Derrault, your maths on expected wounds for the shotguns is wrong.

3.5 hits get through cover

1.75 shields are rolled

1 shield is cancelled

2.75 wounds go through.

Of course, just averages don't tell the whole story. I worked up the full cumulative probability distribution, which better models pierce, but the result is pretty much the same.

Your maths indicates you think pierce removes a defence die, rather than cancelling a shield. This misunderstanding is probably why you disagree with everyone else :).

Edited to add: another flaw in your method is by not correctly modelling the rolls you are overestimating the value of cover. Cover only works to it's full potential if at least two hits (not including crits!) are rolled. On white dice with surges, 1/3 of all successes will be crits! This is actually one of the big benefits of the z6 and fleets in general that you are not capturing, which is skewing your perception.

1 hour ago, Derrault said:

Your base wounds on the cover 2 is off, it should be 2.5 x .5 + 1 not 3.5 x .5 + 1.

1 hit of the 3.5 effectively doesn’t get rolled against, only 2.5 of them. By dividing all of the hits and then adding 1 you’ve added two extra rolls that don’t occur.

That's not correct.

Consider the simple case of two hits with pierce 1 vs stormtroopers.

Using your method:

50% to take two wounds

50% to take one wound.

Using correct modelling, cancelling one shield instead one die:

75% chance to take two wounds

25% chance to take one wound (need to roll two shields to keep one)

On 5/23/2018 at 5:31 AM, nashjaee said:

When you work the math down to the level of wounds (not just damage rolled) the shotgun unit outperforms the MPL unit.

For example, shooting against stormtroopers in heavy cover the shotgun averages 2.75 wounds vs the MPL’s 2.5625. That pierce is doing a lot of work.

That's not heavy cover. Those are just half the average hits given by the dice. 5.5 and 5.125 respectively, which doesn't work for calculating wounds in this case.

Through heavy cover, the shotgun has two hits cancelled so its average hits goes down to 3.5.

For wounds, you can't just half like usual as pierce makes the calculation diifferent as it only comes into play if the oppenent rolls a defense.

If the opponent defends no hits:

Launcher 5.125 wounds vs. shotgun 3.5 wounds (1.625 difference) average

Defends one hit:

Laucher 4.125 wounds vs. shotgun 3.5 wounds (0.625 difference) average

Defends two hits

Launcher 3.125 wounds vs. Shotgun 2.5 wounds (0.625) average

Three:

2.125 vs. 1.5 (0.625)

Four:

1.125 vs. 0.5 (0.625)

So, the launcher is, for the most part, doing 0.625 more wounds through heavy cover. More if the opponent does not defend any wounds. Aim on the shotgun can make up for some of this by adding an average of ~0.54.

30 minutes ago, Zepherite said:

That's not heavy cover. Those are just half the average hits given by the dice. 5.5 and 5.125 respectively, which doesn't work for calculating wounds in this case.

They are half the average hits in that case by coincidence. That was not how I calculated them. Remember, we’re talking about averages here with regards to the defensive roll.

Hits = (Average hits) - (Cover)

Defense = (Hits) * (Defense probability) - (Pierce)

Wounds = Hits - Defense

Coincidentally, Wounds = (Average hits) / 2 when the defense probability is 1/2. You can prove it via substitution.

The problem with the HH-12 is not, that it does not do its job as armour killer. The problem is, that you don't need an armour killer as much as stopping core infantry from taking objectives. The main drawback for the HH-12 is therefore the opportunity cost of not being able to field a DLT (which is not exactly useless against armour to boot). Same with Ion Gun and Rotary Blaster.

8 hours ago, Derrault said:

Your base wounds on the cover 2 is off, it should be 2.5 x .5 + 1 not 3.5 x .5 + 1.

1 hit of the 3.5 effectively doesn’t get rolled against, only 2.5 of them. By dividing all of the hits and then adding 1 you’ve added two extra rolls that don’t occur.

I'm not sure I understand. All of the hits get rolled against, and then pierce cancels a block result. 5.5 average hits minus 2 for cover is 3.5. The stormtroopers get 1.75 saves, and then you cancel one of those saves.

Pierce is always going to be worth a full wound as long as there is at least one save.

4 hours ago, nashjaee said:

They are half the average hits in that case by coincidence. That was not how I calculated them. Remember, we’re talking about averages here with regards to the defensive roll.

Hits = (Average hits) - (Cover)

Defense = (Hits) * (Defense probability) - (Pierce)

Wounds = Hits - Defense

Coincidentally, Wounds = (Average hits) / 2 when the defense probability is 1/2. You can prove it via substitution.

