Gunnery and dice probability

[lastspartacus]

Inferno is great, except for the name.  As ive said before, so happy to have a 'Lunar' in my chaos lists.

[Phthisis]

@left of west
Just because Sigi doesn't like it, it doesn't mean you can't use it.  He doesn't have any authority over what GW puts out or what you play.  If the Inferno fits your play style and your opponents allow the list, then theres no reason not to use it.
Also, check out Plaxor's revised lists.  Some very good stuff in there.

@Horizon
Youre somewhat correct about running a Murder straight at the enemy.  5+ armor closing is asking for it.  You either have to do it at an opponent with short range or weak guns or no toward a facing with no guns at all like the shild wall of 6+ prow armor that the IN has.  And it has to be done en masse.  We can't just think of two ships alone in clean space.  Strategy counts a lot in BFG.
Ok, now stats for closing 6+ armor vs Carnage & Murder lance variant broadsides.

Murder, 2  dice at 4+, one dice at 6+
0 hits = 20.83%
1 hits = 54.16%
2 hits = 20.83%
3 hits = 4.16%

Carnage over 30cm, 8 dice at 6+
0 hits = 23.27%
1 hits = 37.21%
2 hits = 26.03%
3 hits = 10.41%
4 hits = 2.6%
5+ hits = negligable

Carnage at 15-30cm, 11 dice at 6+
0 hits = 13.47%
1 hits = 29.62%
2 hits = 29.6%
3 hits = 17.75%
4 hits = 7.09%
5 hits =1.98%
6+ hits = negligable

Analysis:  At longer range the Murder is more likely to hit at all and is stronger in the 1-2 hits range, but the Carnage has a small chance of scoring more than 2.  Personally I'd pick the Murder, but if youre a gambler the Carnage is better.  Of course, with a blast marker in the way the Murder is superior in all respects.
At closer range the Carnage has the advantage, once again if there are no blast markers in the way.  However the advantage isn't a very big one.  The Carnage is more likely to hit, but there isn't much of a chance of rolling that much higher than a Murder.

@Sigirogh
Glad you knew this already.  Did you know that I knew you'd say you knew?  But a lot of people never get past mean average calculations. 
There are three different kinds of average.  The low probability of very high numbers of successes rolled drags the mean average higher than could be normally expected.  I think more than a few people would be surprised that there is a greater chance they will roll lower than the mean average than that they will roll above it and that the difference between rolling under and over grows with each additional dice you roll.  Some of us are gamblers, like yourself, who will trade reliability for a small chance of spectacular success.  Others, like me like reliable steady firepower that is less likely to fail us when we most need it.
Ok, so so far the carnage performs better at close range than a Murder, but the Murder is better at long ranges or close ranges with blasts in the way.
So lets suppose I took 2 lance Murders and a Slaughter instead of 3 Carnages?  That saves me 35pts and if I use Slaughter up close and the Murderd at range I get better damage output.

[horizon]

Do you, based on those math still prefer Murder at long range?

I still fail to see how the Murder can operate at longer range then Carnage.

Also those stats are against 6+ armour, vs 5+ I reckon the Carnage starts to eat more.

You say "think more then 1 ship", good then each % goes up for every combo.

[Phthisis]

Yeah, of course.  The math shows that the Murder is superior at long range.  The Murder becomes even more superior on LO.  The math also shows the Carnage is only really worth its points under 30cm.  And it reveals the Carnage to be a pea shooter at extreme range.  Three of them have only a 32% chance of breaking through 2 shields. The Carnage can also only do its dirt on targets without blast markers because once the target has one its power drops off dramatically.  The Murder is more reliable because it hits more and blast markers don't effect their firepower.  Of course, Ive done this math before and knew I preferred the Murder already.

[left of west]

The Murder is superior at >45cm against all targets if it is closing and the Carnage is closing or broadside.

The Carnage is superior at >45cm against all targets if it is broadside and the Murder is broadside. 

The Murder is superior at 30cm - 45cm against targets which are abeam. 

The Carnage is superior at 30cm -45cm against targets which are closing. 

The Carnage is extremely similar to the Murder at <30cm against targets which are abeam.

The Carnage is superior to the Murder at <30cm against targets which are closing. 

The Carnage is superior to the Murder at <15cm against targets regardless of aspect. 

