Mathhammer - Plasma v. Wyverns

B. Grim and I were debating between plasma guns or an extra wyvern for my Inquisitor's army, and I decided I would try to run the numbers (note - I found out after I wrote this article that it turns out he was debating between melta and plasma and I thought he was debating between wyverns and plasma). Just a warning that I've assumed that you have a bit of stats knowledge for the article.

At S7 AP2, plasmas are very effective. But Wyvens are notorious for putting down a ton of wounds. Let's see how they do against marine equivalents (MEQ) and terminator equivalents (TEQ).

PLASMA

S7 wounds on a 2+. MEQ has no save and TEQ has a 5++. So a shot has a 5/6 chance of killing a MEQ and a 5/9 (= 5/6 x 2/3) chance of killing a TEQ.

Assuming a squad of veterans with two plasma guns (I know you can carry 3, but chimeras only have two firing points), they hit on a 3+ and get 2 shots within 12" and 1 shot between 12" and 24". Four shots means 20/6 = 3.3 MEQ dead, and 20/9 = 2.2 TEQ dead. Assuming of course, no cover save. If they're outside of doubletap range, there will be half as many wounds, so 1.65 against MEQ and 1.1 against TEQ.

WYVERN

A wyvern has four twin-linked small blast shots with S4 and shred. Since you get a chance to reroll to wound and both MEQ and TEQ have T4, every hit has a 3/4 chance to wound. MEQ will then fail their armour save 1/3 of the time, which means that it will take you 4 hits before causing 1 wound on MEQ. As TEQ fails their armour save only half as much as MEQ, you'd need 8 hits before causing 1 wound on TEQ.

Now the difficult part - trying to figure out how many models are hit using theory. TEQ are usually run in groups of 5. Due to squad coherency, you should always be able to get 2 bases covered, but unless they've just deep striked in, you're probably not going to get more than 3 bases covered. I'm going to assume on average that you can place your blast so that it will cover 2.5 TEQs. Now, how to deal with scatter? First of all, since it is twin linked, it will only scatter 4 out of every 9 times (=1 - 1/3 x 1/3). It will scatter an average of 4" (the 7 on the dice minus the 3 BS). Assuming that the TEQ are deployed in a line and that you've placed the blast in the middle of the line, half of the time it will scatter along the line (hitting the one TEQ on the edge) and half of the time it will scatter perpendicular, hitting 0. So, a hit (5/9 odds) will cause 2.5 hits, and a scatter (4/9 odds) will hit 0.5 on average. That means each shot will cause 1.6 hits (=12.5/9+2/9) on average. As you have 4 shots with each wyvern, you're looking at an average of 6.4 hits per turn, which means 0.8 TEQ dead per turn.

For MEQ, based on my empirical experience and assuming a squad of 10 models (and assuming someone is spacing out their models to avoid wyverns), I'm going to say that a hit gets 4 models. I'm going to assume that the 4" average scatter will, on average, catch another 2 models - this is because squads of 10 MEQ are often a little more blobular than TEQ which means there are still 6 other models clustered around your blast template and you've got a decent chance of catching something (or a lot of things) in any direction as long as the scatter distance stays down. So a hit (5/9 odds) on the scatter die will hit 4 models, and a scatter (4/9 odds) will hit 2 models. So each shot hits 3.1 models on average (20/9+8/9). You have four shots, so you're looking at 12.4 hits and (per the above 4 hits for 1 wound), you're looking at 3.1 wounds.

CONCLUSION

So, against MEQ, wyverns are about equivalent to two plasma guns at double tapping range and they're twice as good against MEQ outside of double tapping range.

Against TEQ, you're looking at 0.8 dead vs 2.2 in double tapping range, or 1.1 outside of double tapping range.

Of course, 10 vets with a chimera and 2 plasma comes to 155 pts and a wyvern comes to 65. So, if you're only examing killyness, the wyvern comes on top on a per point basis against both MEQ and TEQ.

Some other things to note:

1. If you're running a CAD, your vets and your chimera will be ObSec, which is quite useful.
2. The calculations above assume a marine enemy. If you're facing something with worse saves (orks, tau, eldar, IG), your wyvern is going to be even better.
3. The vets and chimera have to put themselves in danger to get into double tap range. The plasmas have the biggest relative advantage (to the wyvern) against TEQ, but any TEQ you don't kill are going to hit back pretty hard.
4. Wyverns have much better range.
5. Meltas are cheaper than the plasma but give you more flexibility against armour.

Thoughts? Think any of my assumptions (or worse, my calculations) are off?