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Hearing eye-witness reports on their performance I spent too much time math hammering the Wyvern, and I thought I might as well share my findings. There is a lot of math hammer below for those so inclined. So much that I am quite likely to have made a few mistakes, so please help me out!

I wasn't at all convinced when I started doing the numbers, but I am slowly warming up to it. I think right now my opinion is that the Wyvern is ok with potential to be great!


Non-mathhammer version

The one thing my “Wyvern is good” argument hinges on is that you can re-roll subsequent scatter dice working out “multiple barrages” as a result of the “twin-linked” rule. This rule interpretation is key to the Wyvern’s performance, so I posted a question in YMDC. Please discuss that topic in that thread.

If you are allowed re-rolls it all boils down to this: Do you think there is generally a way to place a blast template that covers 3 or more models? If so, a 3 Wyvern squadron will be an infantry killing workhorse that almost always makes it’s points back and regularly snipes out heavy/special weapons. characters etc. In addition it will occasionally shine when there is a packed target to devastate. Deep-strikers beware!

Assuming there is a "sweet-spot" where 3 targets will be hit by the blast, a conservative estimate of the average number of hits scored by a three Wyvern squadron is 18.3.

Converting these to kills (unsaved wounds):

(T3, 5+ save): 10.9 kills
(T3, 4+ save): 8.1 kills
(T4, 3+ save): 4.6 kills
(T4, 2+ save): 2.3 kills
(T5, 3+ save): 3.4 kills

Note the potential here: If there is a "sweet-spot" where you can hit 6 models with a blast, double these numbers!

Due to the "multiple barrages" rule fewer than three Wyverns will perform worse per point. This is mainly due to the fact that each rolled 'Hit' allows you to place the blast template wherever you like as long as it touches any of the ones placed so far. The first blast template placed then has a "tax" attached to it as it will "only" hit a single model (if you roll 'Hit'), while free placement means subsequent templates will generally score more (if you roll 'Hit'). With 12 blast templates you can also use the free placement to "home in" on the intended target even if you initially scatter. This makes the squadron extremely accurate, while a single Wyvern is more meh...


Mathhammer version

Ignores cover: Situational. Will help against some units that relies on stealth, shrouded etc.


Shred. Improves hit to wound conversion rate.

T3 will be wounded (1 - (1/3)*(1/3)) = 1 - 1/9 = 8/9 (= 89%)
T4 will be wounded (1 - (1/2)*(1/2)) = 1 - 1/4 = 3/4 (= 75%)
T5 will be wounded (1 - (2/3)*(2/3)) = 1 - 4/9 = 5/9 (= 56%)


Twin-linked. Re-rolls a scatter dice that is not a Hit.


Assume: Enemy is well spread out, so all models are 2” apart.

Assume: There is an imaginary “sweet-spot” where X models can be hit if a blast template is placed without restriction. If all enemy units are in a line formation X will be 2. If a unit has any depth at all X will likely be 3. For a deep striking unit X could be as much as 10.

Assume: All scatter dice that come up and Arrow score 0 hits.


Resolve multiple barrages:

Place the first blast with the template centred on any model that would be hit by the imaginary “sweet-spot” blast template. Roll scatter dice. With re-roll the chance of a direct hit is 1 - (2/3)(2/3) = 1 - 4/9 = 5/9 (= 56%)

Start rolling scatter dice for the remaining N barrages fired by unit; Each subsequent ‘Hit’ can now be placed on the “sweet-spot” and score X hits.


Assume: Re-rolls allowed on subsequent scatter dice.

Expected hits (initial + subsequent blast templates) = (1 + N * (5/9) * X)


Assume: X = 3

3 wyverns (N = 11): (1 + 11 * 5/9 * 3) = (11 * 5/3) = (55/3) = 18 + 1/3 hits

Apply to-wound and saves.

(T3, 5+ save): 55/3 * 8/9 * 2/3 = 10.9 kills
(T3, 4+ save): 55/3 * 8/9 * 1/2 = 8.1 kills
(T4, 3+ save): 55/3 * 3/4 * 1/3 = 4.6 kills
(T4, 2+ save): 55/3 * 3/4 * 1/6 = 2.3 kills
(T5, 3+ save): 55/3 * 5/9 * 1/3 = 3.4 kills

Assume: T4, 3+ models cost about 15 pts => 68 pts killed per volley that hits home.