I'll grant you, Pthisis, the Lance-variant Murder is a pretty reasonable match against the Carnage (as opposed to the regular Murder, which is substantially worse).  That said, the Carnage comes out ahead in a significant number of the relevant situations.  It's only beaten out at extreme range by the Murder if the Murder is closing (which is bad).  The Murder is basically only better in the 30cm-45cm band, while it loses out in the entire 0cm-30cm band and, really, in the 45cm-60cm band as well, since it has to close to fire there at all. 

I wasn't really aware of the lance variant until recently, and it certainly is a more reasonable pick, but I still have to say that the Carnage seems better. 

[fracas]

this topic amuses me

if you are looking to decide which target to fire at, probability analysis is your friend
if you are looking to decide which ship is better against a certain target over several encounters average will be more reliable

[Phthisis]

@left of west
Several or those conclusions require some big caveats.  Ships have to concentrate fire to really cause any damage.  Once a shield goes down, it is surrounded by a blast marker.  That blast marker forces a right column shift for the Carnage's batteries.  Normally this means that only the first Carnage is going to get full dice.  The only way all your Carnages get full dice is if they are all squadroned and all the conditions are met to roll the simultaneously.  The closer the target is, the harder this is to do.  Murders don't have to worry about blast markers in any of its facings. 
Many of the situations discussed actually go to the Murder's favor once a BM is in the way.

The Murder would now be superior abeam at 15-30cm, superior abeam at 30-45cm, superior closing at 30-45, and very close at closing 15-30cm.  Blast markers are very common, and those 4 situations are by far the most common.
Also LO tilts things in the Murder's favor.
The Carnage is superior at above 45 and below 15.  If I want close up power I will get a Slaughter, or long range I will use an Acheron.

In another post you brought up the Devestation being better at broadsides than the lance Murder.  This is true (and now I'm fairly sure you aren't sigiroth in disguise) but I'm not going to LO with a Dev or use any special order but RO.  Also, the Devs are too valuable to risk, don't have forward lances and cost more.  I take a Carnage and several Devs along side my Murders.

[horizon]

The Murder is superior at >45cm against all targets if it is closing and the Carnage is closing or broadside.

?


Since Carnage shoots first it has less issues with blast markers.
Acheron is awesome and best mid-range ship (45cm) but not best long range.

[Phthisis]

I use the Carnage myself and always fire it first.  But this exercise isn't about whether a single Carnage should be taken.  Its about which chaos cruiser makes a better backbone for the fleet, ie which cruiser should you take more of.  Multiple Carnages can step on each others toes.  Multiple Murders work great in concert, squadroned or not.

Glad we agree on the Acheron!  Too bad its a heavy cruiser and not a standard cruiser. 

Left of west is referring to the 2 lances on the front of the Murder being better than anything the Carnage cn put out at that range.

[horizon]

So... 2 lances is better then 10wb? (LoW remark)?

[Phthisis]

Erm.... Yeah.  10WB at 60 is 2 dice on a 5+.  2 lances at 60 at an abeam target is 2 dice on a 4+.    It's quite a bit better.

The stats on closing 6+ armor for a carnage at 5 dice still favors the lances, though I didn't post the numbers its easy to infer from both the mean average and the probability of 8 dice I posted earlier.

[horizon]

Erm.... Yeah. 10WB at 60 is 2 dice on a 5+. 2 lances at 60 at an abeam target is 2 dice on a 4+. It's quite a bit better.

The stats on closing 6+ armor for a carnage at 5 dice still favors the lances, though I didn't post the numbers its easy to infer from both the mean average and the probability of 8 dice I posted earlier.

10wb above 30cm:
vs closing capital = 5 dice.
vs moving away capital = 4 dice.
vs abeam capital = 2 dice.

Thus:
closing: 5 wb dice on a 6+  vs  2 lance on a 4+
moving away* 4wb dice on 5+ vs 2 lance on a 4+
abeam* 2wb dice on a 5+ vs 2 lance on a 4+

* = Only Marines & Necrons have 6+ all round armour. 5+ is more common. Even some races have 5+ worth mentioning.

So...

[Sigoroth]

Also, I never said the Carnage was identical--I said that the broadside-only guns on the Lance Murder are identical to the broadside-only guns on the Inferno, which means that the Inferno (with its lfr prow battery) has strictly better effective broadsides.  I haven't offered a comparison between the Inferno and the Carnage.

Which it does. However, when you said that you were comparing broadsides of the Inferno and Murder you put Inferno/Carnage in the comparison, which suggests you were equating these two ships. Of course, you weren't comparing the total broadsides, just the value of the 6WBs. That is the source of the confusion.

