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Background
I was discussing the chances of an assault cannon penetrating armor values with my friend. He has a masters in statistics, and informed me that 4 shots with a BS of 4 does not give 8/3 hits, but instead gives 4 chances of 2/3 hitting. When factoring in the other variables of the AC penetrating due to rending, the numbers quickly become very complex.
Rising to the challenge, he spend a few hours computing out the exact chances, as shown below.



Results
The TL LC chances are linear. This is expected.
The TL AC has better chances in all instances except AV12, which is quite odd. When facing an AV12 wall, the LC is more dangerous than the AC. In all other instances the AC wins out.

I don't understand. What's so special about AV12 that it magically makes Assault Cannons less effective?

I assume it has something to do with how rending factors in

Paladin Blake wrote:I don't understand. What's so special about AV12 that it magically makes Assault Cannons less effective?

Same reason why the lascannons become less effective or AV 14 is harder to penetrate than AV 10: it takes a higher penetration roll because 12 is higher than 11. Why there is a large drop off from 11 to 12 is that assault cannons need to roll a 6 instead of a 5 to get a roll on the damage table.

Ahh. I see. It's the chance to glance OR Pen. Not just Pen. It makes sense now. My bad for not reading properly.

On AV 12, the LC effects 2/3 of the time.
On AV 13, the LC effects 1/2 of the time.
That is where the 4 shots + rending of the AC pull ahead.

I'd like to see the same graph, but only with chance to score a 5 or 6 on the damage table. We have information on simply getting to the damage table at least once, but that glosses over how much more effective the TL AC is against low armor targets. Any chance on getting him to do a graph for that?

If anything this chart just show how much it's a waste to fire just about any of those things at AV14. Which is quite obvious to why I don't shoot my lascannons or assault cannons at anything AV14 unless it to get that lucky game winning break. The only reliable way to deal with AV14 is Melta weapons or Assaulting with a can opener.

Statsically looks good. But doesnt take range into effect. You'd get at least a turn earlier shooting with the lascannon.

66.6..% , 55.5..% , 44.4..% , 33.3..% , 22.2..%(Lascannon) ((4/6 x A/6) x 100 = %)
88.8..% , 74.0..% , 59.2..% , 44.4..% , 29.6..%(+TL) ((32/36 x A/6) x 100 = %)

80.2..% , 63.4..% , 37.5..% , 37.5..% , 26.4..%(Assault cannon) ( * )
90.4..% , 75.4..% , 47.3..% , 47.3..% , 34.0..%(+TL) ( * )

* hard to put the formular down but its the same as above but since there are multiple shots what you do is work out the chance of failling to glance/ pen and multiply it by its self (power) by the number of shots . Thats the chance that all the shots will fail then invenrt for the chance pe/glance ... would look like this

(1-((1-(4/6*3/6*3/3))^4))*100 = AV10%


Reasons simple for the AV12 blip thats where rending takes over. (if you ignore glancing its AV11)

I think its further important to note that not only does the Assault cannon have a better chance of penetrating and destroying most vehicles (save AV 12), it is the only one capable of inflicting multiple hits. This means that while it will overall perform better, it will also have better potential damage. However, the assault cannon suffers from a shorter range, meaning it will spend less rounds firing than the lascannon, and have less target options.

Shouldn't the Lascannon have a 100% chance of glancing or penetrating AV10?

Nurglitch wrote:Shouldn't the Lascannon have a 100% chance of glancing or penetrating AV10?

BS 4 = 4/6 chance of hitting
TL thats 32/36 chance of hitting

Nurglitch wrote:Shouldn't the Lascannon have a 100% chance of glancing or penetrating AV10?

It's factoring in accuracy as well. That's why the twin-linked line is different from the non twin-linked line.

It should be noted when just talking about measures of central tendency like averages that assault cannons get 8/3 hits as well, that number giving you the average number of hits. If you were to roll the 4 dice infinite times, the average of your averages would be 8/3 hits. The only time it would matter for 4 2/3 chances of hitting would be when you start describing the shape of the entire distribution, not just the midpoint, as then it's worth noting that it can't exceed 4. Just a semantic note, seeing as how this is a graph of central tendency.

Dracos wrote:I think its further important to note that not only does the Assault cannon have a better chance of penetrating and destroying most vehicles (save AV 12), it is the only one capable of inflicting multiple hits. This means that while it will overall perform better, it will also have better potential damage. However, the assault cannon suffers from a shorter range, meaning it will spend less rounds firing than the lascannon, and have less target options.

I think that is the biggest issue.
Multi-shots vs longer range. Depending on the type of armor you are fighting you might have more/less chances to fire a long range weapon like the Lascannon.

minigun762:

It depends on the platform. A Dreadnought, for example, is going to benefit more from a Twin-Linked Lascannon than an Assault Cannon if its starting on the board, but otherwise if it's in a Drop Pod.