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It's usually pretty easy to see what a weapon in 40k is good for. Models cost more as toughness increases and save decreases. Guns cost more as strength increases and AP decreases. Guns tend to be most cost-effective against models with toughness comparable to the weapon strength (usually equal or 1 below is ideal, so S5 wants to shoot T5 or T4) and against saves equal to their AP (and are least effective against saves that are just barely lower than their AP). There are some wrinkles here - particularly how S8 and S10 guns pick up effectiveness vs T4 and T5, respectively, but this is basically how things work. This means that you want to shoot T4 2+ with S4 or S5 AP2, if at all possible. S6 is decent. S7+ is wasteful. AP3 is incredibly wasteful, and the second-best AP after AP2 is AP-.

Shuriken weapons are a bit more complicated than this because of their pseudo-rending rule, and it's useful to look at the numbers to see exactly how they stack up to other weapons against certain defensive profiles. I was looking at this, and figured I might as well share. The numbers I present here are normalized per-shot kills against single wound models outside of cover.

For example, a Bolter looks like:
T\Sv “-” “6+” “5+” “4+” “3+” “2+”
T3 1.0000 1.0000 1.0000 0.5000 0.3333 0.1667
T4 0.7500 0.7500 0.7500 0.3750 0.2500 0.1250
T5 0.5000 0.5000 0.5000 0.2500 0.1667 0.0833
T6 0.2500 0.2500 0.2500 0.1250 0.0833 0.0417
T7 0.2500 0.2500 0.2500 0.1250 0.0833 0.0417
T8 0.0000 0.0000 0.0000 0.0000 0.0000 0.0000

It's maximally effective per shot against T3 with a 5+ or worse save. It inflicts 12.5% as many unsaved wounds per shot against T6 4+. Bolters are ideal against T4 5+, good against T3 5+, and pretty bad against T5+ and/or 4+ or better. Anything with a similar normalized wound chart will be similarly cost-effective against those targets.

Here's a Lascannon:
T\Sv “-” “6+” “5+” “4+” “3+” “2+”
T3 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
T4 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
T5 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
T6 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
T7 1.0000 1.0000 1.0000 1.0000 1.0000 1.0000
T8 0.8000 0.8000 0.8000 0.8000 0.8000 0.8000

Which just says that it's overkill against T6- and against worse than 2+ saves.

Most weapons have charts somewhere in between these two, and by comparing the variety of weapons in the game it's easy to see why guns end up being maximally cost-effective against comparable toughness and armor that they just barely pierce. Shuriken weapons look different, however.

Shuriken Catapult:
T\Sv “-” “6+” “5+” “4+” “3+” “2+”
T3 1.0000 1.0000 1.0000 0.6250 0.5000 0.3750
T4 0.7500 0.7500 0.7500 0.5000 0.4167 0.3333
T5 0.5000 0.5000 0.5000 0.3750 0.3333 0.2917
T6 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
T7 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500
T8 0.2500 0.2500 0.2500 0.2500 0.2500 0.2500

Compared to the Bolter, the Catapult is no more effective vs higher toughness with bad saves until T8, which the Bolter is incapable of wounding - the Catapult wounds T8 as if it were S5. The Catapult is decent against good saves. Where it really shines is against both high T /and/ good saves. It wounds T8 2+ as easily as it wounds T6 5+. Its effectiveness falls off much more slowly as save increases, and this curve flattens out as toughness increases. The Shuriken Catapult is an incredibly cost-effective MC killer. I note also that the presence of cover biases its relative effectiveness towards low-toughness low-save; only the upper-right quadrant is affected.

The Shuriken Cannon has the same rule but comes with higher strength:
T\Sv “-” “6+” “5+” “4+” “3+” “2+”
T3 1.0000 1.0000 1.0000 0.6000 0.4667 0.3333
T4 1.0000 1.0000 1.0000 0.6000 0.4667 0.3333
T5 0.8000 0.8000 0.8000 0.5000 0.4000 0.3000
T6 0.6000 0.6000 0.6000 0.4000 0.3333 0.2667
T7 0.4000 0.4000 0.4000 0.3000 0.2667 0.2333
T8 0.2000 0.2000 0.2000 0.2000 0.2000 0.2000

Clearly it's less cost-effective than the Catapult against T8, and probably against T7 as well. It's even going to be less efficient against T6 with good saves. It's probably only more efficient against T4, T5, and T6 with bad saves (4+ at best). The Bladestorm rule is just much better for a weaker gun. The Cannon's effectiveness falls off faster as toughness increases beyond T6 and /much/ faster as saves improve beyond 5+ for T7-.