Horizon is right though, there's no point in comparing the prow weapon value of the Inferno with that of the Murder. You need to compare the Murders' prow weaponry to the entire combined broadside/prow of the Inferno. At > 45cm this does equate to simply comparing the prow weaponry since the Infernos' broadside has nothing to add in this bracket.

It wasn't a comparison between the Carnage and the Inferno--it was a comparison between the Inferno and the Lance-Murder.  The Inferno's effective broadside is strictly superior to the Lance-Murder's (and its broadside-only armament is identical), which means that the comparison between the Lance-Murder's forward armament and the Inferno's forward armament (which happens to be identical to that of the Carnage) certainly does have a point--it's the only point on which the Lance-Murder can hope to offer competition against the Inferno (except price). 

Yes, the only reason to take the Murder would be to make use of its prow weaponry.

Even if the Carnage never intentionally sets itself up for forward shots, they do have the potential to arise, and they're only one of the three relevant points of comparison between the Lance-Murder and the Inferno whose conclusion isn't obvious. 

Hmm, in all the times I've played with and against Carnages this hasn't arisen once.

Again, you guys need to read what I wrote a little more carefully.  =P

Indeed.

The Murder is superior at >45cm against all targets if it is closing and the Carnage is closing or broadside.

Incorrect. Against a closing ship with 6+ armour the (abeam) Carnage equals the Murders performance when on LO (Murder better by 1/6 of a hit otherwise). Against a closing ship with 5+ armour the Carnage beats the Murder by 1/6 of a hit when the Carnage is not locked on and the Murder is locked on. When both locked on the Carnage scores 2.78 hits vs only 1.5. That's a hell of a difference for a supposedly inferior long range ship.

The Carnage is superior at >45cm against all targets if it is broadside and the Murder is broadside. 

Correct.

The Murder is superior at 30cm - 45cm against targets which are abeam. 

The lance-variant Murder is superior against all non-Eldar abeam ships by 0.33 to 0.38 hits. The regular Murder is not. It's worth noting that the normal Murder has its advantages over the lance variant at normal to close range. Against Eldar the Carnage averages 1.5~2.25 hull hits (ie, functions like 3 shield ignoring lances). The normal Murder is 1~1.5 hits, the lance variant averages 0.74~1.1 hits including incidental BM damage (half the damage of the Carnage).

The Carnage is superior at 30cm -45cm against targets which are closing. 

Yarp.

The Carnage is extremely similar to the Murder at <30cm against targets which are abeam.

Incorrect. 2 hits for Carnage on average, 1.33 for the Murder (3.33 vs 2.06 on LO). That's a clear advantage to the Carnage, much more than the slight advantages the Murder has seen.

The Carnage is superior to the Murder at <30cm against targets which are closing. 

Yarp.

The Carnage is superior to the Murder at <15cm against targets regardless of aspect. 

Yarp.

[Sigoroth]

@left of west
Just because Sigi doesn't like it, it doesn't mean you can't use it.  He doesn't have any authority over what GW puts out or what you play.  If the Inferno fits your play style and your opponents allow the list, then theres no reason not to use it.
Also, check out Plaxor's revised lists.  Some very good stuff in there.

He asked why I didn't recommend it, I told him. Just because I don't like it does not mean he can't use it, yes. However I have reasons for not liking it. He hasn't asked or been informed of those, and he may or may not agree with them.

@Horizon
Youre somewhat correct about running a Murder straight at the enemy.  5+ armor closing is asking for it.  You either have to do it at an opponent with short range or weak guns or no toward a facing with no guns at all like the shild wall of 6+ prow armor that the IN has.  And it has to be done en masse.  We can't just think of two ships alone in clean space.  Strategy counts a lot in BFG.

Right, so let's assume that your opponent has no guns that can take advantage of your prow whatsoever. What is gained by closing with an IN fleet? The IN depend on getting close so they can use both broadsides. You're playing into their hands. Also, it makes it harder to avoid their torps when you're closing and easier for them to be able to shotgun them.

If you're going to do this sort thing then why not use Slaughters instead? At least when you do get to broadside range you'll have the firepower to compete.

Ok, now stats for closing 6+ armor vs Carnage & Murder lance variant broadsides.