So far missing the initial shot has been disregarded altogether. Now here is the thing. Each time you roll a ‘Hit’ you can use that blast template to “home” on the “sweet-spot”. For each ‘Hit” your can place the blast template another 3” closer to the “sweet-spot” so in most cases you will only waste about two to three ‘Hit’ results before your can start piling blast templates on the “sweet-spot”. I’ll assume you need 3 of the average 6.5 ‘Hits’

Assume: Missing the initial shot will halve the number of hits.

Expected kills (initial hit + initial miss) = (5/9) * 68 + (4/9) * 34 = 53 pts

Now this is a really pessimistic estimate totally ignoring lucky scatters. I would expect “real” results to be better!

What's amusing is that these are pinning, even though they ignore cover. I can see a lone wyvern or two being the bane of low Ld units.

After sleeping on the matter I felt this article needed more actual numbers.

Updated with kill counts for five different infantry types.

So, Blasts and Multiple Models.

First off there are 3 Formations of Units when you boil everything down:

1) Regimented or Clumped, Models not much more than an inch apart. Most people do not do this because of Blasts and Templates. Templates are a true reason not to do this, but blasts(especially no-direct Barrage) are not; I will get to this in a Minute.

The next 2 are more likely and have other problems.

2) Full 2-inch Spread about. While it is impossible to get multiple hits on a Hit or reduced to hit Blast Marker, any scatter is going to net several hits per Marker.

3) Full 2" Conga Line. While this is the best way to reduce Blast Marker damage you limit your own ability to fire effectively(Wings out of Range), or Assault Effectively(Wings again).

Now for the math that proves 1 and 2:

The first part is the Accuracy of any given Blast weapon.
You have a 33.333% chance to hit your initial Marker Placement.
Then depending on your BS you will have a further chance to hit your initial Marker placement no matter the direction of the arrow.
Then you have a further chance that could be expressed(if I actually felt like doing the Math) by finding the angle between 2 Points that are about 6.75" apart at any given distance, in 1" increments, and a Single point being the Target location. For every inch you move from the target point that angle becomes more acute.That angle can be expressed as X/360 giving you a percentage for your Blast to fall in that area. There are generally several of these areas that can be added together to find how much higher a percentage you have for your blast to fall on a desired target unit.

Because of this 2 things wind up happening on a miss with higher scatter: you either completely miss the regiment, or you achieve more hits on the skirmish formation. When your opponent is a Space Army player with Manticores or Deathstrikes you are actually better off with the regimented formation(Smaller unit footprint)

So...is it worth it?

How many turns of shooting are you going to get before your enemies close into melta range or otherwise destroy the Wyverns? I am a big fan of massed long-range shooting, and it sounds to be like it could definitely keep low-Ld units away from your lines, and if you panic one, you can then change targets.

The reason all this flurry of wyvern talk is failing so badly in the math department is because there isn't a common consensus on how many models each blast template is going to hit. If you put in absurdly high numbers, then you're going to get a wyvern that looks pretty good, of course, and if you don't, it will look less so.

As for determining if wyverns are strong or not, you have to take this problem and compound it by circumstance. For example, how many infantry models will a wyvern hit when the infantry models are embarked in a transport? Zero. How many models will a wyvern hit per shot against models in ruins? 0-1, assuming that the infantry are properly displaced. How many infantry models will you hit out in the open? It's the displacement problem straight-up. The answer is somewhere between 1 and 9, depending on how stupid your opponent is.

When you want to mathhammer wyverns, you're heavily reliant on the assumptions you have going into it. If you assume it's going to be wildly successful, then your numbers are going to make it look wildly successful. If you assume your opponent isn't an idiot, then it looks pretty crappy.

It's hard to mathhammer multiple barrage weapons. Add in rerolls to-hit. Add in small blasts that are even more dependent on the enemie's troop formations.

I play orkses and often run lobbas - s5 ap5 small blast guns with one-use rerolls. And can definitely tell you that it's effectiveness varies hugely. In some games they kill 2-3 times more their initial price, snipe out characters and specialists and pin the enemy. No matter if they face geq or meq. And in some games they can't do much even vs infantry cause the enemy spreads out as much as possible or sith in transports and you score a few kills across the whole game.