Conclusion: The Shuriken Cannon should probably just be treated almost like any other gun with a similar profile. Bladestorm doesn't make a huge difference for it until toughness rises very high, and at that point its extra strength is completely wasted relative to the Catapult. The Catapult, however, shreds the hardest wounds in the game. Probably it is more cost-effective than even specialized weaponry like Lascannons because Lascannons are priced for their tank-killing ability as well. Put another way - 90 points of Guardians, provided they can get in range to fire without taking casualties, will force 2.22 invulnerable/cover saves on /anything/, on average, including Wraithknights, Riptides, and Greater Daemons.

The cannon is used for wounding the regular targets on a 2+, and being ok against AV10 and 11 en-mass. Bladestorm is like a little bonus you get against T6 3+/2+ monsters with it, I guess.

The biggest advantage is the range, compared with the Catapult so I would always take them in Jetbike squads.

The range thing is a pretty good bonus to it. Being able to wound things outside of catapult range but within cannon range (after killing the front couple of guys) is a big deal.

ummm yeah...not necessarily...you get bolters for 16 points needing rapid fire to shoot twice.

you get 2shots of catapult for 9 points each...so looking at it at a shot per wound basis is off...

plus your math...Lascannons don't auto wound. They still need a 2+ to wound. there is no way a Lascannon could have a 1.0 kills per shots hit.

if anything you should do per round how many wounds can one gun cause...not per each shot hit.

How does a 1/6 chance to wound end up with .250? And why would a Shuriken Cannon, with extra strength and the same Bladestorm rule, have lower results in so many categories than a Shuriken Catapult?

Yeah bad math is bad

I thought I'd explained what I was doing pretty clearly. People seem not to understand what "cost-effectiveness" or "normalized" mean.

Again, the numbers presented are normalized per-shot kills against single-wound models outside of cover. That's why the highest value in each table is a 1. After computing non-normalized values, I divide all of the numbers by the highest number found. Incidentally, this means that "normalized per-round kills" or "normalized per-point per-round kills" tables would look exactly the same, so I'm pretty confused by some of the objections along those lines. I do this to enable easy comparisons of different guns' effectiveness curves. Lascannons are 80% as effective against the hardest models in the game as they are against the softest. Shuriken Catapults are only 25% as effective against the hardest models in the game as they are against the softest. But this is actually an incredibly shallow effectiveness curve for anything that doesn't have huge S and AP1 or AP2.

The reason for doing this is because I'm interested in figuring out what different weapons are maximally cost-effective against rather than what they're absolutely effective against. Absolute effectiveness is something of a silly thing to be worried about, since armies are constrained by point costs.

The point is to look at particular weapons and determine what they most want to be shooting at. So it's a little weird to bring up how Shuriken Cannons have an advantage over Shuriken Catapults in that they have longer range. They'll have this advantage no matter what they're shooting at, unless the idea is that you need to deal with certain defensive profiles at long range.

The question being asked is, basically - "given that I have a model with a Shuriken Catapult and the option to shoot any of a variety of defensive profiles in the enemy army, which one should I shoot at with the Catapult." The usefulness of this sort of math is to see how the effectiveness of Catapults falls off only slowly as toughness increases, and even as Sv improves for higher T. The counterintuitive finding is that the Cannon falls off more quickly as targets get harder, in a relative sense. If these guns are roughly balanced, this requires that the Catapult be significantly more cost-effective than the Cannon against harder targets. If I have a bunch of Catapults and Cannons in an army, and the enemy has a bunch of Orks and a bunch of Wraithguard, probably the Catapults should aim for the Wraithguard while the Cannons shoot at the Orks. This is reversed from the usual optimal strategy of targeting things with T comparable to the gun's S. I'm certainly not saying that you should prefer Catapults over Cannons regardless of cost or in every situation - if you're going to take a Serpent, obviously you should upgrade its Catapults to a Cannon, and probably the same is true for Jetbikes. Again, the question is not "which is better?" but "given that I have this gun, what should I aim it at?". What are Shuriken weapons maximally cost-effective against (relative to other guns)?