Murder, 2  dice at 4+, one dice at 6+
0 hits = 20.83%
1 hits = 54.16%
2 hits = 20.83%
3 hits = 4.16%

Carnage over 30cm, 8 dice at 6+
0 hits = 23.27%
1 hits = 37.21%
2 hits = 26.03%
3 hits = 10.41%
4 hits = 2.6%
5+ hits = negligable

So the lances have a 75% chance of getting 0-1 hits whereas the Carnage has only a 60% chance of 0-1 hit. Hmm, seems like advantage to the Carnage to me.

Carnage at 15-30cm, 11 dice at 6+
0 hits = 13.47%
1 hits = 29.62%
2 hits = 29.6%
3 hits = 17.75%
4 hits = 7.09%
5 hits =1.98%
6+ hits = negligable

Analysis:  At longer range the Murder is more likely to hit at all and is stronger in the 1-2 hits range, but the Carnage has a small chance of scoring more than 2.  Personally I'd pick the Murder, but if youre a gambler the Carnage is better.  Of course, with a blast marker in the way the Murder is superior in all respects.
At closer range the Carnage has the advantage, once again if there are no blast markers in the way.  However the advantage isn't a very big one.  The Carnage is more likely to hit, but there isn't much of a chance of rolling that much higher than a Murder.

The Murder has a 25% of scoring 2 hits, the Carnage has a 40% chance of 2+ hits. So greater chance at significant damage and an actual possibility of more than 2 hits.

@Sigirogh
Glad you knew this already.  Did you know that I knew you'd say you knew?

 

But a lot of people never get past mean average calculations. 
There are three different kinds of average.

I take it you're talking about the mean, median and mode. Mode is pretty worthless, since it's 1 for each ship. Mean is similarly uninformative since the Carnage has equal or greater mean for the most part and you're not willing to accept that as evidence. So you're looking at the median? So you're reducing it to a pass/fail based on the number of dice you're rolling? If we take that idea to its logical conclusion then having 1 dice that hits on a 1+ is better than having 3 dice hitting on a 4+ because you have a higher proportion of successes.

The low probability of very high numbers of successes rolled drags the mean average higher than could be normally expected.  I think more than a few people would be surprised that there is a greater chance they will roll lower than the mean average than that they will roll above it and that the difference between rolling under and over grows with each additional dice you roll.  Some of us are gamblers, like yourself, who will trade reliability for a small chance of spectacular success.  Others, like me like reliable steady firepower that is less likely to fail us when we most need it.
Ok, so so far the carnage performs better at close range than a Murder, but the Murder is better at long ranges or close ranges with blasts in the way.
So lets suppose I took 2 lance Murders and a Slaughter instead of 3 Carnages?  That saves me 35pts and if I use Slaughter up close and the Murderd at range I get better damage output.

Actually, at long range the 3 Carnages would demolish the 2 Murders and up close it's 34WB+2L vs 48WB, so again the Carnages win convincingly. You could say that the SMM will get to close range quicker and so it will be a comparison of those 3 ships up close vs the 3 Carnages from further away. This is valid, but also, you'll get hammered on the way in as well as having less long ranged fire for on the way in.

Anyway, as it happens, I'm not a gambling type. It's just that the mechanics of the game favour the Carnage and the Carnage has far more potential up close than the Murder. Since these two ships compete for the same spot in the fleet there's just no room for the Murder. In fact, you know, the very best place I can see for the Murder is against Necrons. The Carnage is a great ship against Necrons. If you need to do 1 extra point of damage (rather than force a brace) then the Carnage has the best chance. If already braced it's a numbers game, and WBs are superior. The WBs actually have a slightly better chance of causing damage when the ship is unbraced and because there's less gain for bracing against WBs than lances they might not. So best chance of causing that damage is with the Carnage. However, the Murder loses nothing by firing its prow lances at a separate target, and since both WBs and lances are needed against Necrons it is just as good as any other hybrid (like the Lunar) so the Murder comes into its own here. Carnage is not weak, but the Murder is not completely owned like it is against other fleets. In effect, having both ships in the one fleet becomes viable.

[left of west]

It's worth noting that use of squadroning pretty much obviates the blast marker problem.  Two or three Carnages firing in sequence suffer from reduced firepower.  Two or three Carnages firing as a squadron don't.

With regards to ships beyond 45cm: it's true that the Carnage is better against ones which are closing.  Same with the 15-30 band against targets abeam. Not sure what numbers I was looking at, there.  Sorry.