I'd say that if it's your only blast weapon in the army and your enemies have at least some infantry that's gona be on board at least from turn 2 than the Wyvern is gona be useful. If you allready have blast weapons like artillery or eradicator, wivern's probably not worth it. It's still a cover-ignoring multiple-blast weapon but now ig has ignore-cover orders armywide.

So, all in all, it's not a bad thing if you got a hundreed spare points and don't know where to put them. And if you got no other blasts so that a single tank can force your enemy to spread troops.

 pantheralegionnaire wrote:
So...is it worth it?

How many turns of shooting are you going to get before your enemies close into melta range or otherwise destroy the Wyverns? I am a big fan of massed long-range shooting, and it sounds to be like it could definitely keep low-Ld units away from your lines, and if you panic one, you can then change targets.

48" range that doesn't need line of sight... might be awhile. And if he deep strikes and fails to kill them, you have some guys that are bunched up in perfect formation to be a best case scenario for one of these pro-wyvern posts. Really, I see the wyvern as an anti-deep strike tool. Sure, those guys get to fire, then they get murdered.

20 conscripts = 60 pts
The look on your opponent's face when he realizes he can't get close enough to the wyverns to melta them = priceless

A bike army would probably just ignore them with their T5 3+ models that can be spaced far enough apart.

 Ailaros wrote:

When you want to mathhammer wyverns, you're heavily reliant on the assumptions you have going into it

This pretty much sums up the problem. With one template on a vehicle (well any model really), you can do this sort of exercise. Once you start adding more blasts and more targets, the assumptions that you need to make just wreck your model, as well as any conclusions that you can take from the analysis.

With that said,I still think that Wyverns have a place in some guard lists. But there is already a lengthy discussion in the big guard tactics thread.

 Ailaros wrote:
The reason all this flurry of wyvern talk is failing so badly in the math department is because there isn't a common consensus on how many models each blast template is going to hit. If you put in absurdly high numbers, then you're going to get a wyvern that looks pretty good, of course, and if you don't, it will look less so.

As for determining if wyverns are strong or not, you have to take this problem and compound it by circumstance. For example, how many infantry models will a wyvern hit when the infantry models are embarked in a transport? Zero. How many models will a wyvern hit per shot against models in ruins? 0-1, assuming that the infantry are properly displaced. How many infantry models will you hit out in the open? It's the displacement problem straight-up. The answer is somewhere between 1 and 9, depending on how stupid your opponent is.

When you want to mathhammer wyverns, you're heavily reliant on the assumptions you have going into it. If you assume it's going to be wildly successful, then your numbers are going to make it look wildly successful. If you assume your opponent isn't an idiot, then it looks pretty crappy.

A hit on a follow up shot can flip between 3 models.

It's not possible to deploy 3 models with all 3 within 2" of each other without a small pie being able to catch all 3 models.

The only way 3 models can remain in coherency and not all be caught in a small blast is if they are deployed in a line where the outside models are only in coherency with the middle model.

The line can curve to form a C or an S shape, but if 3 models are all within coherency of each other at any point they can all be caught in a small pie.

 Ailaros wrote:
The reason all this flurry of wyvern talk is failing so badly in the math department is because there isn't a common consensus on how many models each blast template is going to hit. If you put in absurdly high numbers, then you're going to get a wyvern that looks pretty good, of course, and if you don't, it will look less so.

As for determining if wyverns are strong or not, you have to take this problem and compound it by circumstance. For example, how many infantry models will a wyvern hit when the infantry models are embarked in a transport? Zero. How many models will a wyvern hit per shot against models in ruins? 0-1, assuming that the infantry are properly displaced. How many infantry models will you hit out in the open? It's the displacement problem straight-up. The answer is somewhere between 1 and 9, depending on how stupid your opponent is.

When you want to mathhammer wyverns, you're heavily reliant on the assumptions you have going into it. If you assume it's going to be wildly successful, then your numbers are going to make it look wildly successful. If you assume your opponent isn't an idiot, then it looks pretty crappy.

Transports should be a boon to wyverns strength... What happens when you blow up a transport? (which should be easy as IG I might add) You get a clusterfeth of 10 dudes waiting for that sweet, sweet wyvern.