Interesting concept. I would argue that the the catapult if given a choice between T5 and T8 should target T8 as the efficiency of the catapult vs the cannon is relatively negligible as compared to the shot cost. The Example of T4 vs T6 is a more complex example as T6 for the cannon is still about 2x as efficient as the catapult.

I believe a lot of the problem you are having with the reception of this data is that you are not talking about how many of a weapon you should bring but rather target priority of who you should shoot with what weapon for maximum theoretical efficiency.

I would be interested in seeing a similar evaluation with a common squad of shooting and a BL vs PL vs SL against AV. Thanks for sharing.

Let me take one more stab at clarity - I think I have a good way of explaining what I'm doing here.

Suppose you were taking your favorite TAC list to target practice. You set up a bunch of different kinds of models across a barren tabletop, and they won't be moving or shooting or anything like that. Your own models are just going to be standing there shooting at them. You want to solve the optimization problem: "How do I target each of my guns each turn in order to wipe out every target in the shortest number of turns possible, on average." The answer will obviously not be "Shoot all my guns at the T3 5+ models, then when they all die go for the T5 3+ models, etc.". The answer will be something like "Shoot my bolters at the T3 5+ models, my plasma at the T5 3+, and my lascannons at the T8 2+". The thing that surprised me a little is that, if my list has a whole bunch of Shuriken Catapults and Shuriken Cannons, it's the Cannons which should probably be firing at the lower-T models with worse saves.

Obviously this isn't the only thing we care about in a real game of 40k. Maybe there's a particularly dangerous unit that simply has to die ASAP. Maybe I can't move into position to shoot the unit I'd really like to shoot without exposing my unit to too much return fire. But it's useful to know in which cases a gun is being "wasted" to any extent.


Automatically Appended Next Post:
Going back to my Ork and Wraithguard example -

I set up 80 T4 6+ models and 50 T5 3+ models. I give you 21 Shuriken Catapults and 6 Shuriken Cannons. How do you go about trying to wipe all of those models off the board?

Somewhat counterintuitively, it turns out that the answer is to shoot the Cannons at the T4 6+ and the Catapults at the T5 3+. That will wipe out all of the enemy models in just about 8 turns. I should stress that the difference isn't enormous here (you expect to take only 8.22 turns shooting both weapons at T4 6+ before shooting both at the T5 3+), but it becomes a much bigger deal as toughness increases and save improves. If the second model type was T6 2+ instead of T5 3+ the difference would be more significant.

That's something really interesting. But nothing new to me. I myself also did some quick mathhammer after the codex release.
While everyone was whining about the loss of the third shot during the Bladestorm, I was actually pleased with the new changes.
It's funny how those "stupid" and weak guardians still do 25% of their maximum damage to Tyranid MCs. Even with Iron Arm.
That's probably why Tyranid players have (at least in the batreps I've seen so far, haven't played against one yet) problems dealing with our little elvish ninja units.

This might be an oversimplification but, if I my Guardians are close enough to shoot something they will likely die next turn. I might destroy the unit I am shooting at but, likely other unit's fire will kill them.

In that sense with the pseudo rend wouldn't it make more sense for me to shoot my 90some pts of Guardias at some 160pt plus MC or FMC?

qballony wrote:
ummm yeah...not necessarily...you get bolters for 16 points needing rapid fire to shoot twice.

you get 2shots of catapult for 9 points each...so looking at it at a shot per wound basis is off...

plus your math...Lascannons don't auto wound. They still need a 2+ to wound. there is no way a Lascannon could have a 1.0 kills per shots hit.

if anything you should do per round how many wounds can one gun cause...not per each shot hit.

I get bolters for 5 points. Doesn't everyone have a Coteaz? Still working on converting 72 warriors with bolters.

RancidHate wrote:
This might be an oversimplification but, if I my Guardians are close enough to shoot something they will likely die next turn. I might destroy the unit I am shooting at but, likely other unit's fire will kill them.

In that sense with the pseudo rend wouldn't it make more sense for me to shoot my 90some pts of Guardias at some 160pt plus MC or FMC?

