting the volume of fire for the ion cannon it cannot expect to beat the railgun in expected wounds against paladins because of their armor save (0.370 vs 0.278).

Now let's consider the Ork nob.  Either on foot or mounted, the railgun can inflict instant death, but the ion cannon cannot.  Both weapons will be testing against a cover save if the squad can muster one, but let's run the numbers.  Against a foot squad, the railgun can either fire a solid shot with 1.111 expected wounds or a blast marker that will wound 0.556 of those it hits if they have cover, 0.833 if they do not.  The ion cannon can expect 1.667 wounds against a foot squad and 0.833 against a bike squad.  The railgun can expect 1.111 wounds against a foot squad and 0.556 against a bike squad, as its built in cover save effectively negates the instant death property of the railgun.  If the cover save were negated by pathfinders, both would double their expected wounds and the ion cannon still wins out.

Dear Tau: Please go die.  Thank you.
Now let's move into the realm of fighting less resilient targets.  Again the question of armor save comes into play and it is joined by questions of toughness and model placement.  It is difficult to judge how many models will be caught under the hammerhead's blast, so let us just say that if you expect to play a horde army, the blast will probably do more for you than the three shots of the ion cannon.  When you're looking at models with a carapace armor save or worse both weapons are equal hit for hit, so which is better is more dependent on model placement.  When you consider models with power armor that are toughness four or less, the hammerhead needs to wound three models for each wound the ion cannon can cause to get the same results.  Against models in 2+ armor, the railgun can fire a solid shot which is between twice and six times as effective as a shot from the ion cannon.  The ion cannon's volume of fire leads to a poor, but higher expected value against storm shield terminators than a railgun solid shot (0.277 vs 0.185).  Against Tzeenchen terminators they are equally potent (0.277 expected wounds), but against basic terminator armor the railgun wins out (0.370 vs 0.277).

As we saw with the chances to kill a vehicle through hull points, which turret weapon is a better choice for a hammerhead is dependent on what you expect to see in your local tournament setting.  If you're expecting medium armor values or marines on foot  I'll cover the utility of the secondary weapon in my next post on the skyray, as I did not expect this post to run as long as it did.  I apologize if this post was too long, but I hope this has illuminated the complexities of a choice that I had taken for granted for as long as I've played 40k.  That's all for the hammerhead, next time I'll take a look into the other staple vehicle of the Tau Empire that was given a hilarious new lease on life.

I'm Underground Heretic and I get to live with that every day!

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