How you derived it is largely irrelevant to my comment.

They still aren't the average wounds through heavy cover as I stated. The values you gave are equivalent to half the average wounds with no cover and therefore cannot be representative of the wounds through heavy cover for the shotgun, regardless of how they were derived.

The values you have given are not taking into account the effect of the shotgun shooting through cover and then having pierce applied only when the defender gets a defence. I showed this in my original post.

You can already see this in your math here:

4 hours ago, nashjaee said:

Defense = (Hits) * (Defense probability) - (Pierce)

This only applies if the opponent actually gets a defence result. Pierce is, mathematically, a step function and cannot be calculated with a linear equation like this as there is a probabilty that pierce will not trigger at all. That is not taken into acount in your equation.

However, even if it was taken into account, the grenade launcher still does more damage through cover as I showed in my original.

@Zepherite, once again, I’m talking about the average case. There is at least 1 defense rolled in the average case. I’m saying exactly the same as @Orkimedes above. For a scattergun shooting at stormtroopers:

Hits = 5.5 -2 = 3.5

Defense = 3.5 x 0.5 - 1 = 1.75 - 1 = 0.75

Wounds = 3.5 - 0.75 = 2.75

Where is my mistake?

2 hours ago, Zepherite said:

How you derived it is largely irrelevant to my comment.

They still aren't the average wounds through heavy cover as I stated. The values you gave are equivalent to half the average wounds with no cover and therefore cannot be representative of the wounds through heavy cover for the shotgun, regardless of how they were derived.

The values you have given are not taking into account the effect of the shotgun shooting through cover and then having pierce applied only when the defender gets a defence. I showed this in my original post.

You can already see this in your math here:

This only applies if the opponent actually gets a defence result. Pierce is, mathematically, a step function and cannot be calculated with a linear equation like this as there is a probabilty that pierce will not trigger at all. That is not taken into acount in your equation.

However, even if it was taken into account, the grenade launcher still does more damage through cover as I showed in my original.

My apologies, you are right; using averages is a little rudimentary, and doesn’t account for the fact that pierce may not trigger at all.

I ran a simulation with 100,000 iterations (again vs. storms in heavy cover). The actual number of average wounds for the the shotgun is closer to 2.62, not 2.75, when you account for the fact that pierce may not always trigger.

The number for the grenade launcher was still about 2.5625.

So the shotgun is still better vs. storms in heavy cover.

I think the point here simply is that the impact 2 is what differentiates the two and gives the MPL the higher cost and exhaust. I’m not sure whether that’s good, bad, right, or wrong, but it’s worth knowing that just because the MPL has blast doesn’t mean it’s better vs. troopers in cover in absolute terms.

33 minutes ago, Orkimedes said:

My apologies, you are right; using averages is a little rudimentary, and doesn’t account for the fact that pierce may not trigger at all.

I ran a simulation with 100,000 iterations (again vs. storms in heavy cover). The actual number of average wounds for the the shotgun is closer to 2.62, not 2.75, when you account for the fact that pierce may not always trigger.

The number for the grenade launcher was still about 2.5625.

So the shotgun is still better vs. storms in heavy cover.

I think the point here simply is that the impact 2 is what differentiates the two and gives the MPL the higher cost and exhaust. I’m not sure whether that’s good, bad, right, or wrong, but it’s worth knowing that just because the MPL has blast doesn’t mean it’s better vs. troopers in cover in absolute terms.

That at least makes more sense.

I'll go back and have a look at my math and see if I've made some mistakes but I was under the impression that shotgun was less through cover.

1 hour ago, Orkimedes said:

My apologies, you are right; using averages is a little rudimentary, and doesn’t account for the fact that pierce may not trigger at all.

I ran a simulation with 100,000 iterations (again vs. storms in heavy cover). The actual number of average wounds for the the shotgun is closer to 2.62, not 2.75, when you account for the fact that pierce may not always trigger.

The number for the grenade launcher was still about 2.5625.

So the shotgun is still better vs. storms in heavy cover.

I think the point here simply is that the impact 2 is what differentiates the two and gives the MPL the higher cost and exhaust. I’m not sure whether that’s good, bad, right, or wrong, but it’s worth knowing that just because the MPL has blast doesn’t mean it’s better vs. troopers in cover in absolute terms.

Edited: sorry I write a bunch of stuff without fully reading your post, mirroring exactly what you said