In some cases the incredible performance of the Catapult means that the answer is yes. Guardians are often able to "make back" their points cost in a single round of firing. As I mentioned, 90 points of Guardians will force 2.22 invulnerable or cover saves on anything they shoot at (that isn't currently flying). So they make sense as an investment even as a suicide squad against any T6+ unit which costs 40 points per wound, although a 5++ of some sort bumps that up to 60 PPW. I'll expand on this below, but they're also decent as a suicide squad vs Terminators.

This is not to endorse this use of Guardians. I think Dire Avengers are generally to be preferred because of their ability to fire earlier and from farther way while being much more survivable. The point re: Catapults is that DAs or Guardians are your real anti-MC choice in the codex, and are even competitive against smaller armored targets like Terminators. To start getting into comparisons between different army list choices, note that in the most favorable possible comparison to Fire Dragons, FDs pay 39.6 points per AP2 wound vs T6 while Guardians pay 40.5 points. They're nearly identical in terms of pure offensive efficiency, and you're getting 2.44 times as many /scoring/ models with the Guardians per point spent. There'd be an argument for Dragons as MC hunters if Serpents were a necessary evil, but Serpents are fantastic and it's not a disadvantage to have to take more of them. Against T7 and T8 the FDs fall off to 49.5 and 66 PPW while the Guardians are still at 40.5. Against Terminators the Guardians /still/ pull off 40.5 PPW while the invulnerable save drops the Dragons to 59.4 PPW. Even against regular Marines, Guardians are significantly more efficient at pure offense than even Dark Reapers, although obviously their range is a disadvantage. But even Dire Avengers are almost exactly as efficient as Dark Reapers, and they're a hell of a lot more survivable per point. Guardians likewise beat out Starcannon War Walkers vs even T6 2+. It's a little more difficult to compare to Wraithguard, but neglecting their ID rule and ability to instakill T5 on any wound they work a lot like (much more expensive) Fire Dragons. Scytheguard are competitive, probably.

The Shuriken Catapult is simply the weapon of choice for Eldar going up against 2+ saves or high Toughness, and isn't half bad against even T4 3+ MEQs. Its effectiveness is wasted against the sorts of things small arms are typically fired at, and Eldar prefer to use their stronger weapons like Scatter Lasers and even Shuriken Cannons for that sort of work. Guardians actually make sense as suicide squads against many of the hardest-to-kill units in the game, and Avengers are a ridiculously efficient and survivable basic Troops choice.

Edit: I should add that Jetbikes are also pretty plausible as a combat-oriented Troops choice. Even with only Catapults, they''re good for basically the same firepower per point as Avengers, and they're more durable per point against everything that isn't both AP3 /and/ Ignores Cover. Their problem is just that they generally end up closer to the enemy after firing and will sometimes fail to make it out of rapid fire range. But Catapult-armed Jetbikes are still a good answer to high-T MCs. I'm actually a little unsure as to whether the Cannon upgrade makes sense. You might just want to turbo-boost anytime you're outside of Catapult range, and inside Catapult range the Cannon really isn't worth it (it's 88% better than the TL Catapult against Orks, with less of an advantage against everything else, but costs 60% more). Obviously the Cannon is hugely better vs vehicles, but that's what Warp Spiders are for.

Actually jetbikes can fall back farther than DA in the assault phase, no. Aren't they more likely to avoid rapid fire range than DA. I'm not sure I'm following your logic there.

They are for killing off MEQs and TEQs like everything else in this Edition.

Do I detect some bitterness?

Martel732 wrote:
Do I detect some bitterness?

Not compleatly, but I did go though a 2 game streak were I never even got a chance to make one of my 3+ Saves thanks to Plasma and Pie.

Actualt the true ones that should be complaning. they dont have a single unit that is imune them.

 felixcat wrote:

Actually jetbikes can fall back farther than DA in the assault phase, no. Aren't they more likely to avoid rapid fire range than DA. I'm not sure I'm following your logic there.

Jetbikes get 2D6 instead of DAs' D6 rerollable, but the Jetbikes have to be 6" closer to shoot in the first place. Jetbikes have more real mobility over the course of a game, but DAs have a longer effective range, and, when that longer effective range isn't required, can move after shooting so as to end up farther away than the Jetbikes, usually. DAs starting 12-24" away can shoot and then retreat to 19-24" away. DAs starting at 26-30" away may still be able to shoot. Jetbikes starting at 1-24" can shoot and then retreat to 14-24", and can't shoot (catapults) if they start at >24".