Trying to figure out if a Wyvern is good due to blast vs enemy deployment is the same issue as finding out if a Executioner is good (or any other unit tossing multiple blasts).

IMO, having a unit throw out a ton of accurate blasts with re-rolls to wound pairs really well with massed firepower.

If you force your opponent to spread out, your slowing/limiting his advance on the rest of the guard.
Doing that for 130 points (8 S4 blasts) seems like a steal.

-Matt

I removed the spoiler tags as a lot of people seem to have missed what assumptions I actually made. I might update the non-mathhammer version to reflect this later.


Two things that people generally miss.

1) The shots are twin-linked, thus the probability for rolling a 'Hit' is actually abuot 56%

2) The restrictions for placing normal blast markers only applies the first one you place. After that the multiple barrage rules state that for each subsequent 'Hit' rolled you may placed the blast template freely. The only restriction is that some part of the new marker must touch any of the ones placed before it. With twin-linked this means 6.1 (56% of 11) blasts can be placed as you please, so that even if you initially miss you can use subsequent 'Hits' to widen the blast pattern towards where you initially aimed.


Just to sum up the key assumptions made:

1) Enemy is perfectly spaced out (2" apart)
2) There is a sweet-spot where a blast marker will score the maximum amount of hits X when placed without restriction (not the initial marker). For a unit in line formation X is 2. For any non-line formation X is at least 3 (schadenfreude got it right. Try placing 3 models 2" apart forming a triangle and put the blast center in the middle). If your opponents never uses anything but line formation you need to multiply my results with 2/3.
3) Every time you roll an 'Arrow' that blast scores 0 hits. I only use hits generated by blast markers when you roll a 'Hit'
4) If the initial shot scatters it scatters on average 9" from the "sweet-spot" (pessimistic). Thus you need to use the first 3 'Hit' results to "home in" on the "sweet-spot".

I used these assumptions because they allow me to ignore directions of scatters and the general size and layout of the unit targeted.

If my math is good the results represent a lower bound of what I can expect when I get to fire the Wyvern.


@Mavnas

Pinning could be interesting. On a packed enemy you could use the 'Hit' s rolled to maximize the number of units that needs to take pinning test. Many units ignores pinning though.


@pantheralegionnaire

That's for you to figure out!

Personally I will probably avoid using Wyverns simply because working out 12 blast templates and watching my opponent move his pedantically spaced out units is not why I find 40k fun. Maybe if I can find a way to use skill to create good circumstances. Tank shocking comes to mind for example.


@Ailaros

You are more or less correct as usual. Mathhammering generally ignore context. It will tell you what to expect when firing under certain circumstances. Players need to figure out how to create these circumstances and if they can be created often enough.

I think what surprised me doing the math was that "good enough" circumstances might not be so hard to find after all. I can also see where all these stories with Wyverns doing amazing things come from. Hitting a packed unit would be murder!


@HawaiiMatt

I agree. Depending on how dense your tables are it could be really big deal.

People who don't understand the wyverns efficiency are people who don't know how brutal barrage sniping is from mutiple barrages. It's even more insane when its accurate like this.

Even if they average one hit per blast, which is a humble assumption, if you bean that blob with two, a modest 130, that's 6 wounds on a priest for that one crucial failed LOS, now the blob loses fearless and its war-hymns AND has to take a pinning check.

Knock it all you like but any good players TAC list looks at match-ups like these and includes a battery to shut down the other armies gimmick.

You're assuming that all the hits land directly on the priest and forget that with 4++, you need 12 wounds to snipe him on average. I think firing at a blob, it's easy to hit something despite scatter. Hitting exactly the same guy 12 times?

Mavnas wrote:
You're assuming that all the hits land directly on the priest and forget that with 4++, you need 12 wounds to snipe him on average. I think firing at a blob, it's easy to hit something despite scatter. Hitting exactly the same guy 12 times?

Do you realize how easy it is to get that many hits with a TL barrage weapon with that many shots? Did you miss the part where a unit of 2 getting 8 hits was almost the complete worst side of the spectrum? If you face blob guard with a 2-3 unit of wyverns, expect to lose your fearless and heavy weapons really quick.

I just double checked with my models and with max spacing 2" between three guys, you can clip 3 clipping two and covering more then 50% of ones base... That means even in a conga line you can easily hit two while sniping one model, its so easy to wrack up hits on important models.